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THANK YOU ALL FOR JOINING TODAY.

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FOR THOSE WHO DON'T KNOW, I'M

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GINA NORATO.

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I'M THE LEAD OF THE OFFICE OF

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BIOSTATISTICS FOR THE CLINICAL

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TRIALS UNIT IN NIDS.

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TODAY WE'RE GOING TO BE TALKING

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ABOUT LINEAR REGRESSION AS PART

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OF OUR SIX-PART STATISTICAL

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LECTURE SERIES THIS SPRING.

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PLEASE FEEL FREE, I'M OKAY IF

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YOU WOULD LIKE TO SUBMIT

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QUESTIONS WHILE I AM PRESENTING

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VIA CHAT OR THE Q & A OPTION.

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JUST KNOW THAT, THAT IT IS

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LIKELY BEING RECORDED.

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SO IF YOU WOULD RATHER NOT BE ON

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RECORDING FOR THE FUTURE, JUST

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KEEP THAT IN MIND, BUT I'M HAPPY

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TO READ YOUR QUESTION AND ANSWER

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AS WE GO.

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OKAY.

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SO, JUST TO GIVE A LITTLE

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OUTLINE OF WHAT WE'RE GOING TO

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TRY TO GET THROUGH TODAY:  SO

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FIRST I WANT TO GIVE AN OVERVIEW

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OF WHAT REGRESSION IS AND WHY WE

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USE IT.

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AND THEN, I'M JUST GOING TO GET

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INTO THE MEAT OF HOW WE RUN

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THROUGH MODELING, THE DIFFERENT

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ASSUMPTIONS THAT WE NEED TO

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CONSIDER WHEN WE DEAL WITH

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REGRESSION.

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WHAT THE MODEL STRUCTURE LOOKS

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LIKE.

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HOW TO DEAL WITH THINGS LIKE

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COVARIANTS AND CONFOUNDING IN

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THE MODEL, AND ADD INTERACTIONS

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TERMS AND THROUGHOUT WE WILL BE

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TALKING ABOUT CHECKING MODEL

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ASSUMPTIONS.

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THEN, I WILL TALK ABOUT HOW TO

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REPORT THE RESULTS OF THESE

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REGRESSIONS GIVING SOME SAMPLE

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LANGUAGE.

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AND ALSO TALK ABOUT SOME OTHER

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SIMILAR TESTS SUCH AS P-TESTS,

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CORRELATIONS AND NOVA.

50
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THINGS THAT ARE SORT OF IN LINE

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WITH REGRESSION AND TALK ABOUT

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WHEN WE WOULD USE ONE VERSUS THE

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OTHER.

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AND CONCLUDE WITH SUMMARY AND

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KEY POINTS.

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SO GETTING INTO THE OVERVIEW, SO

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WHAT IS LINEAR REGRESSION?

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SO REGRESSION IS BASICALLY JUST

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A STATISTICAL MODEL THAT

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ESTIMATES THE LINEAR

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RELATIONSHIP BETWEEN ONE

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CONTINUOUS VARIABLE AND ONE OR

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MORE OTHER VARIABLES OF

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INTEREST.

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THEY MUST BE USED WITH

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CONTINUOUSLY MEASURED OUTCOME

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METRICS.

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SO, SOMETHING WITH A SMOOTH

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CONTINUOUS SCALE.

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SOMETHING LIKE A MEASURE OF

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WEIGHT OR TIME, VOLUME, BLOOD

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PRESSURE, AND SOME LARGE-RANGE

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FUNCTIONAL SCALES.

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IMPORTANTLY, THEY SHOULD SORT OF

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BEHAVE UNBOUNDED, EVEN IF THERE

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IS A LOGICAL BOUND TO YOUR

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MEASUREMENT, LIKE WE CAN'T HAVE

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A NEGATIVE TIME, WE WANT TO MAKE

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SURE THAT THE DISTRIBUTION OF

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THEIR VALUES IS SUCH THAT WE'RE

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NOT REALLY UP AGAINST THE

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BOUNDARIES, WHO WE HAVE THE NICE

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SMOOTH CONTINUOUS BEHAVE AND WE

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HAVE NICE GRANULARITIES TO THE

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MEASUREMENT AS WELL, IF WE'RE

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DEALING WITH WHOLE NUMBERS OR

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COUNT VALUES THAT WILL FALL

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UNDER A DIFFERENT TYPE OF

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REGRESSION.

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SO JUST CONSIDER THAT AS WELL.

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AND FOR REGRESSION WE ARE

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PRIMARILY CONCERNED ABOUT

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PREDICTING Y FROM X OR MULTIPLE

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Xs AND MULTIPLE COVARIANTS.

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I WANT TO BE CLEAR, WHEN WE SAY

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PREDICTION HERE, WE'RE TALKING

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ABOUT PURELY FROM A CALCULATING

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OR STATISTICAL POINT OF VIEW.

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WE DON'T REALLY MEAN TO HAVE ANY

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CAUSAL PREDICTION OR CAUSAL

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RELATIONSHIP HERE.

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THAT SORT OF INVESTIGATION WOULD

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BE UNDER A TOTALLY DIFFERENT

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BRANCH OF STATISTICS.

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SO WE'RE JUST TALKING ABOUT IF

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WE KNOW SOME CHARACTERISTICS OF

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A PERSON, HOW WELL CAN WE

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PREDICT SOME OTHER VARIABLE THAT

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WE HAVE OBSERVED ALSO.

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SO THIS IS STILL PURELY FROM

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KIND OF A CORRELATIONAL-TYPE OF

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INTERPRETATION, NOT CAUSATION.

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AND SO, JUST TO GO THROUGH SOME

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TERMINOLOGY AND JUST HAVE TO A

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BASIS OR A FRAMEWORK FROM WHERE

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TO GO FROM HERE.

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SO WE'RE GOING TO BE TALKING A

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LOT ABOUT Xs AND Ys.

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SO OUR Y IS GOING TO BE OUR

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DEPENDENT VALUABLE.

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WE IS ALSO CAUSE THIS OUR

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RESPONSE VARIABLE OR OUTCOME

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MEASURE OR VARIABLE.

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AND OUR Xs ARE GOING TO BE OUR

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INDEPENDENT VARIABLES.

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THEY ARE ALSO CALLED EXPLANATORY

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VARIABLES OR PREDICTOR

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VARIABLES.

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AND DEPENDING ON OUR SCIENTIFIC

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VIEW OF THESE THINGS WE CAN ALSO

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CALL THEM COVARIOUS OR

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CONFOUNDERS.

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THESE ARE MORE LIKE A

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QUALITATIVE LABEL.

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BUT THEY ARE ALL BASICALLY

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TREATED THE SAME IN THE MODEL.

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THE MODEL DOESN'T VIEW THEM ANY

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DIFFERENTLY.

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AND THEN, YOU'LL WANT TO PUT

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YOUR PREALGEBRA OR ALGEBRA HATS

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ON, BECAUSE WE ARE GOING TO BE

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TALKING ABOUT LINES AND

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GRAPHING.

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SO WE'RE GOING TO BE TALKING

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ABOUT INTERCEPTS WHERE THIS IS

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REALLY A PREDICTION OF Y WHERE

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ALL OTHER VARIABLES INVESTS ARE

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ZERO.

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THAT KIND OF ALGEBRAIC

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INTERPRETATION OF INTERCEPT AND

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SLOPE.

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AND ALSO WE WILL BE TALKING

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ABOUT COEFFICIENTS.

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WE CAN THINK BROADLY OF THIS AS

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BEING SLOPES, BUT I WANTED TO

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CALL THIS A COEFFICIENT BECAUSE

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IT IS KIND OF HOW THEY ARE

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WRITTEN ABOUT IN THE OUTPUTS OF

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REGRESSIONS AND THINGS LIKE

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THAT, THEY ARE COEFFICIENTS.

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SO, FOR CONTINUOUS MEASURE

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VARIABLES OF X WE CAN THINK OF

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THESE AS A SLOPE, WHEREAS THE

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CHANGE IN THE PREDICTION OF Y

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FOR ONE UNIT CHANGE IN X IS SORT

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OF THE INTERPRETATION THERE.

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BUT, YOU KNOW, FOR A BINARY OR

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CATEGORICAL VARIABLE THIS ISN'T

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REALLY A SLOPE, IT IS JUST A

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SIMPLE CHANGE, BUT THE SAME SORT

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OF LOGIC APPLIES.

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THIS IS A CHANGE IN THE

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PREDICTION OF Y BETWEEN TWO

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DIFFERENT STEP LEVELS OF X.

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AND WE CALL THOSE BROADLY JUST

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COEFFICIENTS OR ESTIMATES EVEN

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MORE BROADLY.

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BUT IN TERMS OF WRITING OF A

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REGRESSION EQUATION, WE CALL

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THEM COEFFICIENTS.

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SO JUST TO GIVE -- JUST TO KIND

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OF GIVE OUR LITTLE OVERVIEW

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HERE.

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SO JUMPING RIGHT INTO SOME

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ASSUMPTIONS FOR REGRESSION.

186
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SO THERE ARE FOUR ASSUMPTIONS

187
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THAT WE NEED TO BE CONSIDERING

188
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WHEN WE DEAL WITH REGRESSION.

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LINEARITY, INDEPENDENCE, NORMAL

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DISTRIBUTION OF ERRORS AND EQUAL

191
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VARIANCE OF ERRORS AND QUITE

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NICELY, IF YOU WRITE THEM IN

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THIS WAY, THEY HAVE THE LINE

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ACRONYM TO MAKE THIS A LITTLE

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BIT EASIER TO REMEMBER.

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SO LET'S GO THROUGH EACH OF

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THEM.

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SO FOR LINEARITY, WE WANT TO

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MAKE SURE THAT LINEAR MODEL TO

200
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DESCRIBE THE RELATIONSHIP IS

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EVEN APPROPRIATE AT ALL.

202
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WE CAN DO THIS VERY SIMPLY IN

203
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MOST CASES BY INVESTIGATING THE

204
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BY VARIANT RELATIONSHIP OR THE

205
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SET OF BIVARIANT RELATIONSHIPS

206
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THAT WE'RE INTERESTED IN.

207
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PERHAPS ANOTHER SORT OF MODEL IS

208
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BEST FOR DESCRIBING THE

209
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RELATIONSHIP.

210
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A NONLINEAR, PERHAPS OR SOME

211
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OTHER LINE MODEL OR

212
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POLYNOMIAL-SORT OF REGRESSION

213
00:07:04,791 --> 00:07:07,293
HERE WITH OTHER SORTS OF COMPLEX

214
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TERMS.

215
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NOT PURELY A LINEAR

216
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RELATIONSHIP.

217
00:07:09,829 --> 00:07:13,366
SO IT CAN BE REALLY IMPORTANT TO

218
00:07:13,432 --> 00:07:14,000
VIEW AN INITIAL INVESTIGATION OF

219
00:07:14,066 --> 00:07:15,468
WHAT YOU'RE DEALING TO MAKE SURE

220
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THIS IS EVEN AN APPROPRIATE

221
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DESCRIPTION OF YOUR DATA AT ALL.

222
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NEXT WE ASSUME, WE NEED TO MAKE

223
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SURE THAT OUR OBSERVATIONS FOR

224
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OUR DATA ARE INDEPENDENT.

225
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SO WE HAVE THIS INDEPENDENT

226
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ASSUMPTION.

227
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AND THIS CAN BE DETERMINED

228
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WHETHER WE ARE ADHERING TO THIS

229
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ASSUMPTION BY DIVINE OR

230
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COLLECTION ALONE.

231
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SO IS THERE CLUSTERING OF DATA

232
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FROM PEOPLE COMING WITH FAMILIES

233
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OR MAYBE WE HAVE THESE

234
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INTERVENTIONAL UNITS, SCHOOLS

235
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AND CLASSES IN SOME SETTINGS OR

236
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WE HAVE PAIRED DATA OR REPEATED

237
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MEASUREMENTS, CLUSTERING WITHIN

238
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A PERSON OF REPEATED

239
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MEASUREMENTS OVER TIME.

240
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LONGITUDINAL DATA.

241
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THIS WOULD ALL MEAN WE'RE NOT IN

242
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A BASIC LINEAR REGRESSION

243
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FRAMEWORK.

244
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MAYBE WE NEED TO RUN A DIFFERENT

245
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SORT OF MODEL TO ACCOUNT FOR

246
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THIS CORRELATED BEHAVIOR WITHIN

247
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THE CROSS OBSERVATIONS WITHIN

248
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GROUPS.

249
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WE ALSO NEED TO MAKE SURE THAT

250
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WE'RE MEETING THE ASHUN OF

251
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NORMAL DISTRIBUTION OF ERRORS.

252
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SO, IMPORTANTLY, THIS IS THE

253
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NORMAL DISTRIBUTION OF ERRORS.

254
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AND NOT NECESSARILY THAT OUR

255
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OUTCOME MEASURE IS NORMALLY

256
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DISTRIBUTED.

257
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SO THIS IS SPECIFICALLY ABOUT

258
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WHEN YOU RUN YOUR MODEL AND

259
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WE'RE GOING TO TALK ABOUT WHAT

260
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ERRORS ARE IN A LITTLE BIT.

261
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BUT WHEN YOU RUN YOUR MODEL AND

262
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OBTAIN THE ERRORS FROM THE

263
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MODAL, WHAT IS THE BEHAVIOR OF

264
00:08:40,253 --> 00:08:42,054
THOSE, THE NEXT TWO MODELS ARE

265
00:08:42,121 --> 00:08:44,056
RELATED TO SPECIFICALLY ERRORS

266
00:08:44,123 --> 00:08:45,258
AND NOT ACTUALLY ANY OF THE

267
00:08:45,324 --> 00:08:47,627
VARIABLES YOU'RE USING IN YOUR

268
00:08:47,693 --> 00:08:48,060
REGRESSION.

269
00:08:48,127 --> 00:08:50,496
WE CAN INVESTIGATE THE BEHAVIOR

270
00:08:50,563 --> 00:08:54,000
OF THESE ERRORS EITHER USE THE

271
00:08:54,066 --> 00:08:58,804
CLASSES LIKE A HISTOGRAM OR BY

272
00:08:58,871 --> 00:09:00,873
DOING CUBE PLOTS WHICH IS

273
00:09:00,940 --> 00:09:04,977
OBSERVING THE QUANTALS OF YOUR

274
00:09:05,044 --> 00:09:07,813
ERRORS VERSUS THE THEORETICAL

275
00:09:07,880 --> 00:09:08,648
NORMAL DISTRIBUTION QUANTILES.

276
00:09:08,714 --> 00:09:12,084
WE SHOULD SEE NICE HISTOGRAM

277
00:09:12,151 --> 00:09:13,219
BEHAVIOR AND/OR SIMILARLY, WE

278
00:09:13,286 --> 00:09:14,887
SHOULD SEE SOMETHING ON THIS X

279
00:09:14,954 --> 00:09:17,757
EQUAL Y LINE FOR A QQ PLOT.

280
00:09:17,823 --> 00:09:20,593
I JUST WANT TO DEMONSTRATE, THIS

281
00:09:20,660 --> 00:09:23,696
IS A SET OF PLOTS THAT ARE

282
00:09:23,763 --> 00:09:25,598
RESAMPLED FROM A NEW UNDER LYING

283
00:09:25,665 --> 00:09:26,532
NORMAL DISTRIBUTION.

284
00:09:26,599 --> 00:09:29,235
YOU CAN SEE EVEN IN CASES WHERE

285
00:09:29,302 --> 00:09:29,769
WE DO HAVE GOOD NORMAL

286
00:09:29,835 --> 00:09:31,704
DISTRIBUTIONAL DATA OF THE

287
00:09:31,771 --> 00:09:33,839
ERROR, THESE AREN'T GOING TO LIE

288
00:09:33,906 --> 00:09:36,108
PERFECTLY, THEY WILL NEVER LIE

289
00:09:36,175 --> 00:09:36,876
PERFECTLY ON THE X EQUALS Y

290
00:09:36,943 --> 00:09:38,177
LINE.

291
00:09:38,244 --> 00:09:40,079
PART OF WHAT WE WILL TALK ABOUT

292
00:09:40,146 --> 00:09:41,213
MEETING ASSUMPTIONS IS

293
00:09:41,280 --> 00:09:42,882
UNDERSTANDING YOU WILL NEVER

294
00:09:42,949 --> 00:09:45,084
HAVE PERFECT BEHAVIOR IN THIS

295
00:09:45,151 --> 00:09:48,387
WAY, WHEN YOU KNOW THE

296
00:09:48,454 --> 00:09:48,921
UNDERLYING DISTRIBUTION IS

297
00:09:48,988 --> 00:09:50,856
NORMAL, THE SAMPLE SIZE IS

298
00:09:50,923 --> 00:09:52,391
SMALL, WE WILL NOT HAVE THIS

299
00:09:52,458 --> 00:09:53,926
PERFECT X EQUAL Y LINE.

300
00:09:53,993 --> 00:09:55,995
BUT WE SHOULD SEE IF THERE'S

301
00:09:56,062 --> 00:09:57,563
ANYTHING REALLY MAJOR GOING ON

302
00:09:57,630 --> 00:10:01,233
HERE WHEN WE DO THIS

303
00:10:01,300 --> 00:10:01,801
INVESTIGATION.

304
00:10:01,867 --> 00:10:03,035
AND THEN WE SHOULD ALSO

305
00:10:03,102 --> 00:10:04,537
INVESTIGATE EQUAL VARIANCE OF

306
00:10:04,603 --> 00:10:05,404
ERRORS.

307
00:10:05,471 --> 00:10:07,940
SO, WE DO THIS BY LOOKING AT,

308
00:10:08,007 --> 00:10:10,176
THERE ARE A COUPLE OF DIFFERENT

309
00:10:10,242 --> 00:10:11,577
VERSIONS OF THIS TYPE OF PLOT,

310
00:10:11,644 --> 00:10:13,879
BUT WE WILL MAINLY BE LOOKING AT

311
00:10:13,946 --> 00:10:15,982
FITTED VALUES PREDICTED VALUES

312
00:10:16,048 --> 00:10:18,384
OF OUR OUTCOME MEASURE AGAINST

313
00:10:18,451 --> 00:10:19,085
OUR RECIPIENTS THAT WE ED MATE

314
00:10:19,151 --> 00:10:21,954
FROM THE MODEL.

315
00:10:22,021 --> 00:10:23,689
WE SHOULD SEE THAT THE SPREAD

316
00:10:23,756 --> 00:10:24,690
AROUND THE VERTICAL SPREAD

317
00:10:24,757 --> 00:10:27,860
AROUND THIS ZERO LINE IS EVEN

318
00:10:27,927 --> 00:10:30,463
ACROSS ALL PREDICTED VALUES OF

319
00:10:30,529 --> 00:10:31,831
Y.

320
00:10:31,897 --> 00:10:36,402
AND WE CALL THIS -- HOME

321
00:10:36,469 --> 00:10:37,303
SCUDASTICITY.

322
00:10:37,370 --> 00:10:42,141
WE WANT TO SEE THIS ON THE LEFT

323
00:10:42,208 --> 00:10:42,675
WITH RECTANGULAR BEHAVIOR.

324
00:10:42,742 --> 00:10:46,479
AND FOR CERTAIN PREDICTED VALUES

325
00:10:46,545 --> 00:10:48,080
OF Y WE HAVE LESS VARIABLE.

326
00:10:48,147 --> 00:10:49,815
AND OTHER VALUES OF Y, MORE

327
00:10:49,882 --> 00:10:53,352
VARIABLE, WHETHER WE HAVE THIS

328
00:10:53,419 --> 00:10:54,787
SHAPE, OR OTHER TYPE OF CONE

329
00:10:54,854 --> 00:10:55,421
SHAPE WE SEE FLIPPED THE OTHER

330
00:10:55,488 --> 00:10:56,122
WAY.

331
00:10:56,188 --> 00:10:59,191
WE WANT TO MAKE SURE THAT ACROSS

332
00:10:59,258 --> 00:11:02,194
ALL PREDICTED VALUES OF Y THAT

333
00:11:02,261 --> 00:11:06,332
THE PREDICTABILITY, ALL OF THE

334
00:11:06,399 --> 00:11:07,199
RESIDUALS CAN BE EXPLAININGED

335
00:11:07,266 --> 00:11:10,770
ACROSS WITH THE SAME STANDARD

336
00:11:10,836 --> 00:11:11,037
DEVIATION.

337
00:11:11,103 --> 00:11:15,041
SO THOSE ARE THE FOUR

338
00:11:15,107 --> 00:11:16,375
ASSUMPTIONS.

339
00:11:16,442 --> 00:11:18,611
SO TO GET INTO SPECIFICALLY WHAT

340
00:11:18,677 --> 00:11:23,015
THE MODEL LOOKS LIKE.

341
00:11:23,082 --> 00:11:27,053
SO-- SO A SIMPLE SCENARIO OF ONE

342
00:11:27,119 --> 00:11:28,954
X VERSUS A Y REGRESSION, WOULD

343
00:11:29,021 --> 00:11:30,689
TRY TO FIND THE RELATIONSHIP

344
00:11:30,756 --> 00:11:32,158
BETWEEN X AND Y WITH A LINEAR

345
00:11:32,224 --> 00:11:35,428
FIT WITH THE BLUE LINE.

346
00:11:35,494 --> 00:11:35,995
SPECIFICALLY, FOR ONE

347
00:11:36,062 --> 00:11:38,798
INDEPENDENT VARIABLE X AND

348
00:11:38,864 --> 00:11:40,032
DEPENDENT MEASURE Y, THE

349
00:11:40,099 --> 00:11:42,601
RELATIONSHIP FOR PREDICTING THE

350
00:11:42,668 --> 00:11:43,969
ESTIMATED Y WILL BE CALLED Y-HAT

351
00:11:44,036 --> 00:11:46,605
FOR EACH SUBJECT CAN BE WRITTEN

352
00:11:46,672 --> 00:11:48,274
IN THIS WAY.

353
00:11:48,340 --> 00:11:50,109
WHERE WE ARE ABLE TO FORM THIS

354
00:11:50,176 --> 00:11:52,078
REGRESSION LINE WHICH IS

355
00:11:52,144 --> 00:11:57,750
BASICALLY MADE UP OF OUR

356
00:11:57,817 --> 00:11:58,617
PREDICTED Y VALUES.

357
00:11:58,684 --> 00:12:00,453
AND FROM THIS LITTLE EVASION IS

358
00:12:00,519 --> 00:12:03,656
WHY WE'RE ESTIMATING THESE BETAS

359
00:12:03,722 --> 00:12:04,957
OR THESE COEFFICIENTS FROM THE

360
00:12:05,024 --> 00:12:09,061
OUTPUT OF OUR REGRESSION MODEL.

361
00:12:09,128 --> 00:12:11,097
SO BETA-1 IS OUR ESTIMATED

362
00:12:11,163 --> 00:12:13,132
CHANGE IN Y FOR ONE UNIT CHANGE

363
00:12:13,199 --> 00:12:13,466
IN X.

364
00:12:13,532 --> 00:12:14,834
THIS IS OUR LITTLE SLOPE THAT WE

365
00:12:14,900 --> 00:12:19,905
WOULD ABSTAIN FROM THE MODEL.

366
00:12:19,972 --> 00:12:23,342
AND BETA-0 IN PRETTY MUCH ALL

367
00:12:23,409 --> 00:12:26,512
CASES WE WILL CALL BETA-0 IS THE

368
00:12:26,579 --> 00:12:29,515
INTERCEPT, BETA-1 IS THE FIRST

369
00:12:29,582 --> 00:12:30,616
OBSERVED VARIABLE, NOT A SLOPE,

370
00:12:30,683 --> 00:12:34,453
BUT IN THIS CASE IT IS A SLOPE,

371
00:12:34,520 --> 00:12:35,054
BETA-0 IS ALWAYS THE INTERCEPT

372
00:12:35,121 --> 00:12:35,888
IN A FORMAL LIFE.

373
00:12:35,955 --> 00:12:39,525
THIS IS THE ESTIMATED VALUE OF Y

374
00:12:39,592 --> 00:12:41,494
WHEN ALL X ARE ZERO.

375
00:12:41,560 --> 00:12:45,397
OR IN THE SIMPLE ALGEBRAIC WAY,

376
00:12:45,464 --> 00:12:47,900
THIS IS THE SIMPLE INTER SENT ON

377
00:12:47,967 --> 00:12:49,368
THE GRAPH WHERE WE RUN INTO

378
00:12:49,435 --> 00:12:49,768
ZERO.

379
00:12:49,835 --> 00:12:53,272
AND THE DEGREE OF ERROR FROM THE

380
00:12:53,339 --> 00:12:55,174
TRUE Y, SO ALL THESE BLACK

381
00:12:55,241 --> 00:12:57,309
POINTS ARE OUR TRUE OBSERVE Y

382
00:12:57,376 --> 00:12:57,543
VALUES.

383
00:12:57,610 --> 00:13:00,279
THE DISTANCE THAT EACH OF THOSE

384
00:13:00,346 --> 00:13:03,883
POINTS ARE FROM OUR -- OUR

385
00:13:03,949 --> 00:13:06,919
PREDICTED LINE ARE SET OF ERROR

386
00:13:06,986 --> 00:13:07,186
TERMS.

387
00:13:07,253 --> 00:13:08,120
THIS EPSILON.

388
00:13:08,187 --> 00:13:08,988
I FOR EACH PERSON.

389
00:13:09,054 --> 00:13:12,925
SO EACH PERSON IS GIVEN AN ERROR

390
00:13:12,992 --> 00:13:15,628
OF HOW FAR THEIR PREDICTION,

391
00:13:15,694 --> 00:13:18,130
THEIR OBSERVED BEHAVIOR IS FROM

392
00:13:18,197 --> 00:13:18,697
THE PREDICTED BEHAVIOR.

393
00:13:18,764 --> 00:13:21,901
THIS IS SET OF ERRORS I HAVE

394
00:13:21,967 --> 00:13:23,669
BEEN TALKING ABOUT FOR MEETING

395
00:13:23,736 --> 00:13:25,171
OUR ASUNS OR NOT.

396
00:13:25,237 --> 00:13:27,373
AND THIS PIECE OF THE EDUCATION

397
00:13:27,439 --> 00:13:33,779
HERE IS OUR PREDICTED Y, OR

398
00:13:33,846 --> 00:13:35,514
Y-HAT.

399
00:13:35,581 --> 00:13:36,982
AND SO THIS IS KIND OF THE CRUX

400
00:13:37,049 --> 00:13:39,818
OF THE REGRESSION WHICH IS TO

401
00:13:39,885 --> 00:13:41,954
ESTIMATE THE BETA-0 AND BETA-1,

402
00:13:42,021 --> 00:13:43,155
OR AS MANY COEFFICIENTS AS WE

403
00:13:43,222 --> 00:13:45,357
HAVE, SUCH THAT THE SUM OF ALL

404
00:13:45,424 --> 00:13:47,326
PREDICTED ERRORS ARE ALL OF OUR

405
00:13:47,393 --> 00:13:49,195
EPSILONS IS AS SMALL AS

406
00:13:49,261 --> 00:13:49,662
POSSIBLE.

407
00:13:49,728 --> 00:13:51,931
WE FORMALIZE THAT, THIS IS JUST

408
00:13:51,997 --> 00:13:54,366
A SUMMATION ACROSS ALL OF THESE

409
00:13:54,433 --> 00:13:58,437
RED LINES HERE SQUARED.

410
00:13:58,504 --> 00:14:01,040
SO THIS LITTLE Y, I MINUS Y-HAT,

411
00:14:01,106 --> 00:14:04,109
I IS THE LITTLE DISTANCE OF

412
00:14:04,176 --> 00:14:05,444
ERRORS AND WE SQUARE THEM SO

413
00:14:05,511 --> 00:14:07,079
WE'RE NOT CANCELING OUT ALL OF

414
00:14:07,146 --> 00:14:08,247
THE BUNCH OF ERRORS BY HAVING

415
00:14:08,314 --> 00:14:10,649
SOME POSITIVE AND SOME NEGATIVE.

416
00:14:10,716 --> 00:14:12,618
SO WE'RE JUST INTERESTED IN THE

417
00:14:12,685 --> 00:14:12,918
MAGNITUDE.

418
00:14:12,985 --> 00:14:15,621
AND SUMMING ALL OF THOSE AND

419
00:14:15,688 --> 00:14:16,889
MINIMIZING, FITTING THE LINE

420
00:14:16,956 --> 00:14:24,296
SUCH THAT WE'RE MINIMIZING THAT

421
00:14:24,363 --> 00:14:27,700
SUMMED SQUARE OF ERRORS.

422
00:14:27,766 --> 00:14:31,337
SO I WANT TO USE THAT FRAMEWORK

423
00:14:31,403 --> 00:14:34,139
AND WALK THROUGH SOME EXAMPLES

424
00:14:34,206 --> 00:14:36,108
OF DOING REGRESSION USING SAMPLE

425
00:14:36,175 --> 00:14:36,909
DATA.

426
00:14:36,976 --> 00:14:42,248
AND THIS IS REAL, REAL DATA THAT

427
00:14:42,314 --> 00:14:44,917
IS AVAILABLE ONLINE SOURCED FROM

428
00:14:44,984 --> 00:14:49,388
THE UC IRVINE MACHINE LEARNING

429
00:14:49,455 --> 00:14:51,724
REPOSITORY USING 279 CARDIAC

430
00:14:51,790 --> 00:14:52,858
PATIENTS AND I SPECIFICALLY

431
00:14:52,925 --> 00:14:54,226
PULLED THE DATA USING THE

432
00:14:54,293 --> 00:14:54,960
PACKAGE AVAILABLE THERE.

433
00:14:55,027 --> 00:14:59,031
THIS IS A SET OF PATIENTS THAT

434
00:14:59,098 --> 00:15:01,000
ARE REFERRED FOR CORONARY

435
00:15:01,066 --> 00:15:02,134
ANGIOGRAPHY AT THE CLEVELAND

436
00:15:02,201 --> 00:15:02,368
CLINIC.

437
00:15:02,434 --> 00:15:06,305
NO PATIENTS HAD A HISTORY OF MI

438
00:15:06,372 --> 00:15:08,040
OR CARDIOMYOPATHIC DISEASE.

439
00:15:08,107 --> 00:15:11,176
AND ALL PATIENTS UNDERWENT ECG

440
00:15:11,243 --> 00:15:13,846
AT REST, AND CHOLESTEROL, AND

441
00:15:13,912 --> 00:15:15,981
FASTING BLOOD SUGAR MEASUREMENT

442
00:15:16,048 --> 00:15:18,550
AND OTHER DATA COLLECTION

443
00:15:18,617 --> 00:15:20,019
MEASUREMENTS HERE.

444
00:15:20,085 --> 00:15:23,622
AND ALSO UNDERWENT EXERCISE ECG,

445
00:15:23,689 --> 00:15:25,124
AND CARDIAC FLUOROSCOPY.

446
00:15:25,190 --> 00:15:27,059
SO WE HAVE A SMALL SET OF

447
00:15:27,126 --> 00:15:30,195
VARIABLES, AGAIN, THIS IS JUST A

448
00:15:30,262 --> 00:15:32,197
PUBLICLY AVAILABLE DATASET THAT

449
00:15:32,264 --> 00:15:34,833
I'M USING TO HELP US WALK US

450
00:15:34,900 --> 00:15:36,602
THROUGH SOME OF THESE EXAMPLES.

451
00:15:36,669 --> 00:15:39,071
I WILL BE SHOWING CODE SNIPPETS

452
00:15:39,138 --> 00:15:41,106
AND OUTPUTS FROM OUR SOFTWARE

453
00:15:41,173 --> 00:15:42,241
SPECIFICALLY, WHICH IS WHAT I'M

454
00:15:42,308 --> 00:15:48,280
MOST OF THE TIME USING.

455
00:15:48,347 --> 00:15:51,116
I GUESS I SHOULD JUST JUMP TO

456
00:15:51,183 --> 00:15:51,850
THE DISCLAIMER PART, WHICH IS

457
00:15:51,917 --> 00:15:53,085
THAT MOST SOFTWARE IS GOING TO

458
00:15:53,152 --> 00:15:54,920
BE MORE OR LESS THE SAME IN

459
00:15:54,987 --> 00:15:56,255
TERMS OF OUTPUT.

460
00:15:56,322 --> 00:15:59,291
BUT YOU MAY NEED TO MAKE SURE

461
00:15:59,358 --> 00:16:02,428
THAT YOU'RE LOOKING AT YOUR

462
00:16:02,494 --> 00:16:02,961
DOCUMENTATION FOR WHATEVER

463
00:16:03,028 --> 00:16:06,098
SOFTWARE YOU MAY BE USING TO DO

464
00:16:06,165 --> 00:16:07,299
THIS, TO SET THE MODEL PROPERLY,

465
00:16:07,366 --> 00:16:07,966
HOW THE SOFTWARE WOULD LIKE YOU

466
00:16:08,033 --> 00:16:09,201
TO SET IT.

467
00:16:09,268 --> 00:16:12,237
AND SIMILAR THAT YOUR DATA AND

468
00:16:12,304 --> 00:16:13,205
EACH VARIABLE IS SPECIFIED AS

469
00:16:13,272 --> 00:16:15,107
EXPECTED FOR USE WITH

470
00:16:15,174 --> 00:16:15,441
REREGRESSION.

471
00:16:15,507 --> 00:16:18,143
BECAUSE IT IS NOT ALWAYS, IT IS

472
00:16:18,210 --> 00:16:20,045
NOT ALWAYS THE SAME IN EVERY

473
00:16:20,112 --> 00:16:20,312
SOFTWARE.

474
00:16:20,379 --> 00:16:21,647
AND IF YOU HAVE SPECIFIC

475
00:16:21,714 --> 00:16:23,949
QUESTIONS ABOUT THIS, YOU KNOW,

476
00:16:24,016 --> 00:16:26,852
OUR TEAM IS AVAILABLE FOR

477
00:16:26,919 --> 00:16:28,520
QUESTIONS.

478
00:16:28,587 --> 00:16:30,789
AS YOU WORK, BUT BROADLY, TO --

479
00:16:30,856 --> 00:16:32,791
THE POINT SOME OF THE KEY ISSUES

480
00:16:32,858 --> 00:16:36,095
THAT MAY COME UP WITH THIS,

481
00:16:36,161 --> 00:16:37,629
WHICH IS DATA THAT'S

482
00:16:37,696 --> 00:16:39,698
CATEGORICAL, SO DATA WITH THREE

483
00:16:39,765 --> 00:16:41,834
OR MORE LEVELS SPECIFICALLY, BUT

484
00:16:41,900 --> 00:16:44,269
ARE IN THE DATASET AS NUMBERS.

485
00:16:44,336 --> 00:16:46,505
ZERO, ONE, TWO, ETC.

486
00:16:46,572 --> 00:16:48,340
THAT MAY BE RECODED THIS FROM

487
00:16:48,407 --> 00:16:52,111
BEING WRITTEN OUT WORD TO THEN

488
00:16:52,177 --> 00:16:54,279
ONE, TWO.

489
00:16:54,346 --> 00:17:00,352
I THINK MOST BY DEFAULT WILL

490
00:17:00,419 --> 00:17:01,420
THINK THIS IS A NUMERICAL

491
00:17:01,487 --> 00:17:02,821
VARIABLE.

492
00:17:02,888 --> 00:17:05,157
WE DON'T WANT TO TREAT THIS AS A

493
00:17:05,224 --> 00:17:06,058
NUMERICAL VARIABLE.

494
00:17:06,125 --> 00:17:10,362
WE WANT THIS CODED AS A CODED

495
00:17:10,429 --> 00:17:12,564
VARIABLE, SO WE WOULD NEED TO

496
00:17:12,631 --> 00:17:13,699
SPECIFY TO THE SOFTWARE THAT'S

497
00:17:13,766 --> 00:17:16,568
WHAT THIS IS, AND NOT BE

498
00:17:16,635 --> 00:17:18,971
AUTOMATICALLY IN THE REGRESSION

499
00:17:19,037 --> 00:17:21,140
AS A CONTINUOUS NUMERICAL

500
00:17:21,206 --> 00:17:21,774
VARIABLE AND WE WANT AN ESTIMATE

501
00:17:21,840 --> 00:17:25,711
FOR EACH OF THE LEVELS.

502
00:17:25,778 --> 00:17:27,946
BINARY 0/1 VARIABLES DON'T NEED

503
00:17:28,013 --> 00:17:31,049
TO BE RECODED BECAUSE THEY ARE

504
00:17:31,116 --> 00:17:32,284
ONE LEVEL.

505
00:17:32,351 --> 00:17:34,253
BUT CATEGORY VARIABLES WE WANT

506
00:17:34,319 --> 00:17:40,292
TO SPECIFY THESE THE RIGHT WAY

507
00:17:40,359 --> 00:17:41,593
FOR OUR SOFTWARE.

508
00:17:41,660 --> 00:17:44,930
SO IN THIS DATA, WE COULD ASK A

509
00:17:44,997 --> 00:17:46,498
QUESTION SUCH AS:  IS AGE

510
00:17:46,565 --> 00:17:48,934
RELATED TO THE MAXIMAL HEART

511
00:17:49,001 --> 00:17:50,936
RATE ACHIEVED IN THESE PATIENTS

512
00:17:51,003 --> 00:17:52,571
UNDERGOING EXERCISE TESTING?

513
00:17:52,638 --> 00:17:54,173
I HAVE INCLUDED A GRAPH HERE TO

514
00:17:54,239 --> 00:17:57,009
SHOW WHAT THIS DATA LOOKS LIKE.

515
00:17:57,075 --> 00:17:59,278
AGAIN, WE HAVE ALMOST 300 DATA

516
00:17:59,344 --> 00:17:59,511
POINTS.

517
00:17:59,578 --> 00:18:01,747
AGE AND YEARS, AND THE MAXIMUM

518
00:18:01,814 --> 00:18:03,582
HEART RATE ACHIEVED IN BEATS PER

519
00:18:03,649 --> 00:18:04,216
MINUTE.

520
00:18:04,283 --> 00:18:06,919
AND PERHAPS WERE INTERESTED IN

521
00:18:06,985 --> 00:18:07,519
DESCRIBING THIS RELATIONSHIP.

522
00:18:07,586 --> 00:18:10,155
AS I SAID BEFORE, WE MIGHT, WE

523
00:18:10,222 --> 00:18:12,758
SHOULD VISUALLY LOOK AT THE DATA

524
00:18:12,825 --> 00:18:13,892
BEFORE WE DO ANYTHING.

525
00:18:13,959 --> 00:18:14,793
THE RELATIONSHIP DOES LOOK LIKE

526
00:18:14,860 --> 00:18:16,929
SOMETHING THAT WE COULD DESCRIBE

527
00:18:16,995 --> 00:18:18,997
WITH A LINE THAT LOOKS ROUGHLY

528
00:18:19,064 --> 00:18:20,098
LINEAR.

529
00:18:20,165 --> 00:18:22,367
THERE ARE NO MAJOR OUTLIERS ORAD

530
00:18:22,434 --> 00:18:24,236
DISTRIBUTIONS THAT I CAN SEE

531
00:18:24,303 --> 00:18:26,305
THAT MIGHT ALREADY GIVE US SORT

532
00:18:26,371 --> 00:18:27,573
OF SOME RED FLAGS WITH RUNNING

533
00:18:27,639 --> 00:18:27,873
REGRESSION.

534
00:18:27,940 --> 00:18:29,208
SO AGAIN, THIS IS JUST A GOOD

535
00:18:29,274 --> 00:18:31,276
WAY TO CHECK OUR DATA AND MAKE

536
00:18:31,343 --> 00:18:32,878
SURE THAT ALL OF IT LOOKS THE

537
00:18:32,945 --> 00:18:36,081
WAY IT SHOULD BEFORE WE EVEN

538
00:18:36,148 --> 00:18:38,350
THINK ABOUT RUNNING THE

539
00:18:38,417 --> 00:18:38,650
REGRESSION.

540
00:18:38,717 --> 00:18:42,087
AND USING THE -- THE --

541
00:18:42,154 --> 00:18:43,188
TERMINOLOGY FROM PRIOR SLIDES,

542
00:18:43,255 --> 00:18:44,122
WE CAN WRITE SOMETHING LIKE THIS

543
00:18:44,189 --> 00:18:46,358
TO SHOW WHAT IT IS WE'RE

544
00:18:46,425 --> 00:18:50,062
ACTUALLY GOING TO TRY TO BE

545
00:18:50,128 --> 00:18:50,696
ESTIMATING, I'M CALLING THIS THE

546
00:18:50,762 --> 00:18:51,396
HEART RATE MAX.

547
00:18:51,463 --> 00:18:52,898
THIS IS OUR OUTCOME OF INTEREST.

548
00:18:52,965 --> 00:18:56,468
THEN WE WANT TO ESTIMATE BETA-0

549
00:18:56,535 --> 00:18:57,636
AND BETA-1.

550
00:18:57,703 --> 00:18:58,937
PARTICULARLY, WE'RE INTERESTED

551
00:18:59,004 --> 00:19:04,076
IN, AGAIN, THIS BETA-1, THIS

552
00:19:04,142 --> 00:19:04,710
SLOPE, THIS RELATIONSHIP BETWEEN

553
00:19:04,776 --> 00:19:05,143
AGE AND HEART RATE.

554
00:19:05,210 --> 00:19:09,381
AND AGE IS OUR KEY COVARIANT OF

555
00:19:09,448 --> 00:19:09,648
INTEREST.

556
00:19:09,715 --> 00:19:10,883
OUR INDEPENDENT VARIABLE.

557
00:19:10,949 --> 00:19:13,018
SO, THIS IS, THESE ARE THE ONLY

558
00:19:13,085 --> 00:19:14,653
THINGS WE NEED TO CONSIDER TO

559
00:19:14,720 --> 00:19:17,356
ANSWER THIS QUESTION THE WAY

560
00:19:17,422 --> 00:19:21,393
THAT WE PHRASE IT.

561
00:19:21,460 --> 00:19:23,262
AND SO IN R, THE WAY YOU WOULD

562
00:19:23,328 --> 00:19:25,030
SPECIFY THAT IS LIKE THIS.

563
00:19:25,097 --> 00:19:27,366
AGAIN, THIS IS OBVIOUSLY GOING

564
00:19:27,432 --> 00:19:30,903
TO BE DEPENDENT DEPENDING ON

565
00:19:30,969 --> 00:19:31,436
WHAT SOFT YOU'RE USING.

566
00:19:31,503 --> 00:19:33,705
THERE IS THIS LITTLE LM FUNCTION

567
00:19:33,772 --> 00:19:34,940
THAT RUNS LINEAR REGRESSION.

568
00:19:35,007 --> 00:19:38,877
WE TELL THE SOFTWARE WHAT DATA

569
00:19:38,944 --> 00:19:39,311
WE'RE PULLING FROM.

570
00:19:39,378 --> 00:19:40,812
THIS REALLY POORLY NAMED

571
00:19:40,879 --> 00:19:43,682
VARIABLE, I THINK, FOR A

572
00:19:43,749 --> 00:19:44,783
PUBLICLY AVAILABLE DATASET IS

573
00:19:44,850 --> 00:19:46,518
OUR MAXIMUM HEART RATE ACHIEVED

574
00:19:46,585 --> 00:19:48,520
VARIABLE AND OUR SINGLE

575
00:19:48,587 --> 00:19:50,589
PREDICTOR OF AGE AND THE

576
00:19:50,656 --> 00:19:53,292
REGRESSION IS SPLIT ON EITHER

577
00:19:53,358 --> 00:19:55,761
SIDE OF PREDICTORS AND OUTCOME

578
00:19:55,827 --> 00:19:57,963
VARIABLES BY THIS LITTLE THING.

579
00:19:58,030 --> 00:19:59,831
WE CAN CALL, SO WE RUN THE

580
00:19:59,898 --> 00:20:02,267
MODEL, WE CALL THE OUTPUT USING

581
00:20:02,334 --> 00:20:03,435
THE SUMMARY FUNCTION AND WE GET

582
00:20:03,502 --> 00:20:04,903
THIS OUTPUT.

583
00:20:04,970 --> 00:20:07,005
WHICH IS JUST A SIMPLE TABLE

584
00:20:07,072 --> 00:20:09,308
BROKEN DOWN INTO A SUPPLE

585
00:20:09,374 --> 00:20:11,810
COLUMNS AND ONE ROW FOR EACH

586
00:20:11,877 --> 00:20:12,911
BETA OR EACH COEFFICIENT THAT

587
00:20:12,978 --> 00:20:14,947
WE'RE ESTIMATING FROM THE

588
00:20:15,013 --> 00:20:15,247
REGRESSION.

589
00:20:15,314 --> 00:20:17,082
AND THE COLUMNS GIVE US ALL OF

590
00:20:17,149 --> 00:20:18,617
THIS STATISTICAL DETAILS THAT WE

591
00:20:18,684 --> 00:20:18,817
NEED.

592
00:20:18,884 --> 00:20:20,919
FIRST IT GIVES US THE ESTIMATE,

593
00:20:20,986 --> 00:20:22,955
WHICH IS THE ACTUAL VALUE OF THE

594
00:20:23,021 --> 00:20:23,855
BETA THAT WE'RE ESTIMATING.

595
00:20:23,922 --> 00:20:25,624
WE ALSO HAVE A STANDARD ERROR

596
00:20:25,691 --> 00:20:28,026
FOR THAT ESTIMATE.

597
00:20:28,093 --> 00:20:29,695
A T-VALUE TO, AGAIN, GO ALONG

598
00:20:29,761 --> 00:20:30,929
WITH THAT ESTIMATE.

599
00:20:30,996 --> 00:20:39,504
AND THE P-VALUE, WHICH IS

600
00:20:39,571 --> 00:20:40,038
DENOTED IN R WITH THE

601
00:20:40,105 --> 00:20:40,772
TERMINOLOGY, AND THE STAR HERE

602
00:20:40,839 --> 00:20:44,076
THAT TEMPS US IT IS SIGNIFICANT.

603
00:20:44,142 --> 00:20:46,178
THAT'S IMPORTANT TO US.

604
00:20:46,244 --> 00:20:47,079
IT WILL LOOK FAIRLY SIMILAR FOR

605
00:20:47,145 --> 00:20:48,347
MOST ORT SOFTWARES AS WELL.

606
00:20:48,413 --> 00:20:51,783
WHEN WE LOOK AT THIS, THIS IS

607
00:20:51,850 --> 00:20:53,385
HOW WE WOULD INSTILL IN OUR

608
00:20:53,452 --> 00:20:54,853
EQUATION, I PUT IT OVER HERE ON

609
00:20:54,920 --> 00:20:55,587
THIS GRAPH.

610
00:20:55,654 --> 00:20:57,923
I'VE ALSO SHOWN THE ESTIMATED

611
00:20:57,990 --> 00:20:58,890
LINES THAT WE GET.

612
00:20:58,957 --> 00:21:04,096
THIS RED LINE IS ACTUALLY THIS Y

613
00:21:04,162 --> 00:21:05,430
EQUALS NX PLUS B-LINE DIRECTLY

614
00:21:05,497 --> 00:21:08,133
OVERLAID ON OUR DATA.

615
00:21:08,200 --> 00:21:12,304
AND AGAIN, OUR BETA-0 IS OUR

616
00:21:12,371 --> 00:21:12,838
ESTIMATE.

617
00:21:12,904 --> 00:21:13,805
204 ROUGHLY.

618
00:21:13,872 --> 00:21:18,910
AND OUR SLOPE IS NEGATIVE SLOPE

619
00:21:18,977 --> 00:21:23,415
OF ABOUT ONE OF, ONE.

620
00:21:23,482 --> 00:21:26,618
SO AGAIN, THIS IS SORT OF HOW WE

621
00:21:26,685 --> 00:21:28,086
FILL THIS IN HERE, INTO EACH.

622
00:21:28,153 --> 00:21:31,356
AND SO, I WANT TO TALK ABOUT THE

623
00:21:31,423 --> 00:21:34,092
SPECIFIC INTERPRET TASE OF EACH

624
00:21:34,159 --> 00:21:34,793
OF THESE.

625
00:21:34,860 --> 00:21:36,762
-- INTERPRETATION OF EACH OF

626
00:21:36,828 --> 00:21:38,030
THESE.

627
00:21:38,096 --> 00:21:40,098
SO THE INTERCEPT, AGAIN, IS THE

628
00:21:40,165 --> 00:21:41,266
ESTIMATED HEART RATE FOR AN

629
00:21:41,333 --> 00:21:44,903
INDIVIDUAL AT AGE ZERO.

630
00:21:44,970 --> 00:21:47,806
AND THIS IS 204.15 BEATS PER

631
00:21:47,873 --> 00:21:48,240
MINUTE.

632
00:21:48,306 --> 00:21:50,442
THIS IS ALSO NOTED TO BE

633
00:21:50,509 --> 00:21:52,978
STATISTICAL SIGNIFICANT.

634
00:21:53,045 --> 00:21:55,947
AND THIS IS COMPARING TO ZERO,

635
00:21:56,014 --> 00:21:57,849
STATISTICAL GREATER THAN ZERO.

636
00:21:57,916 --> 00:22:01,753
IF WE WANT THIS TO BE A MORE

637
00:22:01,820 --> 00:22:03,722
INTERPRETABLE INTERCEPT, WE CAN

638
00:22:03,789 --> 00:22:04,623
DO SOMETHING CALLED MEAN

639
00:22:04,690 --> 00:22:06,458
CENTERING, OR CENTERING, SOME OF

640
00:22:06,525 --> 00:22:07,559
YOU MAY HAVE HEARD OF THIS

641
00:22:07,626 --> 00:22:10,262
BEFORE, THIS WOULD BASICALLY

642
00:22:10,328 --> 00:22:14,433
JUST DO SOMETHING WHICH GIVES US

643
00:22:14,499 --> 00:22:15,267
MORE INTERPRETABLE INTERCEPT.

644
00:22:15,333 --> 00:22:16,535
WE WOULD TAKE EACH AGE OF THE

645
00:22:16,601 --> 00:22:18,437
PERSON IN THE COHORT, CALCULATE

646
00:22:18,503 --> 00:22:22,974
A COHORT AVERAGE AGE, AND FOR

647
00:22:23,041 --> 00:22:24,476
EACH PERSON CALCULATE THE CHANGE

648
00:22:24,543 --> 00:22:25,377
FROM THAT COHORT MEAN.

649
00:22:25,444 --> 00:22:28,447
AND SO EACH PERSON'S NEW MEAN

650
00:22:28,513 --> 00:22:31,083
CENTERED AGE WOULD BE RELATIVE

651
00:22:31,149 --> 00:22:31,850
TO THAT AGE.

652
00:22:31,917 --> 00:22:35,220
THEN IF WE USE THAT RECALCULATED

653
00:22:35,287 --> 00:22:35,554
IN A VARIABLE.

654
00:22:35,620 --> 00:22:38,156
THE INTERCEPT WOULD BE THE

655
00:22:38,223 --> 00:22:38,957
ESTIMATED HEART RATE AT THE

656
00:22:39,024 --> 00:22:41,426
COHORT MEAN AGE, INSTEAD OF AT

657
00:22:41,493 --> 00:22:41,860
ZERO AGE.

658
00:22:41,927 --> 00:22:44,096
IT WOULD BE AT ZERO, WHICH IS IS

659
00:22:44,162 --> 00:22:45,197
NOW ZERO THAT MEANS THE MEAN.

660
00:22:45,263 --> 00:22:46,998
WE CAN DO THINGS LIKE THAT TO

661
00:22:47,065 --> 00:22:48,767
OUR VARIABLES TO HELP US

662
00:22:48,834 --> 00:22:50,235
INTERPRET INTERCEPTS A LITTLE

663
00:22:50,302 --> 00:22:50,836
BIT BETTER.

664
00:22:50,902 --> 00:22:55,574
BUT ALTHOUGH, I THINK, BROADLY.

665
00:22:55,640 --> 00:22:57,642
WE AREN'T USUALLY INTERESTED IN

666
00:22:57,709 --> 00:22:58,543
INTERPRETING INTERCEPTS.

667
00:22:58,610 --> 00:23:01,046
AND THEN THE AGE COEFFICIENT.

668
00:23:01,113 --> 00:23:03,215
AND THIS IS, WE WOULD INTERPRET

669
00:23:03,281 --> 00:23:08,320
THIS AS THE ESTIMATED HEART RATE

670
00:23:08,386 --> 00:23:09,955
DECREASES BY 1.0002 BEATS PER

671
00:23:10,021 --> 00:23:12,924
MINUTE PER YEAR INCREASE IN AGE.

672
00:23:12,991 --> 00:23:15,460
AGAIN, THAT'S THE, OUR NICE

673
00:23:15,527 --> 00:23:16,294
INTERPRETATION OF SLOPE THAT

674
00:23:16,361 --> 00:23:18,764
MOST OF US ARE FAMILIAR WITH.

675
00:23:18,830 --> 00:23:22,134
THE TRICK IS JUST KNOWING HOW --

676
00:23:22,200 --> 00:23:24,569
AGAIN, IT IS WHAT OUR OUTCOME

677
00:23:24,636 --> 00:23:25,137
VARIABLE, WHICH IS MEASURING

678
00:23:25,203 --> 00:23:27,339
BEATS PER MINUTE, AND THEN PER

679
00:23:27,405 --> 00:23:28,573
INCREASING UNIT IN AGE.

680
00:23:28,640 --> 00:23:29,975
AGAIN, THIS IS A NEGATIVE SLOPE,

681
00:23:30,041 --> 00:23:31,743
SO WE HAVE A DECREASE IN HEART

682
00:23:31,810 --> 00:23:32,477
RATE OVER TIME.

683
00:23:32,544 --> 00:23:34,513
THIS IS WHERE HAVING THE FIGURE

684
00:23:34,579 --> 00:23:36,848
ALSO HELPS, YOU CAN MAKE SURE

685
00:23:36,915 --> 00:23:37,649
THAT YOU'RE INTERPRETING IT

686
00:23:37,716 --> 00:23:38,817
RIGHT WAY.

687
00:23:38,884 --> 00:23:39,951
IT SHOULD ALL JIVE WITH HOW

688
00:23:40,018 --> 00:23:42,387
YOU'VE THINKING ABOUT IT.

689
00:23:42,454 --> 00:23:44,256
THIS IS STATISTICAL

690
00:23:44,322 --> 00:23:44,890
SIGNIFICANTLY DIFFERENT FROM A

691
00:23:44,956 --> 00:23:46,558
SLOPE OF ZERO WHICH IS NO

692
00:23:46,625 --> 00:23:49,895
RELATIONSHIP, AND NO CHANGE

693
00:23:49,961 --> 00:23:50,362
ACROSS INCREASING AGE.

694
00:23:50,428 --> 00:23:52,798
AND I WANT TO POINT OUT THAT

695
00:23:52,864 --> 00:23:56,368
MAYBE THIS IS LIKE A TECHNICAL

696
00:23:56,434 --> 00:23:58,136
POINT, BUT THIS SLOPE, I WANT TO

697
00:23:58,203 --> 00:24:00,605
JUST BE CAREFUL ESPECIALLY WHEN

698
00:24:00,672 --> 00:24:03,975
WE TALK ABOUT AGE AND PER YEAR.

699
00:24:04,042 --> 00:24:06,044
THIS IS A COHORT-LEVEL BEHAVIOR

700
00:24:06,111 --> 00:24:07,913
IN TERMS OF WE'RE NOT TALKING

701
00:24:07,979 --> 00:24:10,348
ABOUT AS A PERSON AGES, BECAUSE

702
00:24:10,415 --> 00:24:11,650
THIS ISN'T LONGITUDINAL DATA.

703
00:24:11,716 --> 00:24:13,118
THIS IS SAYING AS WE LOOK AT

704
00:24:13,185 --> 00:24:16,188
PEOPLE WHO ARE OLDER WE HAVE

705
00:24:16,254 --> 00:24:16,888
THIS RELATIONSHIP.

706
00:24:16,955 --> 00:24:18,924
IT YOU WANTED TO ACTUALLY SAY AS

707
00:24:18,990 --> 00:24:22,828
A PERSON AGES OR WITH -- AS A

708
00:24:22,894 --> 00:24:24,529
PERSON GETS OLDER YOU WOULD HAVE

709
00:24:24,596 --> 00:24:28,233
TO BE DOING REPEATED MEASURES ON

710
00:24:28,300 --> 00:24:29,301
THE SAME PERSON.

711
00:24:29,367 --> 00:24:32,204
SO THIS IS A FUNNY

712
00:24:32,270 --> 00:24:36,341
INTERPRETATION HERE, AND BOTH OF

713
00:24:36,408 --> 00:24:38,176
ARE GOING TO EXTRAPOLATE TO SAY,

714
00:24:38,243 --> 00:24:39,411
AS YOU ARE OLDER YOUR MAXIMUM

715
00:24:39,477 --> 00:24:40,412
HEART RATE IS LOWER.

716
00:24:40,478 --> 00:24:44,850
BUT TO BE CAUTIOUS AND SAY THIS

717
00:24:44,916 --> 00:24:45,951
IS NOT ACTUALLY LONGITUDINAL

718
00:24:46,017 --> 00:24:46,685
DATA, THIS IS A CROSS-SECTION,

719
00:24:46,751 --> 00:24:48,820
WE MIGHT NOT HAVE A GOOD INTERN

720
00:24:48,887 --> 00:24:51,957
TRUITATION OF THAT HERE.

721
00:24:52,023 --> 00:24:54,125
AND JUST TO SPEAK TO THE

722
00:24:54,192 --> 00:24:55,360
PREDICTION POINT OF THIS A

723
00:24:55,427 --> 00:24:55,894
LITTLE BIT.

724
00:24:55,961 --> 00:25:00,098
SO I JUST WANT TO POINT OUT THAT

725
00:25:00,165 --> 00:25:01,900
YOU COULD HAVE A SCENARIO WHERE

726
00:25:01,967 --> 00:25:04,135
MAYBE, WITH THIS MODEL, WITH

727
00:25:04,202 --> 00:25:06,137
THIS PREDICTED MODEL, MAYBE YOU

728
00:25:06,204 --> 00:25:07,973
WANT TO KNOW THE BEHAVIOR OF

729
00:25:08,039 --> 00:25:08,373
SOMEBODY WITH SOME

730
00:25:08,440 --> 00:25:09,241
CHARACTERISTICS.

731
00:25:09,307 --> 00:25:10,842
MAYBE IT IS JUST HANE, OR MAYBE

732
00:25:10,909 --> 00:25:13,478
IF WE HAD A LONGER MODEL THIS

733
00:25:13,545 --> 00:25:15,480
MIGHT BE MORE USEFUL, WE HAD

734
00:25:15,547 --> 00:25:16,481
DIFFERENT SETS OF

735
00:25:16,548 --> 00:25:17,415
CHARACTERISTICS ON A PERSON.

736
00:25:17,482 --> 00:25:20,051
SAY, FOR EXAMPLE, WE JUST WANTED

737
00:25:20,118 --> 00:25:23,355
TO KNOW WHAT PREDICTED MAXIMUM

738
00:25:23,421 --> 00:25:26,157
HEART RATE ACHIEVED FOR AN AGE

739
00:25:26,224 --> 00:25:28,793
AGE 50 WOULD BE, WE WOULD PLUG

740
00:25:28,860 --> 00:25:29,394
THAT IN AND DO THE CALCULATION

741
00:25:29,461 --> 00:25:29,961
IN THE WAY YOU WOULD EXPECT.

742
00:25:30,028 --> 00:25:34,466
AND GET A NUMBER OF 154.15 BEATS

743
00:25:34,532 --> 00:25:35,634
PER MINUTE.

744
00:25:35,700 --> 00:25:36,334
YOU CAN SEE NOW YOU WOULDN'T GET

745
00:25:36,401 --> 00:25:38,570
A NUMBER FROM THIS, BUT YOU CAN,

746
00:25:38,637 --> 00:25:41,039
THE WAY THAT THIS IS HAPPENING,

747
00:25:41,106 --> 00:25:43,074
AGAIN, WE'RE JUST USING AGE.

748
00:25:43,141 --> 00:25:44,976
WHEREAS ON THE PREDICTED LINE

749
00:25:45,043 --> 00:25:46,711
AND WHAT IS THE Y ATTRIBUTED TO

750
00:25:46,778 --> 00:25:49,981
THAT VALUE ON THE PREDICTED

751
00:25:50,048 --> 00:25:55,420
LINE.

752
00:25:55,487 --> 00:25:56,988
AND IN R AND IN MOST OTHER

753
00:25:57,055 --> 00:25:58,957
SOFTWARES THERE ARE GOING TO BE

754
00:25:59,024 --> 00:26:01,159
A BUNCH OF OTHER PIECES OF THE

755
00:26:01,226 --> 00:26:02,193
OUTPUT AS WELL.

756
00:26:02,260 --> 00:26:03,461
I'M NOT GOING TO TALK A WHOLE

757
00:26:03,528 --> 00:26:04,829
LOT ABOUT A LOT OF THIS STUFF.

758
00:26:04,896 --> 00:26:06,998
JUST FOR THE SAKE OF TIME.

759
00:26:07,065 --> 00:26:09,467
REALLY.

760
00:26:09,534 --> 00:26:10,702
AND COMPLEXITY.

761
00:26:10,769 --> 00:26:11,770
BUT THERE ARE A COUPLE PIECES

762
00:26:11,836 --> 00:26:15,407
HERE THAT I'M SHOWING IN THE R

763
00:26:15,473 --> 00:26:16,074
OUTPUT.

764
00:26:16,141 --> 00:26:17,876
THE FIRST IS RESIDUAL STANDARD

765
00:26:17,943 --> 00:26:19,277
ERROR, THIS IS THE STANDARD

766
00:26:19,344 --> 00:26:21,680
DEVIATION OF THOSE ERRORS.

767
00:26:21,746 --> 00:26:23,114
AGAIN, THIS IS, THE PIECE OF --

768
00:26:23,181 --> 00:26:25,050
THE PUZZLE THAT WE TALKED ABOUT

769
00:26:25,116 --> 00:26:28,086
EARLIER WHICH IS THAT ALL THOSE

770
00:26:28,153 --> 00:26:31,056
ERRORS SHOULD HAVE THE SAME --

771
00:26:31,122 --> 00:26:32,157
THERE SHOULD BE UNIFORM

772
00:26:32,223 --> 00:26:33,124
VARIABILITY ACROSS THE ERRORS.

773
00:26:33,191 --> 00:26:35,226
THIS IS KIND OF COMING, THIS IS

774
00:26:35,293 --> 00:26:36,928
WHERE THAT PIECE COMES IN.

775
00:26:36,995 --> 00:26:39,798
THEY ARE ALL ABLE TO BE WELL

776
00:26:39,864 --> 00:26:41,399
DESCRIBED BY A SINGLE DEVIATION

777
00:26:41,466 --> 00:26:42,400
OR VARIABILITY.

778
00:26:42,467 --> 00:26:43,935
THIS GIVES YOU THAT STATISTIC.

779
00:26:44,002 --> 00:26:46,705
WE ALSO HAVE A MULTIPLE R

780
00:26:46,771 --> 00:26:48,573
SQUARED, ADJUSTED R SQUARED.

781
00:26:48,640 --> 00:26:50,141
THIS IS THE REPORTERRING OF THIS

782
00:26:50,208 --> 00:26:53,378
TYPE OF THING IS VARYING BY

783
00:26:53,445 --> 00:26:54,012
SOFTWARE AS WELL.

784
00:26:54,079 --> 00:26:56,247
PREFER TO YOUR DOCUMENTATION

785
00:26:56,314 --> 00:26:57,282
WHAT IS SPECIFICALLY BEING

786
00:26:57,349 --> 00:26:58,016
RECORDED THERE.

787
00:26:58,083 --> 00:26:59,985
AND I, AGAIN, A LOT OF PEOPLE

788
00:27:00,051 --> 00:27:00,919
LIKE TO TALK ABOUT R SQUARED.

789
00:27:00,986 --> 00:27:04,089
I'M NOT GOING TO REALLY SAY TOO

790
00:27:04,155 --> 00:27:06,057
MUCH ABOUT THAT HERE BECAUSE I

791
00:27:06,124 --> 00:27:07,592
DON'T REALLY FIND THEM TO BE

792
00:27:07,659 --> 00:27:08,460
THAT HELPFUL, HONESTLY.

793
00:27:08,526 --> 00:27:10,395
I THINK THEY ARE REALLY

794
00:27:10,462 --> 00:27:12,664
DEPENDENT ON YOUR DATA AND, AND

795
00:27:12,731 --> 00:27:15,367
Ns AND THE NUMBER OF VARIABLES

796
00:27:15,433 --> 00:27:16,601
THAT YOU PUT IN HERE.

797
00:27:16,668 --> 00:27:20,205
ALTHOUGH, IN SOME WAYS ADJUSTED

798
00:27:20,271 --> 00:27:21,206
AND MULTIPLE R SQUARES ACCOUNT

799
00:27:21,272 --> 00:27:23,508
FOR THE VARIABLES IN THE MODEL.

800
00:27:23,575 --> 00:27:24,809
ESSENTIALLY WHAT R SQUARED IS

801
00:27:24,876 --> 00:27:27,345
TRYING TO DO IS DESCRIBE THE

802
00:27:27,412 --> 00:27:29,047
PORTION OF VARIANCE RELATIVE TO

803
00:27:29,114 --> 00:27:32,017
THE VARIANCE OF THE ERRORS.

804
00:27:32,083 --> 00:27:34,619
SO, HOW WELL DOES THE MODEL

805
00:27:34,686 --> 00:27:37,055
CAPTURE ALL OF THE VARIABILITY

806
00:27:37,122 --> 00:27:37,555
THAT'S BEING EXPLAINED?

807
00:27:37,622 --> 00:27:41,493
AND I THINK YOU CAN KIND OF SEE

808
00:27:41,559 --> 00:27:43,395
VISUALLY THAT WHILE THERE IS A

809
00:27:43,461 --> 00:27:47,665
NEGATIVE SLOPE HERE, WHILE THERE

810
00:27:47,732 --> 00:27:49,134
IS SOME EXPLANATORY POWER OF

811
00:27:49,200 --> 00:27:52,103
THIS LINE, THAT OBVIOUSLY, IT IS

812
00:27:52,170 --> 00:27:54,205
NOT PERFECTLY PREDICTIVE OF A

813
00:27:54,272 --> 00:27:55,774
PERSON'S MAXIMUM HEART RATE

814
00:27:55,840 --> 00:27:56,041
ACHIEVED.

815
00:27:56,107 --> 00:27:58,143
THERE IS SOME OTHER VARIABLE

816
00:27:58,209 --> 00:27:59,344
THAT IS IN?

817
00:27:59,411 --> 00:28:00,078
EACH PERSON'S OBSERVATION THAT

818
00:28:00,145 --> 00:28:02,647
WE ARE NOT ABLE TO CAPTURE WITH

819
00:28:02,714 --> 00:28:04,115
THE SIMPLE MODEL.

820
00:28:04,182 --> 00:28:06,684
BUT I THINK MOST OF US HAVE

821
00:28:06,751 --> 00:28:07,886
INTUITIVE UNDERSTANDING WHEN WE

822
00:28:07,952 --> 00:28:09,254
LOOK AT THIS, THERE ARE A LOT

823
00:28:09,320 --> 00:28:10,889
MORE VARIABLES AT PLAY HERE THAT

824
00:28:10,955 --> 00:28:13,491
WOULD BE INFLUENCING A PERSON'S

825
00:28:13,558 --> 00:28:15,360
OBSERVED HEART RATE.

826
00:28:15,427 --> 00:28:17,862
THERE IS ALSO AN F-STATISTIC AND

827
00:28:17,929 --> 00:28:19,597
A P-VALUE FOR, THIS SHOULD SAY

828
00:28:19,664 --> 00:28:21,633
MODEL, FOR THE MODEL OVERALL,

829
00:28:21,699 --> 00:28:25,904
AGAIN, I DON'T REALLY WANT TO

830
00:28:25,970 --> 00:28:27,038
SPEND TIME TALKING ABOUTCIFICLY.

831
00:28:27,105 --> 00:28:28,273
WE WILL TALK ABOUT F-TESTS

832
00:28:28,339 --> 00:28:28,973
LATER.

833
00:28:29,040 --> 00:28:31,776
THIS IS JUST TELLING YOU IS THE

834
00:28:31,843 --> 00:28:32,811
MODEL USEFUL TO RUN AT ALL.

835
00:28:32,877 --> 00:28:34,579
I THINK HONESTLY THAT HAS MORE

836
00:28:34,646 --> 00:28:36,848
TO DO WITH THE GOALS OF THE

837
00:28:36,915 --> 00:28:38,716
INVESTIGATION THEN IT DOES WITH

838
00:28:38,783 --> 00:28:44,522
F-STATISTICS, BUT -- YEAH.

839
00:28:44,589 --> 00:28:47,225
AND SO FROM THAT MODEL THAT WE

840
00:28:47,292 --> 00:28:48,760
JUST RAN, WE WOULD ALSO CHECK

841
00:28:48,827 --> 00:28:49,060
MODEL FIT.

842
00:28:49,127 --> 00:28:52,363
THIS IS ACTUALLY A SET OF

843
00:28:52,430 --> 00:28:53,031
OUTPUTS FROM R.

844
00:28:53,098 --> 00:28:55,800
R AND SOME OTHER SOFTWARES WILL

845
00:28:55,867 --> 00:28:57,669
HAVE BUILT IN MODEL CHECKING

846
00:28:57,735 --> 00:28:59,270
THAT YOU COULD DO DEPENDING ON

847
00:28:59,337 --> 00:29:00,705
HOW YOU ACCESS THOSE.

848
00:29:00,772 --> 00:29:02,207
AGAIN, THAT'S GOING TO DEPEND ON

849
00:29:02,273 --> 00:29:02,941
YOUR SOFTWARE.

850
00:29:03,007 --> 00:29:05,743
BUT IN R, YOU CAN PULL UP THESE

851
00:29:05,810 --> 00:29:07,011
THINGS TO INVESTIGATE MODEL FIT.

852
00:29:07,078 --> 00:29:08,713
SO ON THE LEFT, WE WOULD BE

853
00:29:08,780 --> 00:29:13,751
INVESTIGATING THE NORMALITY OF

854
00:29:13,818 --> 00:29:16,287
THE RESIDUALS AND ON THE RIGHT,

855
00:29:16,354 --> 00:29:22,026
IS THERE THAT NICE EVEN

856
00:29:22,093 --> 00:29:24,462
DISTRIBUTION OF RESIDUALS ACROSS

857
00:29:24,529 --> 00:29:26,264
ALL VALUES OF Y.

858
00:29:26,331 --> 00:29:29,968
SO, ON THE LEFT, AGAIN, WE

859
00:29:30,034 --> 00:29:30,902
TALKED ABOUT HOW, A LITTLE BIT

860
00:29:30,969 --> 00:29:34,105
HOW WE'RE NOT REALLY EVER GOING

861
00:29:34,172 --> 00:29:36,674
TO SEE A PERFECT X EQUALS Y

862
00:29:36,741 --> 00:29:36,875
HERE.

863
00:29:36,941 --> 00:29:38,776
WE DO SEE A LITTLE BIT OF THIS

864
00:29:38,843 --> 00:29:39,477
TAILING OFF HERE.

865
00:29:39,544 --> 00:29:40,545
SO MAYBE THERE IS A LITTLE BIT

866
00:29:40,612 --> 00:29:43,214
OF SKEWED BEHAVIOR.

867
00:29:43,281 --> 00:29:45,984
BUT PERHAPS NOT ENOUGH TO REALLY

868
00:29:46,050 --> 00:29:47,051
DO ANYTHING ABOUT JUST WORTH

869
00:29:47,118 --> 00:29:48,186
NOTING.

870
00:29:48,253 --> 00:29:49,654
AGAIN, I THINK VISUALLY, THE

871
00:29:49,721 --> 00:29:52,457
MODEL THAT WE FIT SORT OF JIVES

872
00:29:52,524 --> 00:29:53,124
WITH WHAT WE WOULD EXPECT TO

873
00:29:53,191 --> 00:29:53,291
SEE.

874
00:29:53,358 --> 00:29:58,062
SO I DON'T THINK THAT WE'RE

875
00:29:58,129 --> 00:30:00,098
SEEING ANY BEHAVIOR UNEXPECTED

876
00:30:00,165 --> 00:30:02,634
OR DUE TO POOR MODEL FIT.

877
00:30:02,700 --> 00:30:04,302
AND THE RESIDUAL BEHAVIOR FOR

878
00:30:04,369 --> 00:30:05,670
VARIANCE ALSO PRETTY GOOD.

879
00:30:05,737 --> 00:30:09,140
IT MAY BE MORE CIRCULAR, BUT IT

880
00:30:09,207 --> 00:30:09,641
IS STILL FAIRLY EVEN.

881
00:30:09,707 --> 00:30:10,675
THERE IS A LITTLE BIT MORE

882
00:30:10,742 --> 00:30:11,576
VARIABILITY TOWARDS THE MIDDLE

883
00:30:11,643 --> 00:30:14,746
THEN AT THE END, PERHAPS.

884
00:30:14,812 --> 00:30:16,614
BUT AGAIN, NOTHING SUPER CRAZY

885
00:30:16,681 --> 00:30:24,656
LOOKING HERE FOR MODEL FIT.

886
00:30:24,722 --> 00:30:26,124
SO MOVING ONTO ADDING

887
00:30:26,191 --> 00:30:26,558
COVARIANTS.

888
00:30:26,624 --> 00:30:30,995
SO, WE CAN MAKE A MODEL MUCH

889
00:30:31,062 --> 00:30:33,097
MORE COMPLEXES BY ADDING

890
00:30:33,164 --> 00:30:34,332
COVARIANCES INTO THE REGRESSION.

891
00:30:34,399 --> 00:30:37,468
SO PERHAPS WE WANT TO CONTROL

892
00:30:37,535 --> 00:30:40,205
FOR FASTING BLOOD SUGAR, SERUM

893
00:30:40,271 --> 00:30:46,077
CHOLESTEROL, AND THE SLOPE OF ST

894
00:30:46,144 --> 00:30:49,147
SEGMENT, THREE -- SMALLINAL,

895
00:30:49,214 --> 00:30:49,814
UPSLOPING, FLAT, AND

896
00:30:49,881 --> 00:30:50,114
DOWNSLOPING.

897
00:30:50,181 --> 00:30:52,083
PERHAPS WE WANT TO ASK ABOUT AGE

898
00:30:52,150 --> 00:30:53,184
AND ALSO CONTROLLING FOR THE

899
00:30:53,251 --> 00:30:54,953
OTHER VARIABLES.

900
00:30:55,019 --> 00:30:58,690
IN THIS CASE, FASTING BLOOD

901
00:30:58,756 --> 00:30:59,057
SUGAR IS BINARY.

902
00:30:59,123 --> 00:31:02,794
SPLIT IT 120.

903
00:31:02,860 --> 00:31:06,397
AND SERUM CHOLESTEROL IS A

904
00:31:06,464 --> 00:31:06,798
CONTINUOUS METRIC.

905
00:31:06,864 --> 00:31:09,234
SO WE CAN RUN THAT MODEL OUTPUT

906
00:31:09,300 --> 00:31:10,768
LOOKS SIMILAR, BUT JUST WITH

907
00:31:10,835 --> 00:31:11,502
MORE ROWS, RIGHT?

908
00:31:11,569 --> 00:31:12,937
BECAUSE WE HAVE MORE

909
00:31:13,004 --> 00:31:13,538
COEFFICIENTS.

910
00:31:13,605 --> 00:31:14,606
AND RECALL THAT THE

911
00:31:14,672 --> 00:31:16,007
INTERPRETATION OF THE INTERCEPT

912
00:31:16,074 --> 00:31:17,442
IS HOLDING ALL OF THE OTHER

913
00:31:17,508 --> 00:31:19,177
ITEMS THAT ZERO, WHICH MEANS

914
00:31:19,244 --> 00:31:20,411
EACH GROUP NEEDS TO HAVE A

915
00:31:20,478 --> 00:31:23,081
REFERENCE GROUP.

916
00:31:23,147 --> 00:31:23,915
SO FOR CONTINUOUS VARIABLES THIS

917
00:31:23,982 --> 00:31:26,351
IS ZERO NATURALLY.

918
00:31:26,417 --> 00:31:27,485
AND FOR BINARY VARIABLES OR

919
00:31:27,552 --> 00:31:29,320
CONTINUOUS VARIABLES WE JUST

920
00:31:29,387 --> 00:31:30,521
NEED TO BE CLEAR ABOUT WHAT THE

921
00:31:30,588 --> 00:31:33,258
REFERENCE GROUPS ARE AND PERHAPS

922
00:31:33,324 --> 00:31:33,858
WE ACTUALLY WANT TO SET THOSE

923
00:31:33,925 --> 00:31:35,793
BEFORE WE RUN THE MODEL.

924
00:31:35,860 --> 00:31:36,961
AS FAR AS THE OUTPUT, THE

925
00:31:37,028 --> 00:31:38,563
MISSING ITEM IN THE ROWS IS THE

926
00:31:38,630 --> 00:31:40,398
REFERENCE GROUP.

927
00:31:40,465 --> 00:31:42,267
AND SO, WE SEE TWO ROWS

928
00:31:42,333 --> 00:31:45,036
ACCOUNTED FOR HERE FOR ST SLOPE,

929
00:31:45,103 --> 00:31:46,404
THE DOWNSLOPE AND UPSLOPING

930
00:31:46,471 --> 00:31:50,208
GROUP, THE REFERENCE IN THIS

931
00:31:50,275 --> 00:31:52,043
CASE WOULD BE FLAT.

932
00:31:52,110 --> 00:31:53,811
FASTING BLOOD SUGAR TRUE THAT

933
00:31:53,878 --> 00:31:56,547
MEANS IT IS GREATER THAN 120,

934
00:31:56,614 --> 00:31:58,583
THE REFERENCE LEVEL IS 120.

935
00:31:58,650 --> 00:32:00,852
AND AGAIN, FOR AGE AND

936
00:32:00,918 --> 00:32:02,020
CHOLESTEROL, THE -- THE

937
00:32:02,086 --> 00:32:04,555
REFERENCE REALLY IS ZERO.

938
00:32:04,622 --> 00:32:05,757
AS FAR AS THAT.

939
00:32:05,823 --> 00:32:07,892
AND BOTH OF THESE ARE NOT

940
00:32:07,959 --> 00:32:09,227
CENTERED.

941
00:32:09,294 --> 00:32:12,563
IN THIS MODEL.

942
00:32:12,630 --> 00:32:14,565
AND WE CAN WRITE OUT THIS

943
00:32:14,632 --> 00:32:16,401
EQUATION IN A -- SIMILAR WAY

944
00:32:16,467 --> 00:32:17,502
THAT WE WOULD WRITE OUT OUR

945
00:32:17,568 --> 00:32:19,737
SIMPLE EQUATION THAT WE LOOKED

946
00:32:19,804 --> 00:32:20,538
AT.

947
00:32:20,605 --> 00:32:22,440
OUR BETA-0 AND BETA-1.

948
00:32:22,507 --> 00:32:24,008
WE ADD ALL OF THE OTHER

949
00:32:24,075 --> 00:32:25,743
VARIABLES IN.

950
00:32:25,810 --> 00:32:27,578
SO WE HAVE A BINARY VARIABLE

951
00:32:27,645 --> 00:32:29,380
THAT IS ATTACHED TO OUR BETA-2

952
00:32:29,447 --> 00:32:32,083
WHICH TELLS US ABOUT THE FASTING

953
00:32:32,150 --> 00:32:33,418
BLOOD SUGAR BEHAVIOR.

954
00:32:33,484 --> 00:32:35,920
WHETHER IT IS EQUAL, WHETHER OR

955
00:32:35,987 --> 00:32:39,257
NOT IT'S GREATER THAN 120.

956
00:32:39,324 --> 00:32:41,592
WE HAVE OUR CONTINUOUS

957
00:32:41,659 --> 00:32:42,794
CHOLESTEROL MEASUREMENT ATTACHED

958
00:32:42,860 --> 00:32:43,761
TO BETA-3.

959
00:32:43,828 --> 00:32:46,564
AND THEN TWO ADDITIONAL

960
00:32:46,631 --> 00:32:48,966
COEFFICIENTS WHICH ARE ATTACHED

961
00:32:49,033 --> 00:32:49,534
TO INDICATOR VARIABLES ABOUT

962
00:32:49,600 --> 00:32:51,169
WHETHER THE ST SLOPE IS DOWN

963
00:32:51,235 --> 00:32:54,706
SLOPING OR UPSLOPING.

964
00:32:54,772 --> 00:32:55,807
AND AGAIN, THE THINGS IN

965
00:32:55,873 --> 00:32:58,476
PARENTHESES HERE I'M CALLING

966
00:32:58,543 --> 00:32:59,944
THESE INDICATOR VARIABLES ARE

967
00:33:00,011 --> 00:33:02,180
THAT THAT OR THE REFERENCE?

968
00:33:02,246 --> 00:33:03,581
IF THEY ARE NOT DOWN OR UP, BOTH

969
00:33:03,648 --> 00:33:04,282
OF THESE WOULD BE ZERO.

970
00:33:04,349 --> 00:33:06,951
AND WE WOULD BE TALKING ABOUT

971
00:33:07,018 --> 00:33:10,688
THE REFERENCE WHICH IS CONTAINED

972
00:33:10,755 --> 00:33:12,757
IN THE INTERCEPT.

973
00:33:12,824 --> 00:33:14,559
SO LET'S JUST STEP THROUGH THE

974
00:33:14,625 --> 00:33:16,127
INTERPRETATION.

975
00:33:16,194 --> 00:33:17,195
SO, WHEN AGE IS ZERO, THE

976
00:33:17,261 --> 00:33:19,063
FASTING BLOOD SUGAR IS LESS THAN

977
00:33:19,130 --> 00:33:19,731
20.

978
00:33:19,797 --> 00:33:22,333
ABOUT 120, THE CHOLESTEROL IS

979
00:33:22,400 --> 00:33:22,667
ZERO.

980
00:33:22,734 --> 00:33:23,568
AND ST SLOPE IS FAST.

981
00:33:23,634 --> 00:33:28,673
THE HEART RATE IS ESTIMATED TO

982
00:33:28,740 --> 00:33:29,040
BE 178.9.

983
00:33:29,107 --> 00:33:32,009
FOR AGE, AGAIN, THIS IS SORT OF

984
00:33:32,076 --> 00:33:33,745
SIMILAR TO WHAT WE TALKED ABOUT

985
00:33:33,811 --> 00:33:33,978
BEFORE.

986
00:33:34,045 --> 00:33:36,247
BUT WE HAVE THIS ADDITIONAL

987
00:33:36,314 --> 00:33:38,316
LANGUAGE OF WHEN HOLDING ALL

988
00:33:38,383 --> 00:33:38,850
OTHER VARIABLES CONSTANT.

989
00:33:38,916 --> 00:33:41,753
SO WHEN WE LOOK AT PEOPLE WITH

990
00:33:41,819 --> 00:33:44,088
SIMILAR OTHER CHARACTERISTICS OF

991
00:33:44,155 --> 00:33:45,390
FASTING BLOOD SUGAR,

992
00:33:45,456 --> 00:33:47,492
CHOLESTEROL, AND ST SLOPE, THE

993
00:33:47,558 --> 00:33:50,762
ESTIMATED HEART RATE DECREASES,

994
00:33:50,828 --> 00:33:53,731
NEGATIVE SLOPE, BY .8649 BEATS

995
00:33:53,798 --> 00:33:56,134
PER MINUTE FOR ONE YEAR INCREASE

996
00:33:56,200 --> 00:33:58,703
IN AGE.

997
00:33:58,770 --> 00:34:01,339
AND THE INTERPRETATIONS FOLLOW

998
00:34:01,406 --> 00:34:04,075
SIMILARLY TO THAT.

999
00:34:04,142 --> 00:34:05,309
SO, THIS IS BINARY.

1000
00:34:05,376 --> 00:34:07,011
THIS FASTING BLOOD SUGAR IS

1001
00:34:07,078 --> 00:34:07,345
BINARY.

1002
00:34:07,412 --> 00:34:09,447
SO AGAIN, COMPARING FOR OUR

1003
00:34:09,514 --> 00:34:11,983
REFERENCE GROUP.

1004
00:34:12,049 --> 00:34:13,284
THE MAXIMUM HEART RATE IS 2.0059

1005
00:34:13,351 --> 00:34:18,856
BEATS PER MINUTE HIGHER IN THE

1006
00:34:18,923 --> 00:34:19,857
120-MILLIGRAM PER DECILITER

1007
00:34:19,924 --> 00:34:21,926
PATIENT, GREATER THAN, COMPARED

1008
00:34:21,993 --> 00:34:28,099
TO LESS THAN 120-MILLIGRAM PER

1009
00:34:28,166 --> 00:34:28,533
DECILITER PATIENT.

1010
00:34:28,599 --> 00:34:30,468
FOR THE CHOLESTEROL, THE

1011
00:34:30,535 --> 00:34:32,603
ESTIMATED HEART RATE INCREASES

1012
00:34:32,670 --> 00:34:35,239
BY .0343 BEATS PER MINUTE FOR

1013
00:34:35,306 --> 00:34:36,474
EVERY ONE UNIT INCREASE IN

1014
00:34:36,541 --> 00:34:36,774
CHOLESTEROL.

1015
00:34:36,841 --> 00:34:38,543
AGAIN, WE CAN ALSO LOOK AT

1016
00:34:38,609 --> 00:34:40,812
SIGNIFICANCE FOR ALL OF THESE,

1017
00:34:40,878 --> 00:34:42,513
BUT THE LAST TWO WERE NOT

1018
00:34:42,580 --> 00:34:42,814
SIGNIFICANT.

1019
00:34:42,880 --> 00:34:47,318
AND THEN WE HAVE THIS LIKE

1020
00:34:47,385 --> 00:34:48,986
THREE-LEVEL CATEGORICAL VARIABLE

1021
00:34:49,053 --> 00:34:50,521
THAT IS REPRESENTED BY TWO LINES

1022
00:34:50,588 --> 00:34:52,056
OF OUTPUT HERE.

1023
00:34:52,123 --> 00:34:54,792
WE CAN INTERPRET BOTH OF THOSE

1024
00:34:54,859 --> 00:34:55,960
IN RELATIONSHIP TO THE REFERENCE

1025
00:34:56,027 --> 00:34:57,361
GROUP OF FLAT SLOPE, FLAT ST

1026
00:34:57,428 --> 00:34:58,029
SLOPE.

1027
00:34:58,096 --> 00:35:01,732
SO THE ESTIMATED HEART RATE IS

1028
00:35:01,799 --> 00:35:04,068
ROUGHLY FIVE BEATS PER MINUTE

1029
00:35:04,135 --> 00:35:06,037
HIGHER ON AVERAGE FOR ST

1030
00:35:06,103 --> 00:35:07,505
DOWNSLOPES COMPARED TO FLAT ST.

1031
00:35:07,572 --> 00:35:08,072
THIS IS POSITIVE.

1032
00:35:08,139 --> 00:35:11,242
FOR POSITIVE CHANGE FROM THE

1033
00:35:11,309 --> 00:35:12,376
REFERENCE GROUP.

1034
00:35:12,443 --> 00:35:14,178
AND 18, ROUGHLY 18 BEATS PER

1035
00:35:14,245 --> 00:35:16,581
MINUTE HIGHER FOR ST UPSLOPES

1036
00:35:16,647 --> 00:35:17,782
COMPARED TO FLAT ST HAS THE

1037
00:35:17,849 --> 00:35:19,217
REFERENCE GROUP.

1038
00:35:19,283 --> 00:35:20,485
YOU CAN SEE THAT ACTUALLY THAT

1039
00:35:20,551 --> 00:35:21,886
CHANGES SIGNIFICANT, THAT IS

1040
00:35:21,953 --> 00:35:24,088
NOTED HERE ON THIS SLIDE.

1041
00:35:24,155 --> 00:35:26,324
WHAT WE CAN DO WHEN WE HAVE

1042
00:35:26,390 --> 00:35:28,726
VARIABLES WITH THREE OR MORE

1043
00:35:28,793 --> 00:35:34,398
LEVELS, WE CAN TALK ABOUT LIKE

1044
00:35:34,465 --> 00:35:35,867
IN THE ENOVA FRAMEWORK, IF YOU

1045
00:35:35,933 --> 00:35:38,603
WANT TO SAY, F STATISTICS OF THE

1046
00:35:38,669 --> 00:35:40,204
EFFECT OVER ALL OF THAT

1047
00:35:40,271 --> 00:35:40,471
VARIABLE.

1048
00:35:40,538 --> 00:35:42,039
THIS CAN BE A USEFUL WAY TO DO

1049
00:35:42,106 --> 00:35:43,908
SOME OF THE REPORTING OF

1050
00:35:43,975 --> 00:35:45,576
VARIABLES THAT HAVE MULTIPLE

1051
00:35:45,643 --> 00:35:46,310
LEVELS.

1052
00:35:46,377 --> 00:35:50,915
BECAUSE NOW, WE CAN SAY THAT ST

1053
00:35:50,982 --> 00:35:53,384
SLOPE OVERALL, WHICH IS TWO

1054
00:35:53,451 --> 00:35:54,085
DEGREES OF FREEDOM, THREE

1055
00:35:54,151 --> 00:35:55,953
LETHES, IS SIGNIFICANT, WHAT WE

1056
00:35:56,020 --> 00:36:00,091
CAN DO IS, IF WE WANTED ALL

1057
00:36:00,157 --> 00:36:03,661
PAIRWISE COMPARISONS OR IF WE

1058
00:36:03,728 --> 00:36:05,062
STEP ASIDE TO DO PAIRWISE

1059
00:36:05,129 --> 00:36:07,632
COMPARISONS BETWEEN EACH OF

1060
00:36:07,698 --> 00:36:09,000
THESE LEVELS, PERHAPS WE SET UP

1061
00:36:09,066 --> 00:36:10,568
THE REGRESSION IS SUCH THAT WE

1062
00:36:10,635 --> 00:36:12,403
ARE ONLY CARE ABOUT COMP PEERING

1063
00:36:12,470 --> 00:36:14,005
EACH OF THESE TWO FLAT ST SLOPES

1064
00:36:14,071 --> 00:36:15,706
IN THE WAY THAT I ALREADY

1065
00:36:15,773 --> 00:36:16,541
SPECIFIED IT.

1066
00:36:16,607 --> 00:36:18,075
MAYBE WE ALSO JUST WANT TO

1067
00:36:18,142 --> 00:36:18,576
REPORT THIS ONE.

1068
00:36:18,643 --> 00:36:20,077
DEPENDING ON WHAT YOUR GOALS

1069
00:36:20,144 --> 00:36:26,984
ARE, YOU CAN DO IT EITHER WAY.

1070
00:36:27,051 --> 00:36:29,287
AND FOR LAST EXAMPLE I WANT TO

1071
00:36:29,353 --> 00:36:30,087
TALK ABOUT, AGAIN, KIND OF

1072
00:36:30,154 --> 00:36:33,057
GETTING BACK TO A SMALLER MODEL,

1073
00:36:33,124 --> 00:36:36,093
BUT ADDING COMPLEXITY IN TERMS

1074
00:36:36,160 --> 00:36:36,694
OF ADDING AN INTERACTION TERM,

1075
00:36:36,761 --> 00:36:38,963
WHAT WE CAN ASK OF A MODEL, TOO,

1076
00:36:39,030 --> 00:36:40,064
IS THERE A DIFFERENT

1077
00:36:40,131 --> 00:36:42,533
RELATIONSHIP BETWEEN AGE AND

1078
00:36:42,600 --> 00:36:43,301
HEART RATE DEPENDING ON WHETHER

1079
00:36:43,367 --> 00:36:44,235
THE INDIVIDUAL HAS HEART

1080
00:36:44,302 --> 00:36:44,602
DISEASE.

1081
00:36:44,669 --> 00:36:47,972
SO I PUT THE GRAPHS HERE,

1082
00:36:48,039 --> 00:36:48,673
GRAPHED SEPARATELY BY HEART

1083
00:36:48,739 --> 00:36:50,841
DISEASE STATUS FOR THE

1084
00:36:50,908 --> 00:36:51,142
INDIVIDUAL.

1085
00:36:51,208 --> 00:36:52,677
AND AGAIN, DOING AN INDIVIDUAL

1086
00:36:52,743 --> 00:36:53,311
INSPECTOR TO SEE WHAT IS GOING

1087
00:36:53,377 --> 00:36:55,646
ON AND WHETHER WE HAVE BEHAVIOR

1088
00:36:55,713 --> 00:36:58,950
THAT IS EASILY EXPLAINABLE BY A

1089
00:36:59,016 --> 00:36:59,250
REGRESSION.

1090
00:36:59,317 --> 00:37:01,586
WE WRITE THE MODEL AS FOLLOWS.

1091
00:37:01,652 --> 00:37:04,355
SO WE HAVE THE INTERCEPT AS

1092
00:37:04,422 --> 00:37:06,123
BETA-0, OR BETA-1 AGE.

1093
00:37:06,190 --> 00:37:08,292
OR BETA-2, WHICH IS ATTACHED TO

1094
00:37:08,359 --> 00:37:09,126
OUR INDICATOR VARIABLE OF

1095
00:37:09,193 --> 00:37:10,861
WHETHER OR NOT A PERSON HAS

1096
00:37:10,928 --> 00:37:11,395
HEART DISEASE.

1097
00:37:11,462 --> 00:37:14,465
AND THEN OUR BETA-3, WHICH IS

1098
00:37:14,532 --> 00:37:18,603
ATTACHED TO THE INTERACTION, THE

1099
00:37:18,669 --> 00:37:19,570
INTERACTION BETWEEN THOSE TWO

1100
00:37:19,637 --> 00:37:19,804
PIECES.

1101
00:37:19,870 --> 00:37:23,040
AND I JUST WANT TO OUTLINE

1102
00:37:23,107 --> 00:37:25,009
SPECIFICALLY HOW THIS GIVES US

1103
00:37:25,076 --> 00:37:26,410
TWO DIFFERENT SLOPES.

1104
00:37:26,477 --> 00:37:29,814
SO, WE, BECAUSE OF THE WAY THAT

1105
00:37:29,880 --> 00:37:31,015
THESE INDICATOR VARIABLES BREAK

1106
00:37:31,082 --> 00:37:33,818
THE EQUATION APART, WE END UP

1107
00:37:33,884 --> 00:37:34,986
WITH TWO EQUATIONS FOR THOSE

1108
00:37:35,052 --> 00:37:35,586
WITH HEART DISEASE OR WITH OR

1109
00:37:35,653 --> 00:37:36,487
WITHOUT HEART DISEASE.

1110
00:37:36,554 --> 00:37:39,590
SO THE EQUATION FOR THOSE WITH

1111
00:37:39,657 --> 00:37:41,459
HEART DISEASE, THESE INDICATOR

1112
00:37:41,525 --> 00:37:42,059
PIECES TURN TO ONE.

1113
00:37:42,126 --> 00:37:47,131
AND SO WE HAVE BETA-0 PLUS

1114
00:37:47,198 --> 00:37:49,166
BETA-1 TIMES IN A PLUS BETA-2

1115
00:37:49,233 --> 00:37:52,069
PLUS BETA-3 TIMES IN A.

1116
00:37:52,136 --> 00:37:54,372
WE RESHUFFLE IT USING OUR

1117
00:37:54,438 --> 00:37:57,341
ALGEBRA AT, WE GET BETA-0 PLUS

1118
00:37:57,408 --> 00:37:59,777
BETA-2, PLUS BETA-1 PLUS BETA-3

1119
00:37:59,844 --> 00:38:00,611
BOTH TIMES AGE.

1120
00:38:00,678 --> 00:38:02,913
WE CAN THINK OF IT THIS AS BEING

1121
00:38:02,980 --> 00:38:04,448
OUR AGE SLOPE.

1122
00:38:04,515 --> 00:38:05,483
THE EQUATION FOR THOSE WITHOUT

1123
00:38:05,549 --> 00:38:08,352
HEART DISEASE, WE HAVE THE

1124
00:38:08,419 --> 00:38:08,686
ZEROS.

1125
00:38:08,753 --> 00:38:10,888
NOT INDICATING HEART DISEASE.

1126
00:38:10,955 --> 00:38:13,958
AND SO, BOTH BETA-2 AND BETA-3

1127
00:38:14,025 --> 00:38:16,093
DROPOUT OF THE CALCULATION.

1128
00:38:16,160 --> 00:38:18,696
SO WE'RE JUST LEFT WITH BETA-0

1129
00:38:18,763 --> 00:38:21,399
PLUS BETA-1 TIMES IN A.

1130
00:38:21,465 --> 00:38:24,068
SO HIGHLIGHTED IN RED, WE CAN

1131
00:38:24,135 --> 00:38:24,835
ACTUALLY SEE ALGEBRAICALLY, WE

1132
00:38:24,902 --> 00:38:26,637
HAVE IN THOSE WITHOUT HEART

1133
00:38:26,704 --> 00:38:27,972
DISEASE, A BETA-1 SLOPE FOR AGE.

1134
00:38:28,039 --> 00:38:29,907
AND THOSE WITH HEART DISEASE, WE

1135
00:38:29,974 --> 00:38:32,410
HAVE BETA-1 PLUS SOME OTHER UNIT

1136
00:38:32,476 --> 00:38:33,444
TO DESCRIBE THE CHANGE IN THE

1137
00:38:33,511 --> 00:38:35,746
SLOPE FOR THOSE WHO HAVE HEART

1138
00:38:35,813 --> 00:38:35,980
DISEASE.

1139
00:38:36,047 --> 00:38:38,783
SO THAT'S, THAT'S HOW WE DO IT

1140
00:38:38,849 --> 00:38:40,217
MATHEMATICALLY, THAT IS HOW IT

1141
00:38:40,284 --> 00:38:42,887
WILL APPEAR IN THE OUTPUT.

1142
00:38:42,953 --> 00:38:45,222
WE HAVE BETA-0, BETA-1, BETA-2,

1143
00:38:45,289 --> 00:38:47,658
BETA-3 FOR EACH IN THE ROWS OF

1144
00:38:47,725 --> 00:38:49,994
THE OUTPUT.

1145
00:38:50,061 --> 00:38:50,928
IN R THE INTERACTION TERM IS

1146
00:38:50,995 --> 00:38:52,196
NOTE WOULD THIS LITTLE COLON

1147
00:38:52,263 --> 00:38:53,664
SEPARATING THE TWO VARIABLES.

1148
00:38:53,731 --> 00:38:55,599
AGAIN, THIS MIGHT VARY DEPENDING

1149
00:38:55,666 --> 00:38:56,834
ON YOUR SOFTWARE AND BOTH OF THE

1150
00:38:56,901 --> 00:38:58,936
MAIN EFFECTS.

1151
00:38:59,003 --> 00:39:01,005
WE CAN SEE THE INTERACTION TERM

1152
00:39:01,072 --> 00:39:04,008
IS SIGNIFICANT HERE IN THAT EACH

1153
00:39:04,075 --> 00:39:05,309
GROUP IS WELL ESTIMATE TODAY

1154
00:39:05,376 --> 00:39:07,478
HAVE THEIR OWN SLOPE.

1155
00:39:07,545 --> 00:39:09,647
THIS IS A BENEFICIAL ESTIMATION

1156
00:39:09,714 --> 00:39:10,014
TO DO.

1157
00:39:10,081 --> 00:39:12,983
THAT'S A CHANGE IN THE SLOPE

1158
00:39:13,050 --> 00:39:15,119
BETWEEN GROUPS IS .6 9-1-1 BEATS

1159
00:39:15,186 --> 00:39:16,120
PER MINUTE PER YEAR.

1160
00:39:16,187 --> 00:39:18,756
YOU CAN SEE IT VISUALLY HERE.

1161
00:39:18,823 --> 00:39:21,392
THAT, THAT THE SLOPE IS LESS

1162
00:39:21,459 --> 00:39:23,360
NEGATIVE IN THOSE WITH HEART

1163
00:39:23,427 --> 00:39:24,161
DISEASE THAT ACTUALLY THE

1164
00:39:24,228 --> 00:39:25,496
ESTIMATION OF THE SLOPE IS MORE

1165
00:39:25,563 --> 00:39:27,898
POSITIVE IN THOSE WITH HEART

1166
00:39:27,965 --> 00:39:31,736
DISEASE COMPARED TO NO HEART

1167
00:39:31,802 --> 00:39:32,036
DISEASE.

1168
00:39:32,103 --> 00:39:35,539
SO AGAIN, JUST TO BE SPECIFIC,

1169
00:39:35,606 --> 00:39:36,107
IN INDIVIDUALS WITHOUT HEART

1170
00:39:36,173 --> 00:39:37,942
DISEASE, THE MAXIMUM HEART RATE

1171
00:39:38,008 --> 00:39:42,713
ACHIEVED IS ETC. MATED TO BE

1172
00:39:42,780 --> 00:39:42,947
1.0525.

1173
00:39:43,013 --> 00:39:44,682
THIS BETA-1 HERE, LOWER FOR

1174
00:39:44,749 --> 00:39:45,783
EVERY YEAR INCREASE WITH AGE.

1175
00:39:45,850 --> 00:39:48,085
EVERY YEAR INCREASE IN AGE.

1176
00:39:48,152 --> 00:39:49,420
AND INDIVIDUALS WITH HEART

1177
00:39:49,487 --> 00:39:52,089
DISEASE, AGAIN, WE HAVE THIS

1178
00:39:52,156 --> 00:39:56,127
BETA-1 PLUS BETA-3, TO GET OUR

1179
00:39:56,193 --> 00:39:59,663
NEW ESTIMATED SLOPE, AND THIS

1180
00:39:59,730 --> 00:40:01,599
SLOPE IS NEGATIVE .3614 BEATS

1181
00:40:01,665 --> 00:40:04,535
PER MINUTE PER YEAR INCREASE IN

1182
00:40:04,602 --> 00:40:04,969
AGE.

1183
00:40:05,035 --> 00:40:08,339
SO, AGAIN, JUST FORMALIZING IT

1184
00:40:08,405 --> 00:40:08,806
HERE.

1185
00:40:08,873 --> 00:40:11,909
AND IN SOME SOFTWARE AND IN R,

1186
00:40:11,976 --> 00:40:13,644
YOU CAN ACTUALLY ASK THE

1187
00:40:13,711 --> 00:40:15,446
SOFTWARE TO GIVE YOU THESE

1188
00:40:15,513 --> 00:40:17,081
NUMBERS SPECIFICALLY SO YOU

1189
00:40:17,148 --> 00:40:19,083
DON'T HAVE TO CALCULATE IT.

1190
00:40:19,150 --> 00:40:21,185
WITH THIS COMES THE CONVENIENCE

1191
00:40:21,252 --> 00:40:22,052
OF ACTUALLY HAVE A SIGNIFICANT

1192
00:40:22,119 --> 00:40:24,088
TEST FOR EACH SLOPE.

1193
00:40:24,155 --> 00:40:25,022
SO HERE FORMALLY, WE CAN SEE

1194
00:40:25,089 --> 00:40:27,725
THAT THE NO HEART DISEASE GROUP

1195
00:40:27,792 --> 00:40:29,426
STILL DOES HAVE THIS STIG TIFF

1196
00:40:29,493 --> 00:40:30,027
ACCIDENT LATE NEGATIVE

1197
00:40:30,094 --> 00:40:30,728
RELATIONSHIP WITH HANE AND HEART

1198
00:40:30,795 --> 00:40:31,328
RATE.

1199
00:40:31,395 --> 00:40:35,099
AND IN THE HEART DISEASE GROUP,

1200
00:40:35,166 --> 00:40:36,967
WHILE ALSO, WHILE BEING

1201
00:40:37,034 --> 00:40:39,270
DIFFERENT IT ALSO IS, NOT

1202
00:40:39,336 --> 00:40:40,571
SIGNIFICANTLY DIFFERENT FROM

1203
00:40:40,638 --> 00:40:40,771
ZERO.

1204
00:40:40,838 --> 00:40:44,074
SO THEY'RE IN THE HEART DISEASE

1205
00:40:44,141 --> 00:40:44,909
GROUP, THIS NEGATIVE SLOPE IS

1206
00:40:44,975 --> 00:40:46,410
ACTUALLY NOT STATISTICAL

1207
00:40:46,477 --> 00:40:48,279
SIGNIFICANT FROM THE ZERO.

1208
00:40:48,345 --> 00:40:50,047
SO, THIS CAN BE A HELPFUL WAY TO

1209
00:40:50,114 --> 00:40:54,451
FRAME THE RESULTS AS WELL.

1210
00:40:54,518 --> 00:40:57,454
SO, I JUST WANTED TO WALK

1211
00:40:57,521 --> 00:40:59,223
THROUGH A COUPLE LIKE MODEL

1212
00:40:59,290 --> 00:41:01,025
BUILDING FRAMEWORK OR POSSIBLE

1213
00:41:01,091 --> 00:41:02,827
ISSUES THAT MAY COME UP TO THINK

1214
00:41:02,893 --> 00:41:06,463
ABOUT WHILE YOU BUILD YOUR

1215
00:41:06,530 --> 00:41:06,697
MODELS.

1216
00:41:06,764 --> 00:41:08,999
SO, WE OBVIOUSLY RAN THROUGH A

1217
00:41:09,066 --> 00:41:11,635
BUNCH OF EXAMPLES, IT CAN BE

1218
00:41:11,702 --> 00:41:12,703
KIND OF OVERWHELMING TO THINK

1219
00:41:12,770 --> 00:41:13,938
ABOUT HOW TO BUILD A MODEL.

1220
00:41:14,004 --> 00:41:15,573
I THINK IT IS REALLY IMPORTANT

1221
00:41:15,639 --> 00:41:16,907
TO LOOK AT YOUR KEY QUESTION OF

1222
00:41:16,974 --> 00:41:17,174
INTEREST.

1223
00:41:17,241 --> 00:41:18,943
BE VERY CLEAR ABOUT THAT IN

1224
00:41:19,009 --> 00:41:20,444
TERMS OF WHAT YOUR OUTCOME

1225
00:41:20,511 --> 00:41:22,847
MEASURE IS.

1226
00:41:22,913 --> 00:41:24,315
DO WE HAVE A KEY PREDICTOR

1227
00:41:24,381 --> 00:41:27,451
VARIABLE OF INTEREST?

1228
00:41:27,518 --> 00:41:28,586
DO WE HAVE ANY CONFOUNDING

1229
00:41:28,652 --> 00:41:31,222
VARIABLES THAT WE KNOW FROM THE

1230
00:41:31,288 --> 00:41:32,223
LITERATURE OR PRIOR RESEARCH

1231
00:41:32,289 --> 00:41:33,591
THAT WE DEFINITELY WANT TO

1232
00:41:33,657 --> 00:41:33,824
INCLUDE?

1233
00:41:33,891 --> 00:41:34,925
THINKING ABOUT ALL OF THOSE

1234
00:41:34,992 --> 00:41:37,127
THINGS IN ADVANCE ARE GOING TO

1235
00:41:37,194 --> 00:41:40,097
BE HELPFUL TO HELP TARGET YOUR

1236
00:41:40,164 --> 00:41:43,200
BUILDING OF THE MODEL.

1237
00:41:43,267 --> 00:41:46,437
YOU SHOULD ASK ARE WE INCLUDING

1238
00:41:46,503 --> 00:41:47,905
ALL RELEVANT VARIABLES AND

1239
00:41:47,972 --> 00:41:50,207
LEANING ON THE LITERATURE

1240
00:41:50,274 --> 00:41:51,508
PERHAPS AND THE UNDERSTANDING OF

1241
00:41:51,575 --> 00:41:52,877
WHAT IS RELATED TO YOUR OUTCOME

1242
00:41:52,943 --> 00:41:55,179
OF INTEREST.

1243
00:41:55,246 --> 00:41:58,949
AND MORE IMPORTANTLY, ARE WE

1244
00:41:59,016 --> 00:41:59,483
COMPARING VARIABLE

1245
00:41:59,550 --> 00:41:59,884
INTERRELATEDNESS.

1246
00:41:59,950 --> 00:42:01,051
WE CAN CAUSE ISSUE WITH MODEL

1247
00:42:01,118 --> 00:42:03,354
FIT WHEN WE HAVE A BUNCH OF X

1248
00:42:03,420 --> 00:42:05,256
VARIABLES THAT ARE ALL HIGHLY

1249
00:42:05,322 --> 00:42:06,357
CORRELATED WITH EACH OTHER.

1250
00:42:06,423 --> 00:42:08,292
WE DEFINITELY WANT TO MAKE SURE

1251
00:42:08,359 --> 00:42:10,861
THAT WE'RE AVOIDING ANY ISSUES

1252
00:42:10,928 --> 00:42:11,695
ANY OF OUR INDEPENDENT VARIABLES

1253
00:42:11,762 --> 00:42:14,798
BEING TOO HIGHLY CORRELATED OR

1254
00:42:14,865 --> 00:42:16,300
PERHAPS EVEN EXACTLY CORRELATED

1255
00:42:16,367 --> 00:42:18,302
IN WHICH WE WOULD HAVE ISSUES

1256
00:42:18,369 --> 00:42:19,536
WITH MODEL CONVERGENCE, THE

1257
00:42:19,603 --> 00:42:20,537
MODEL WANT RUN, OR ESTIMATE

1258
00:42:20,604 --> 00:42:22,072
THOSE ASPECTS OF THE MODEL.

1259
00:42:22,139 --> 00:42:24,275
THOSE ARE ALSO THINGS TO

1260
00:42:24,341 --> 00:42:24,541
CONSIDER.

1261
00:42:24,608 --> 00:42:27,144
FOR SCENARIO WHERE WE DO HAVE A

1262
00:42:27,211 --> 00:42:29,213
COMPLEX SET OF VARIABLES OR A

1263
00:42:29,280 --> 00:42:30,347
LOT OF VARIABLES, WE CAN

1264
00:42:30,414 --> 00:42:33,083
CONSIDER THINGS SUCH AS STEPWISE

1265
00:42:33,150 --> 00:42:36,453
REGRESSION OR OTHER SORTS OF

1266
00:42:36,520 --> 00:42:37,955
VARIABLE SELECTION TECHNIQUES TO

1267
00:42:38,022 --> 00:42:38,322
BUILD THE MODEL.

1268
00:42:38,389 --> 00:42:40,224
I WOULD SAY MOST OF THE TIME, WE

1269
00:42:40,291 --> 00:42:41,425
DO WANT A LITTLE BIT MORE

1270
00:42:41,492 --> 00:42:42,993
CONTROL OVER THE VARIABLES THAT

1271
00:42:43,060 --> 00:42:43,694
WE INCLUDE.

1272
00:42:43,761 --> 00:42:45,229
SO I WOULD SAY MOST CASES THAT

1273
00:42:45,296 --> 00:42:49,066
MIGHT BE KIND OF A LAST RESORT.

1274
00:42:49,133 --> 00:42:50,901
YOU, I THINK, IN MOST CASES WE

1275
00:42:50,968 --> 00:42:53,037
KNOW WHAT VARIABLES WE WANT TO

1276
00:42:53,103 --> 00:42:55,072
INCLUDE AND PERHAPS WE'RE ONLY

1277
00:42:55,139 --> 00:42:56,073
LIMITED BY SAMPLE SIZE IN TERMS

1278
00:42:56,140 --> 00:42:58,208
OF BEING ABLE TO HAVE A BIGGER

1279
00:42:58,275 --> 00:42:59,777
MODEL.

1280
00:42:59,843 --> 00:43:01,145
YOU CAN GO THROUGHERTERATIONS OF

1281
00:43:01,211 --> 00:43:04,048
MODEL BUILDING WITHIN REASON TO

1282
00:43:04,114 --> 00:43:05,516
EXPLORE MODEL FIT AND FINE-TUNE

1283
00:43:05,582 --> 00:43:06,216
WHAT VARIABLES YOU WANT TO

1284
00:43:06,283 --> 00:43:07,251
INCLUDE.

1285
00:43:07,318 --> 00:43:12,890
I THINK MOST OF THE WITH ERK

1286
00:43:12,957 --> 00:43:16,994
THAT WE DO IN NIMs AS FAR AS

1287
00:43:17,061 --> 00:43:18,862
REGRESSION IS CONCERNED, WHEN WE

1288
00:43:18,929 --> 00:43:21,765
GET TO THAT POINT, WE'RE TALKING

1289
00:43:21,832 --> 00:43:22,333
ABOUT EXPLORATORY ANALYSIS.

1290
00:43:22,399 --> 00:43:23,167
IF YOU FEEL YOU ARE ABLE TO LOOK

1291
00:43:23,233 --> 00:43:25,869
AT THE DATA AND THING ABOUT THE

1292
00:43:25,936 --> 00:43:26,070
MODEL.

1293
00:43:26,136 --> 00:43:29,206
I THINK THE KEY HERE IS THAT BE

1294
00:43:29,273 --> 00:43:29,873
MINDFUL THAT YOU SHOULD PROBABLY

1295
00:43:29,940 --> 00:43:32,576
STILL BE REPORTING ALL OF WHAT

1296
00:43:32,643 --> 00:43:34,178
YOU'RE INVESTIGATING, YOU KNOW

1297
00:43:34,244 --> 00:43:35,980
AT THE BOTTOM, IN TERMS OF THE

1298
00:43:36,046 --> 00:43:37,648
THINGS THAT YOU TRIED.

1299
00:43:37,715 --> 00:43:39,016
THE ISSUES THAT YOU RAN INTO.

1300
00:43:39,083 --> 00:43:41,485
WHY YOU INCLUDED VARIABLES AND

1301
00:43:41,552 --> 00:43:42,019
NOT OTHERS.

1302
00:43:42,086 --> 00:43:43,487
THE FIRST MODEL THAT YOU

1303
00:43:43,554 --> 00:43:45,489
SPECIFIED OR THE 50th.

1304
00:43:45,556 --> 00:43:47,024
SO BE MINDFUL THAT YOU DO WANT

1305
00:43:47,091 --> 00:43:49,393
TO SPEAK TO SOME OF THAT AS

1306
00:43:49,460 --> 00:43:49,693
WELL.

1307
00:43:49,760 --> 00:43:51,295
AS FAR AS PUBLISHING RESULTS AND

1308
00:43:51,362 --> 00:43:54,164
COMING UP WITH THE FINAL MODEL.

1309
00:43:54,231 --> 00:43:56,133
AND WE ALSO NEED TO THINK ABOUT

1310
00:43:56,200 --> 00:43:57,668
WHAT OUR SAMPLE SIZE IS AND HOW

1311
00:43:57,735 --> 00:44:00,004
MANY VARIABLES WE CAN INCLUDE.

1312
00:44:00,070 --> 00:44:01,071
THERE ARE VARIETY OF RULES OF

1313
00:44:01,138 --> 00:44:01,872
SUM FOR THIS.

1314
00:44:01,939 --> 00:44:04,074
JUST BE MINDFUL, IF YOU DON'T

1315
00:44:04,141 --> 00:44:05,142
HAVE A HUGE SAMPLE SIZE, YOU

1316
00:44:05,209 --> 00:44:06,744
CAN'T RUN A HUGE MODEL.

1317
00:44:06,810 --> 00:44:10,514
AND EVERY VARIABLE YOU ADD IS

1318
00:44:10,581 --> 00:44:11,815
GOING TO PULL POWER AND IF WE

1319
00:44:11,882 --> 00:44:13,450
DON'T HAVE ENOUGH PEOPLE TO WELL

1320
00:44:13,517 --> 00:44:13,717
ESTIMATE?

1321
00:44:13,784 --> 00:44:16,086
OF THESE THINGS, IT CAN BE

1322
00:44:16,153 --> 00:44:19,089
DIFFICULT TO HAVE A WELL-BEHAVED

1323
00:44:19,156 --> 00:44:19,656
MODEL.

1324
00:44:19,723 --> 00:44:21,358
SHOW JUST BE MINDFUL, WE CANNOT

1325
00:44:21,425 --> 00:44:22,693
RUN MODELS WITH 20 VARIABLES

1326
00:44:22,760 --> 00:44:28,165
WHEN WE HAVE 20 PEOPLE TO BE

1327
00:44:28,232 --> 00:44:29,233
DRAMATIC HERE.

1328
00:44:29,299 --> 00:44:32,169
SO LET'S QUICKLY GO THROUGH SOME

1329
00:44:32,236 --> 00:44:34,071
RESULTS REPORTING FOR EACH OF

1330
00:44:34,138 --> 00:44:34,405
THE EXAMPLES.

1331
00:44:34,471 --> 00:44:36,240
I WANT TO DO THIS.

1332
00:44:36,306 --> 00:44:38,475
WE TALKED ABOUT THE WAYS THAT WE

1333
00:44:38,542 --> 00:44:39,877
CAN SAY SOME OF THESE THINGS,

1334
00:44:39,943 --> 00:44:41,912
BUT I JUST WANT TO BE SPECIFIC

1335
00:44:41,979 --> 00:44:43,514
HOW WE WOULD WRITE THEM.

1336
00:44:43,580 --> 00:44:44,615
I THINK SOMETIMES PEOPLE

1337
00:44:44,681 --> 00:44:45,416
STRUGGLE WITH THIS PART.

1338
00:44:45,482 --> 00:44:48,085
AND AGAIN, SO JUST GOING BACK TO

1339
00:44:48,152 --> 00:44:48,986
THE PREVIOUS EXAMPLE.

1340
00:44:49,053 --> 00:44:50,721
THIS IS OUR SIMPLE LINEAR

1341
00:44:50,788 --> 00:44:51,688
REGRESSION EXAMPLE, WHERE WE HAD

1342
00:44:51,755 --> 00:44:53,157
JUST AGE AND HEART RATE.

1343
00:44:53,223 --> 00:44:54,758
AND HERE ARE OUR LITTLE FIGURES

1344
00:44:54,825 --> 00:44:55,492
FOR THIS.

1345
00:44:55,559 --> 00:44:59,797
SO IN THE METHODS WE CAN WRITE

1346
00:44:59,863 --> 00:45:01,065
SOMETHING LIKE:  A SIMPLE LINEAR

1347
00:45:01,131 --> 00:45:02,299
REGRESSION WAS PERFORMED TO

1348
00:45:02,366 --> 00:45:03,667
INVESTIGATE THE RELATIONSHIP

1349
00:45:03,734 --> 00:45:05,369
BETWEEN HANE IN YEARS AND THE

1350
00:45:05,436 --> 00:45:07,171
MAXIMUM HEART RATE ACHIEVED BY

1351
00:45:07,237 --> 00:45:09,573
THE PATIENT IN BEATS PER MINUTE

1352
00:45:09,640 --> 00:45:12,242
HERE ACTUALLY.

1353
00:45:12,309 --> 00:45:14,178
MODEL CHECKING WAS PREFORMED TO

1354
00:45:14,244 --> 00:45:14,878
CHECK RESIDUAL BEHAVIOR.

1355
00:45:14,945 --> 00:45:18,282
LINEAR REGRESSION IN THE RESULTS

1356
00:45:18,348 --> 00:45:19,516
SESSION, YOU CAN WRITE SOMETHING

1357
00:45:19,583 --> 00:45:21,218
LIKE LINEAR REGRESSION SHOWS

1358
00:45:21,285 --> 00:45:22,152
THAT AGE WAS SIGNIFICANTLY

1359
00:45:22,219 --> 00:45:25,756
RELATED TO PLAQUE MEMO HEART

1360
00:45:25,823 --> 00:45:28,092
RATE ACHIEVED WITH A DECLINE OF

1361
00:45:28,158 --> 00:45:31,228
ONE HEART RATE PER MINUTE WITH

1362
00:45:31,295 --> 00:45:33,664
AGE, P LESS THAN 0.001.

1363
00:45:33,730 --> 00:45:36,767
INVESTIGATES OF RESIDUAL

1364
00:45:36,834 --> 00:45:37,301
DISTRIBUTION AND BEHAVIOR,

1365
00:45:37,367 --> 00:45:39,670
INDICATED AT A RELATIVE LENORMAL

1366
00:45:39,736 --> 00:45:40,003
DISTRIBUTION.

1367
00:45:40,070 --> 00:45:41,305
O, AGAIN, I WOULD SAY THAT WE

1368
00:45:41,371 --> 00:45:43,307
VERY RARELY SEE THIS SORT OF

1369
00:45:43,373 --> 00:45:44,108
THING WRITTEN IN PAPERS.

1370
00:45:44,174 --> 00:45:46,376
I DON'T THINK IT IS A BAD THING.

1371
00:45:46,443 --> 00:45:48,078
I THINK YOU SHOULD PROBABLY BE

1372
00:45:48,145 --> 00:45:48,612
DOING IT.

1373
00:45:48,679 --> 00:45:51,215
YOU SHOULD BE INVESTIGATING

1374
00:45:51,281 --> 00:45:53,884
MODEL FIT, BUT YOU WON'T ALWAYS

1375
00:45:53,951 --> 00:45:54,518
BE SPECIFICALLY STATED THAT WAS

1376
00:45:54,585 --> 00:45:55,652
DONE HERE.

1377
00:45:55,719 --> 00:45:57,254
I WOULD SAY, ESPECIALLY WHEN IT

1378
00:45:57,321 --> 00:46:00,624
IS INTUITIVE TO DO SO,

1379
00:46:00,691 --> 00:46:01,291
PRESENTATION MIGHT BE HELPFUL.

1380
00:46:01,358 --> 00:46:02,359
IF THE MODEL IS LONG, WHICH IN

1381
00:46:02,426 --> 00:46:04,628
THIS CASE IT IS NOT, YOU CAN

1382
00:46:04,695 --> 00:46:06,063
ALSO INCLUDE A TABLE OF THE

1383
00:46:06,130 --> 00:46:07,364
ESTIMATES AND THE STANDARD

1384
00:46:07,431 --> 00:46:09,933
ERRORS AND REFER TO IT, VERSUS

1385
00:46:10,000 --> 00:46:11,368
IT ALL WRITTEN OUT IN TEXT.

1386
00:46:11,435 --> 00:46:13,170
BUT WE WILL GET TO THAT, TOO.

1387
00:46:13,237 --> 00:46:15,739
BUT IN SOME CASES A FIGURE MAY

1388
00:46:15,806 --> 00:46:19,143
ALSO BE HELPFUL WITH THE MODEL

1389
00:46:19,209 --> 00:46:19,910
FIT ATTACHED.

1390
00:46:19,977 --> 00:46:22,613
AND AGAIN, HERE I'M SHOWING THE

1391
00:46:22,679 --> 00:46:25,149
ESTIMATE AND ERROR.

1392
00:46:25,215 --> 00:46:26,350
YOU CAN ALSO SHOW CONFIDENCE

1393
00:46:26,416 --> 00:46:27,217
INTERVALS IF YOU LIKE.

1394
00:46:27,284 --> 00:46:29,386
BUT SOME MEASURE OF VARIABLES.

1395
00:46:29,453 --> 00:46:31,155
AND CONFIDENCE INTERVALS CAN BE

1396
00:46:31,221 --> 00:46:34,191
EXTRACTED FROM THIS DATA.

1397
00:46:34,258 --> 00:46:38,228
SO IN OUR ADDED COVARIANT

1398
00:46:38,295 --> 00:46:40,264
EXAMPLE, WE HAVE MORE COVARIANTS

1399
00:46:40,330 --> 00:46:43,233
TO TALK ABOUT, WE WOULD

1400
00:46:43,300 --> 00:46:46,170
ENUMERATE ALL OF THOSE THINGS IN

1401
00:46:46,236 --> 00:46:47,771
THE METHOD, A LINEAR REGRESSION

1402
00:46:47,838 --> 00:46:48,906
WAS PREFORMED TO LOOK AT THE AGE

1403
00:46:48,972 --> 00:46:52,075
IN YEARS AND THE MAXIMUM HEART

1404
00:46:52,142 --> 00:46:54,444
RATE BY PATIENTS, OIDATIONAL

1405
00:46:54,511 --> 00:46:56,313
COVARIANCES WERE FASTING BLOOD

1406
00:46:56,380 --> 00:46:58,615
SUGAR, AND GREATER OR LESS THAN

1407
00:46:58,682 --> 00:47:01,018
120 MILLIGRAMS PER DECILITER.

1408
00:47:01,084 --> 00:47:02,252
AND CHOLESTEROL, CONTINUOUS.

1409
00:47:02,319 --> 00:47:04,254
I GUESS, THAT WOULD BE IMPLIED

1410
00:47:04,321 --> 00:47:09,660
BY THE WAY I WROTE THAT.

1411
00:47:09,726 --> 00:47:11,895
AND ST SLOPE TYPE.

1412
00:47:11,962 --> 00:47:15,732
, AND MODEL CHECK S WAS FORMED.

1413
00:47:15,799 --> 00:47:17,734
I DIDN'T  SHOW THAT ON THE

1414
00:47:17,801 --> 00:47:19,169
PRESENTATION, BUT I DID IT.

1415
00:47:19,236 --> 00:47:21,238
SO IN THE RESULTS WE WOULD WRITE

1416
00:47:21,305 --> 00:47:22,239
LINEAR REGRESSION SHOWED THAT

1417
00:47:22,306 --> 00:47:23,807
AFTER CONTROLLING FOR OTHER

1418
00:47:23,874 --> 00:47:26,777
VARIABLES THE HANE WAS

1419
00:47:26,843 --> 00:47:30,747
SIGNIFICANTLY RELATE TO MAXIMUM

1420
00:47:30,814 --> 00:47:31,848
HEART RATE ACHIEVED WITH DECLINE

1421
00:47:31,915 --> 00:47:36,086
OF .86, NEGATIVE SCHLEP,

1422
00:47:36,153 --> 00:47:37,254
STANDARD ERROR INCLUDED, FOR

1423
00:47:37,321 --> 00:47:39,223
EVERY YEAR IN PATIENT AGE.

1424
00:47:39,289 --> 00:47:40,324
ST SLOPE WAS SIGNIFICANTLY

1425
00:47:40,390 --> 00:47:41,992
RELATED TO HEART RATE.

1426
00:47:42,059 --> 00:47:46,129
THIS IS WHERE I'M PULLING IN THE

1427
00:47:46,196 --> 00:47:51,168
OTHER TABLE THAT I SHOWED.

1428
00:47:51,235 --> 00:47:52,869
IT MAKES IT NICER TO WRITE.

1429
00:47:52,936 --> 00:47:54,071
SO ST SLOPE WAS RELATED TO THE

1430
00:47:54,137 --> 00:47:55,405
HEART RATE.

1431
00:47:55,472 --> 00:47:57,507
AND THEN, WE CAN GO ON TO SAY,

1432
00:47:57,574 --> 00:48:02,813
SPECIFICALLY PATIENTS WITH AN

1433
00:48:02,879 --> 00:48:03,947
UPSLOPING ST SEGMENT SHOWED 18.8

1434
00:48:04,014 --> 00:48:05,882
BEATS HIGHER HEART RATE, FROM

1435
00:48:05,949 --> 00:48:07,818
THIS GUY, THEN THOSE WITH FLAT

1436
00:48:07,884 --> 00:48:09,152
SEGMENTS ON AVERAGE.

1437
00:48:09,219 --> 00:48:10,220
AND, AGAIN, INCLUDING THE

1438
00:48:10,287 --> 00:48:12,823
STANDARD ERROR.

1439
00:48:12,889 --> 00:48:14,958
AND THE P-VALUE.

1440
00:48:15,025 --> 00:48:17,527
SPF AND CHOLESTEROL WERE NOT

1441
00:48:17,594 --> 00:48:18,629
SIGNIFICANTLY RELATED TO HEART

1442
00:48:18,695 --> 00:48:19,329
RATE.

1443
00:48:19,396 --> 00:48:20,631
INVESTIGATIONS OF RESIDUAL

1444
00:48:20,697 --> 00:48:22,332
DISTRIBUTION AND BEHAVIOR

1445
00:48:22,399 --> 00:48:26,970
INDICATED A RELATIVELY NORMAL

1446
00:48:27,037 --> 00:48:27,404
DISTRIBUTION.

1447
00:48:27,471 --> 00:48:29,840
THEN FOR THE INTERACTION EXAMPLE

1448
00:48:29,906 --> 00:48:32,075
THAT WE RAN THROUGH, AGAIN, WE

1449
00:48:32,142 --> 00:48:33,710
WANT TO JUST BE CLEAR HOW WERE

1450
00:48:33,777 --> 00:48:35,512
SPECIFYING THE PIECES OF THE

1451
00:48:35,579 --> 00:48:36,213
MODEL AND INCLUDED THE

1452
00:48:36,280 --> 00:48:37,180
INTERACTION TERM.

1453
00:48:37,247 --> 00:48:40,884
SO WE WOULD SAY TO INVESTIGATION

1454
00:48:40,951 --> 00:48:42,586
WHETHER THIS RELATIONSHIP VARIES

1455
00:48:42,653 --> 00:48:44,321
BY HEART DISEASE DIAGNOSES AN

1456
00:48:44,388 --> 00:48:44,988
INVESTIGATION TERM FOR HEART

1457
00:48:45,055 --> 00:48:50,260
DISEASE WAS ALSO INCLUDED IN THE

1458
00:48:50,327 --> 00:48:50,460
MODEL.

1459
00:48:50,527 --> 00:48:53,997
AND WE WOULD REPORT THE RESULTS

1460
00:48:54,064 --> 00:48:54,998
AS FOLLOWS.

1461
00:48:55,065 --> 00:48:56,233
LINEAR REGRESSION SHOWED THAT

1462
00:48:56,300 --> 00:48:57,834
THE INTERACTION BETWEEN AGE AND

1463
00:48:57,901 --> 00:48:58,435
HEART DISEASE WAS SIGNIFICANT

1464
00:48:58,502 --> 00:49:00,604
FOR PREDICTING HEART RATE.

1465
00:49:00,671 --> 00:49:02,205
AND FIRST, I'M CHOOSING TO

1466
00:49:02,272 --> 00:49:03,073
REPORT THE ACTUAL ESTIMATED

1467
00:49:03,140 --> 00:49:03,573
CHANGE IN SLOPE.

1468
00:49:03,640 --> 00:49:05,676
THIS IS THE FIRST PIECE THAT

1469
00:49:05,742 --> 00:49:09,079
TELLS US THAT THE SLOPE, THE

1470
00:49:09,146 --> 00:49:09,913
INTERACTION IS SIGNIFICANT.

1471
00:49:09,980 --> 00:49:12,582
THEN I CAN SAY, SPECIFICALLY

1472
00:49:12,649 --> 00:49:14,117
WHILE INDIVIDUALS WITH HEART

1473
00:49:14,184 --> 00:49:15,686
DISEASE SHOWED NO RELATIONSHIP

1474
00:49:15,752 --> 00:49:17,888
BETWEEN AGE AND HEART RATE,

1475
00:49:17,954 --> 00:49:19,156
REPORTING THAT NONSIGNIFICANT

1476
00:49:19,222 --> 00:49:20,324
SLOPE HERE, FROM EITHER YOUR

1477
00:49:20,390 --> 00:49:21,525
CALCULATION OR THE ONE THAT YOU

1478
00:49:21,591 --> 00:49:25,095
CAN EXTRACT FROM THE SOFTWARE.

1479
00:49:25,162 --> 00:49:26,897
INDIVIDUALS WITHOUT HEART

1480
00:49:26,963 --> 00:49:29,766
DISEASE SHOWED A SIGNIFICANT

1481
00:49:29,833 --> 00:49:33,036
DECLINE OF 1.05 BEATS PER MINUTE

1482
00:49:33,103 --> 00:49:34,037
PER YEAR OF AGING.

1483
00:49:34,104 --> 00:49:36,373
AND REPORTING THAT SLOPE FOR

1484
00:49:36,440 --> 00:49:37,207
THAT GROUP.

1485
00:49:37,274 --> 00:49:39,576
SO AGAIN REPORTING EACH SLOPE

1486
00:49:39,643 --> 00:49:44,581
SECH RATTLY FOR GROUP.

1487
00:49:44,648 --> 00:49:46,383
AND INVESTIGATES SHOWED A NORMAL

1488
00:49:46,450 --> 00:49:47,751
DISTRIBUTION.

1489
00:49:47,818 --> 00:49:49,186
I WOULD SAY IN INTERACTION

1490
00:49:49,252 --> 00:49:51,254
CASES, FIGURE IS USUALLY VERY

1491
00:49:51,321 --> 00:49:52,889
USEFUL FOR HELPING PEOPLE

1492
00:49:52,956 --> 00:49:53,190
UNDERSTAND.

1493
00:49:53,256 --> 00:49:55,559
I MEAN, EVEN, I EVEN WISH I HAD

1494
00:49:55,625 --> 00:49:57,260
IT HERE, EVEN JUST TO

1495
00:49:57,327 --> 00:49:58,929
DEMONSTRATE THE SLOPES CAN BE A

1496
00:49:58,995 --> 00:50:00,097
LOT EASIER TO SEE THE DATA AND

1497
00:50:00,163 --> 00:50:01,965
UNDERSTAND WHAT WE'RE TALKING

1498
00:50:02,032 --> 00:50:02,399
ABOUT.

1499
00:50:02,466 --> 00:50:04,368
THEN JUST READING THE NUMBERS.

1500
00:50:04,434 --> 00:50:06,970
SO, I WOULD ALWAYS ADVOCATE FOR

1501
00:50:07,037 --> 00:50:12,342
USING FIGURES WHEN POSSIBLE.

1502
00:50:12,409 --> 00:50:15,312
SO NOW, JUST TO WALK THROUGH

1503
00:50:15,379 --> 00:50:16,413
SOME OTHER COMMON TESTS THAT

1504
00:50:16,480 --> 00:50:18,615
HAVE A RELATIONSHIP OR HAVE

1505
00:50:18,682 --> 00:50:22,619
QUESTIONS OF RELATIONSHIPS TO

1506
00:50:22,686 --> 00:50:22,919
REGRESSION.

1507
00:50:22,986 --> 00:50:24,020
STARTING WITH CORRELATION.

1508
00:50:24,087 --> 00:50:25,922
SO THIS COMES UP A LOT WHERE

1509
00:50:25,989 --> 00:50:26,990
PEOPLE ARE CONFUSED ABOUT

1510
00:50:27,057 --> 00:50:28,558
WHETHER THEY WANT TO USE A

1511
00:50:28,625 --> 00:50:30,861
CORRELATION OR A REGRESSION.

1512
00:50:30,927 --> 00:50:32,763
SO FOR CORRELATION, WE'RE

1513
00:50:32,829 --> 00:50:33,663
PRIMARILY INTERESTED IN THE

1514
00:50:33,730 --> 00:50:35,832
STRENGTH AND DIRECTION OF THE

1515
00:50:35,899 --> 00:50:37,467
RELATIONSHIP IN A COMMINATIVE

1516
00:50:37,534 --> 00:50:39,803
WAY, NOT REALLY IN TERMS OF ONE

1517
00:50:39,870 --> 00:50:40,971
PREDICTING THE OTHER.

1518
00:50:41,037 --> 00:50:42,239
MAYBE WE JUST WANT TO KNOW IF

1519
00:50:42,305 --> 00:50:44,941
THEY ARE CORRELATED WITH EACH

1520
00:50:45,008 --> 00:50:45,142
OTHER.

1521
00:50:45,208 --> 00:50:47,611
AND AGAIN, THIS WOULD HAVE TO BE

1522
00:50:47,677 --> 00:50:49,546
BOTH VARIABLES MUST BE

1523
00:50:49,613 --> 00:50:52,082
CONTINUOUS, WE WOULD ONLY BE

1524
00:50:52,149 --> 00:50:52,916
INVESTIGATING TWO VARIABLES.

1525
00:50:52,983 --> 00:50:53,984
YOU CAN OBVIOUSLY DO

1526
00:50:54,050 --> 00:50:56,319
CORRELATIONS IN MANY PAIRS OF

1527
00:50:56,386 --> 00:50:58,088
VARIABLES, BUT THIS WOULD ONLY

1528
00:50:58,155 --> 00:51:04,828
ANSWER THE QUESTION ABOUT TWO AT

1529
00:51:04,895 --> 00:51:06,263
A TIME.

1530
00:51:06,329 --> 00:51:07,764
T-TESTS ARE EQUIVALENT TO

1531
00:51:07,831 --> 00:51:12,569
REGRESSION WHEN WE HAVE A SINGLE

1532
00:51:12,636 --> 00:51:13,170
BINARY INDEPENDENT VARIABLE.

1533
00:51:13,236 --> 00:51:14,704
SO MAYBE THIS DOESN'T SEEM LIKE

1534
00:51:14,771 --> 00:51:17,140
A QUESTION ANYBODY WOULD ASK.

1535
00:51:17,207 --> 00:51:19,409
BUT IN A SENSE WHERE PERHAPS YOU

1536
00:51:19,476 --> 00:51:20,811
DO HAVE TWO GROUPS AND ONE

1537
00:51:20,877 --> 00:51:22,012
CONTINUOUS MEASURE AND YOU WANT

1538
00:51:22,078 --> 00:51:23,847
TO KNOW IF IT IS DIFFERENT FOR

1539
00:51:23,914 --> 00:51:26,817
EACH OF YOUR GROUPS, YOU MIGHT

1540
00:51:26,883 --> 00:51:27,651
JUST THINK BY DEFAULT TO RUN A

1541
00:51:27,717 --> 00:51:27,884
T-TEST.

1542
00:51:27,951 --> 00:51:30,387
IF YOU THINK THAT EVENTUALLY

1543
00:51:30,454 --> 00:51:31,955
YOU'RE GOING TO WANT TO RUN

1544
00:51:32,022 --> 00:51:33,623
REGRESSION AND CONTROL FOR OTHER

1545
00:51:33,690 --> 00:51:34,391
VARIABLES IN THERE, YOU SHOULD

1546
00:51:34,458 --> 00:51:37,127
PROBABLY JUST PUT YOURSELF IN A

1547
00:51:37,194 --> 00:51:39,830
REGRESSION FRAMEWORK FROM THE

1548
00:51:39,896 --> 00:51:40,096
BEGINNING.

1549
00:51:40,163 --> 00:51:41,298
SO IF YOU'RE ONLY REALLY

1550
00:51:41,364 --> 00:51:43,700
INTERESTED IN THE TWO VARIABLES

1551
00:51:43,767 --> 00:51:44,000
TOGETHER.

1552
00:51:44,067 --> 00:51:44,501
A SIMPLE T-TEST IS FINE.

1553
00:51:44,568 --> 00:51:46,403
IF YOU THINK YOU'RE USING THAT

1554
00:51:46,470 --> 00:51:49,072
AND WANT TO BUILD ON IT OR ADD

1555
00:51:49,139 --> 00:51:52,242
INTERACTION TERMS AND ADD SORT

1556
00:51:52,309 --> 00:51:54,077
COVARIANTS OR POTENTIAL

1557
00:51:54,144 --> 00:51:55,212
CONFOUNDING FACTORS THEN MAYBE

1558
00:51:55,278 --> 00:51:56,213
WE JUST WANT TO BE IN A

1559
00:51:56,279 --> 00:52:01,218
REGRESSION FRAMEWORK FROM THE

1560
00:52:01,284 --> 00:52:01,418
START.

1561
00:52:01,485 --> 00:52:03,553
AND LASTLY, IS ANOVA, AND I

1562
00:52:03,620 --> 00:52:05,422
GUESS, WHAT I WANT TO SAY ABOUT

1563
00:52:05,489 --> 00:52:07,824
THAT, IS BASICALLY THAT ANOVA IS

1564
00:52:07,891 --> 00:52:08,758
A SPECIAL CASE OF LINEAR

1565
00:52:08,825 --> 00:52:09,559
REGRESSION.

1566
00:52:09,626 --> 00:52:11,461
THEY ARE REALLY THE SAME.

1567
00:52:11,528 --> 00:52:12,963
THEY ARE DOING THE SAME THING.

1568
00:52:13,029 --> 00:52:15,298
IN ANOVA, THE INDEPENDENT

1569
00:52:15,365 --> 00:52:17,501
VARIABLE IS, CAN ONLY BE

1570
00:52:17,567 --> 00:52:18,068
CATEGORICAL.

1571
00:52:18,134 --> 00:52:20,170
AND IN ALL OTHER CASES YOU'RE

1572
00:52:20,237 --> 00:52:22,739
BASICALLY DOING REGRESSION.

1573
00:52:22,806 --> 00:52:24,774
SO IF YOU'RE GOING TO LEARN HOW

1574
00:52:24,841 --> 00:52:27,611
TO DO ANYTHING, I WOULD

1575
00:52:27,677 --> 00:52:28,311
RECOMMEND UNDERSTANDING

1576
00:52:28,378 --> 00:52:29,212
REGRESSION.

1577
00:52:29,279 --> 00:52:31,681
BECAUSE YOU CAN RUN ANOVAS WHEN

1578
00:52:31,748 --> 00:52:32,616
YOU UNDERSTAND REGRESSION.

1579
00:52:32,682 --> 00:52:33,550
WHEN YOU LEARN A95 OFFER, YOU

1580
00:52:33,617 --> 00:52:36,086
ONLY KNOW HOW TO DO ANOVA.

1581
00:52:36,152 --> 00:52:38,755
SO IT IS NORTHWESTERLY

1582
00:52:38,822 --> 00:52:39,523
GENERALIZABLE AND MORE FLEXIBLE

1583
00:52:39,589 --> 00:52:40,223
TO UNDERSTAND REGRESSION

1584
00:52:40,290 --> 00:52:42,392
FORMALLY, LIKE I SAID, ANOVA IS

1585
00:52:42,459 --> 00:52:46,730
JUST A SPECIAL CASE OF LINEAR

1586
00:52:46,796 --> 00:52:47,030
REGRESSION.

1587
00:52:47,097 --> 00:52:51,268
AND WE HAVE, WELL I GUESS, I

1588
00:52:51,334 --> 00:52:53,136
WOULD CALL EXTENSIONS OF

1589
00:52:53,203 --> 00:52:55,138
REGRESSION LOGISTIC REGRESSION

1590
00:52:55,205 --> 00:52:55,739
WOULD USE A BINARY OUTCOME

1591
00:52:55,805 --> 00:52:55,972
MEASURE.

1592
00:52:56,039 --> 00:52:56,873
AND WE'LL BE TALKING ABOUT THAT

1593
00:52:56,940 --> 00:53:01,211
IN THE FUTURE LECTURE FOR THIS

1594
00:53:01,278 --> 00:53:01,444
SERIES.

1595
00:53:01,511 --> 00:53:02,979
POISSON REGRESSION IS USING

1596
00:53:03,046 --> 00:53:07,984
ACCOUNT TOUT COME MEASURE.

1597
00:53:08,051 --> 00:53:09,686
SO, POSITIVE WHOLE NUMBERS.

1598
00:53:09,753 --> 00:53:11,154
COX REGRESSION USING SURVIVAL

1599
00:53:11,221 --> 00:53:11,555
OUTCOME MEASURES.

1600
00:53:11,621 --> 00:53:15,025
AND THEN LINEAR MIXED MODELS

1601
00:53:15,091 --> 00:53:17,394
WHICH IS BASICALLY REGRESSION

1602
00:53:17,460 --> 00:53:18,728
WITH INTERCORRELATED DATA.

1603
00:53:18,795 --> 00:53:20,530
SO MAYBE WE HAVE REPEATED

1604
00:53:20,597 --> 00:53:24,668
MEASURES OR TIME OR CLUSTERED

1605
00:53:24,734 --> 00:53:26,136
DATA OR LONGITUDINAL DATA SO A

1606
00:53:26,202 --> 00:53:27,704
DIFFERENT TYPE OF MODEL WOULD BE

1607
00:53:27,771 --> 00:53:29,205
USED TO ANSWER QUESTIONS FOR

1608
00:53:29,272 --> 00:53:35,478
OUTCOME MEASURES OF THAT TYPE.

1609
00:53:35,545 --> 00:53:37,080
SO IN SUMMARY, LINEAR REGRESSION

1610
00:53:37,147 --> 00:53:40,550
IS A USEFUL AND FLEXIBLE WAY TO

1611
00:53:40,617 --> 00:53:42,319
UNDERSTAND THE PREDICTIVE, BUT

1612
00:53:42,385 --> 00:53:42,953
NOT CAUSAL, BEHAVIOR BETWEEN ONE

1613
00:53:43,019 --> 00:53:44,120
OR MORE VARIABLES IN A

1614
00:53:44,187 --> 00:53:47,023
CONTINUOUS OUTCOME MEASURE.

1615
00:53:47,090 --> 00:53:48,625
AND AS WE DISCUSSED, YOU MUST

1616
00:53:48,692 --> 00:53:49,859
MEET CERTAIN ASSUMPTIONS FOR THE

1617
00:53:49,926 --> 00:53:50,827
MODEL TO BE CONSIDERED

1618
00:53:50,894 --> 00:53:51,695
APPROPRIATE TO USE.

1619
00:53:51,761 --> 00:53:54,297
WE NEED TO CHECK THOSE

1620
00:53:54,364 --> 00:53:55,432
ASSUMPTIONS EITHER SOMETIMES AT

1621
00:53:55,498 --> 00:53:57,434
THE START BY UNDERSTANDING OUR

1622
00:53:57,500 --> 00:54:01,171
DESIGN WHETHER WE HAVE

1623
00:54:01,237 --> 00:54:01,771
INDEPENDENCE.

1624
00:54:01,838 --> 00:54:04,040
AND THE BEHAVIOR OF IF WE HAVE A

1625
00:54:04,107 --> 00:54:06,109
LINEAR BEHAVIOR TO DESCRIBE, BUT

1626
00:54:06,176 --> 00:54:07,177
ALSO WE CHECK ASSUMPTIONS AFTER

1627
00:54:07,243 --> 00:54:12,816
RUNNING THE MODEL WHICH IS --

1628
00:54:12,882 --> 00:54:14,851
WHEN WE ABSTAIN RESIDUALS FROM

1629
00:54:14,918 --> 00:54:16,453
OUR RUN MODEL ARE THEY BEHAVING

1630
00:54:16,519 --> 00:54:18,588
IN A WAY THAT WE SEE ASSUMPTIONS

1631
00:54:18,655 --> 00:54:22,592
OF REGRESSION, WHICH IS THE

1632
00:54:22,659 --> 00:54:23,693
NORMAL DISTRIBUTION OF

1633
00:54:23,760 --> 00:54:24,327
RESIDUALS.

1634
00:54:24,394 --> 00:54:25,528
ADDITIONAL VARIABLES CAN BE

1635
00:54:25,595 --> 00:54:27,864
ADDED AS NEEDED TO ELABORATE ON

1636
00:54:27,931 --> 00:54:29,232
A RELATIONSHIP BETWEEN, YOU

1637
00:54:29,299 --> 00:54:32,002
KNOW, X AND Y OR INVESTIGATE OUR

1638
00:54:32,068 --> 00:54:33,803
ACTIONS OR ADDRESS CONFOUNDING

1639
00:54:33,870 --> 00:54:34,070
BEHAVIORS.

1640
00:54:34,137 --> 00:54:36,673
SO THIS IS OBVIOUSLY INCREASE IN

1641
00:54:36,740 --> 00:54:38,074
COMPLEXITY VERY QUICKLY.

1642
00:54:38,141 --> 00:54:40,877
VISUAL-- I THINK BECAUSE OF

1643
00:54:40,944 --> 00:54:43,246
THAT, VISUAL INSPECTIONS OF THE

1644
00:54:43,313 --> 00:54:44,581
DATA ARE REALLY KEY TO

1645
00:54:44,648 --> 00:54:47,117
UNDERSTANDING THE DATA OVERALL.

1646
00:54:47,183 --> 00:54:49,719
LOOKING AT RESIDUAL BEHAVIOR.

1647
00:54:49,786 --> 00:54:50,787
UNDERSTANDING DISTRIBUTION,

1648
00:54:50,854 --> 00:54:52,088
VARIABILITY, MODEL PERFORMANCE.

1649
00:54:52,155 --> 00:54:54,324
YOU NEED TO SEE YOUR DATA TO

1650
00:54:54,391 --> 00:54:55,291
REALLY UNDERSTAND IT.

1651
00:54:55,358 --> 00:54:59,329
SO DON'T BE AFRAID TO MAKE THE

1652
00:54:59,396 --> 00:54:59,763
VISUALIZATIONS.

1653
00:54:59,829 --> 00:55:01,097
AND DATA REPORTING SHOULD

1654
00:55:01,164 --> 00:55:02,298
INCLUDE INFORMATION ON MOST OR

1655
00:55:02,365 --> 00:55:04,401
ALL MODELING INVESTIGATED DURING

1656
00:55:04,467 --> 00:55:06,169
THE ANALYTICAL PROCESS.

1657
00:55:06,236 --> 00:55:09,706
ESPECIALLY IF IT IS EXPLORATORY,

1658
00:55:09,773 --> 00:55:10,440
IT SHOULD BE AS REPRODUCIBLE AS

1659
00:55:10,507 --> 00:55:12,409
POSSIBLE IN TERMS OF THE THINGS

1660
00:55:12,475 --> 00:55:13,243
THAT YOU TRIED AND WHAT FAILED.

1661
00:55:13,309 --> 00:55:15,211
AND REPORTING AS MUCH AS YOU CAN

1662
00:55:15,278 --> 00:55:19,983
OF THAT IN THE PUBLISHED

1663
00:55:20,050 --> 00:55:20,283
LITERATURE.

1664
00:55:20,350 --> 00:55:25,155
AND I WANT TO CONCLUDE BY

1665
00:55:25,221 --> 00:55:29,726
TALKING ABOUT THIS QUOTE FROM

1666
00:55:29,793 --> 00:55:31,294
STATISTICIAN GEORGE BOX, OF BOX

1667
00:55:31,361 --> 00:55:33,329
COX TRANSFORMATION, IF YOU HEARD

1668
00:55:33,396 --> 00:55:34,564
OF SUCH A THING.

1669
00:55:34,631 --> 00:55:36,066
HE ATTRIBUTED TO SAYING

1670
00:55:36,132 --> 00:55:37,267
SOMETHING LIKE ALL MODELS ARE

1671
00:55:37,333 --> 00:55:40,236
WRONG, BUT SOME ARE USEFUL.

1672
00:55:40,303 --> 00:55:43,139
THIS IS ORIGINALLY EXTRAP A

1673
00:55:43,206 --> 00:55:45,408
LOTTED FROM SOMETHING HE WROTE

1674
00:55:45,475 --> 00:55:48,845
ABOUT IN 1976 IN JAZZA PAPER,

1675
00:55:48,912 --> 00:55:52,082
CALLED SCIENCE AND STATISTICS.

1676
00:55:52,148 --> 00:55:53,249
HE WROTE ABOUT THIS CONCEPT IN

1677
00:55:53,316 --> 00:55:54,718
TWO PARTICULAR PASSAGES.

1678
00:55:54,784 --> 00:56:02,092
I JUST WANT TO READ THEM HERE.

1679
00:56:02,158 --> 00:56:04,094
SO ABOUT PARSIMONY, HE WRITES

1680
00:56:04,160 --> 00:56:06,963
THIS ALL MODELS ARE WRONG,

1681
00:56:07,030 --> 00:56:08,765
SCIENTISTS CANNOT OBTAIN A

1682
00:56:08,832 --> 00:56:10,567
CORRECT ONE, BY EXCESSIVE

1683
00:56:10,633 --> 00:56:10,867
ELABORATION.

1684
00:56:10,934 --> 00:56:14,971
ON THE CONTRARY, HE WOULD SEEK A

1685
00:56:15,038 --> 00:56:17,107
DESCRIPTION OF NATURAL

1686
00:56:17,173 --> 00:56:18,908
PHENOMENA, TO HAVE SIMPLE,

1687
00:56:18,975 --> 00:56:23,747
MODELS IS THE SIGNATURE OF A

1688
00:56:23,813 --> 00:56:25,815
GREAT SCIENTIST, OVERELABORATION

1689
00:56:25,882 --> 00:56:29,052
IS OFTEN THE MARK AT

1690
00:56:29,119 --> 00:56:29,719
MERITOCRACY.

1691
00:56:29,786 --> 00:56:30,253
AND WORRYING SELECTIVELY.

1692
00:56:30,320 --> 00:56:32,522
HE SAYS SINCE ALL MODALS ARE

1693
00:56:32,589 --> 00:56:35,158
WRONG, THE SCIENTIST MUST BE

1694
00:56:35,225 --> 00:56:40,396
ALERT TO WHAT IS APPROPRIATELY

1695
00:56:40,463 --> 00:56:40,597
WRONG.

1696
00:56:40,663 --> 00:56:42,165
IT IS INAPPROPRIATE TO BE

1697
00:56:42,232 --> 00:56:45,635
CONCERNED ABOUT MICE WHEN THERE

1698
00:56:45,702 --> 00:56:46,503
ARE TIGERS ABROAD.

1699
00:56:46,569 --> 00:56:49,072
THIS IS OVERLY DRAMATIC.

1700
00:56:49,139 --> 00:56:50,840
BUT NOT INCLUDING EVERY

1701
00:56:50,907 --> 00:56:54,110
VARIABLE, NOT HAVING PERFECT

1702
00:56:54,177 --> 00:56:57,046
MODEL FIT, BECAUSE IT REALLY

1703
00:56:57,113 --> 00:56:58,948
OVER EMPHASIZES HOW MUCH WE

1704
00:56:59,015 --> 00:57:00,216
SHOULD BELIEVE THE MODELS

1705
00:57:00,283 --> 00:57:00,850
ANYWAY.

1706
00:57:00,917 --> 00:57:03,787
WE SHOULD BE IF THE MODEL IS

1707
00:57:03,853 --> 00:57:04,854
ELIMINATING, LEARNING SOMETHING

1708
00:57:04,921 --> 00:57:06,923
FROM IT, AND GOOD ENOUGH FOR

1709
00:57:06,990 --> 00:57:08,158
THIS PARTICULAR APPLICATION AND

1710
00:57:08,224 --> 00:57:10,627
THIS PARTICULAR COHORT FOR OUR

1711
00:57:10,693 --> 00:57:11,027
PARTICULAR GOALS.

1712
00:57:11,094 --> 00:57:13,630
AND MODEL FIT IS IMPORTANT IN

1713
00:57:13,696 --> 00:57:14,430
THE SENSE THAT DO WE WILL

1714
00:57:14,497 --> 00:57:16,733
UNDERSTAND THE LIMITATIONS OF

1715
00:57:16,800 --> 00:57:18,434
THE MODEL AND WHERE WE MIGHT

1716
00:57:18,501 --> 00:57:21,905
POSSIBLY BE FAILING.

1717
00:57:21,971 --> 00:57:22,472
I THINK THAT'S BROADLY MORE

1718
00:57:22,539 --> 00:57:24,974
IMPORTANT HAS YOU GO THROUGH THE

1719
00:57:25,041 --> 00:57:26,476
MODELING PROCESS AND LEARN TO DO

1720
00:57:26,543 --> 00:57:27,677
THESE THINGS AND REGRESSION AND

1721
00:57:27,744 --> 00:57:31,714
HONESTLY OTHER THINGS.

1722
00:57:31,781 --> 00:57:35,118
I THINK THIS IS AN INTERESTING

1723
00:57:35,185 --> 00:57:36,119
AND USEFUL QUOTE TO KEEP IN MIND

1724
00:57:36,186 --> 00:57:36,920
AS YOU DO SCIENCE.

1725
00:57:36,986 --> 00:57:38,621
ANY QUESTIONS IN THE LAST-MINUTE

1726
00:57:38,688 --> 00:57:38,855
OR TWO?

1727
00:57:38,922 --> 00:57:41,057
FEEL FREE TO PUT THEM IN THE

1728
00:57:41,124 --> 00:57:41,724
CHAT.

1729
00:57:41,791 --> 00:57:43,259
IF YOU HAVE OTHER QUESTIONS HOAR

1730
00:57:43,326 --> 00:57:44,594
YOU LIKE TO SPEAK FURTHER I'M

1731
00:57:44,661 --> 00:57:46,796
ALWAYS AVAILABLE TO BE EMAILED

1732
00:57:46,863 --> 00:57:57,040
AS WELL.

1733
00:58:19,162 --> 00:58:19,395
ALL RIGHT.

1734
00:58:19,462 --> 00:58:21,764
I DON'T SEE ANY QUESTIONS.

1735
00:58:21,831 --> 00:58:23,600
THANK YOU SO MUCH FOR JOINING,

1736
00:58:23,666 --> 00:58:23,766
ALL.

1737
00:58:23,833 --> 00:58:25,602
LIKE I SAID, PLEASE REACH OUT IF

1738
00:58:25,668 --> 00:58:26,669
YOU HAVE FURTHER QUESTIONS.

1739
00:58:26,736 --> 00:58:27,904
AND THE RECORDING WILL BE

1740
00:58:27,971 --> 00:58:30,907
AVAILABLE AND SLIDES WILL BE

1741
00:58:30,974 --> 00:58:31,741
DISSEMINATED AT SOME POINT.

1742
00:58:31,808
IF YOU'RE INTERESTED IN THAT.