Multiple Regression

Why to ControlMarch 18, 2004

17.871

Gore Likeability Example

• Suppose:– Gore’s* likeability is a function of Clinton’s

likeability and not directly a function of party– Clinton’s likeability is a function of one’s

partisan identification plus other factors

– What would the regression of Gore likeability on Clinton likeability look like?

Party ID Clinton Likeability

GoreLikeability

e1 e2

*This example probably works better if we’re predicting the likeability of Socks the cat.

Democratic picture

Clinton thermometer

Independent picture

Clinton thermometer

Republican picture

Clinton thermometer

Combined data picture

Clinton thermometer

Combined data picture with regression

Clinton thermometer

Combined data picture with “true” regression lines overlaid

Clinton thermometer

Tempting yet wrong normalizations

Clinton thermometer

Clinton thermometer

Summary: Why we control• Remove confounding effects

• Improve efficiency

Party

Clintonlikeability

Gorelikeability

e

e

Party

Clintonlikeability

Gorelikeability

e

Clinton thermometer

Look at actual data

Gore thermometer

0

100

0 100

0 100

Clintonthermometer

0

100

-1 1-1

1

Party (3 pointscale)

graph7 clinton gore party3, matrix

Look at actual data (jitter)

Gore thermometer

0

100

0 100

0 100

Clintonthermometer

0

100

-1 1-1

1

Party (3 pointscale)

graph7 gore clinton party3, matrix jitter(5)

Another way to deal with the mass point problem

Clin

ton

ther

mom

eter

Gore thermometer0 100

0

100 . collapse (count) n=party3,by(clinton gore)

. graph7 clinton gore [fweight=n]

Gore vs. ClintonG

ore

ther

mom

eter

Graphs by Party (3 point scale)Clinton thermometer

Gore thermometer pyp Fitted values

party3==-1

0

100

party3==0

0 100party3==1

0 1000

100 Overall

Within party

Rep. Ind.

Dem.

Gore vs. partyG

ore

ther

mom

eter

Graphs by clinton_levelParty (3 point scale)

Gore thermometer Fitted values py_party3_all

clinton_level==-1

0

100

clinton_level==0

-1 1clinton_level==1

-1 10

100

Overall

Within party

Clinton low Clinton med.

Clinton high