Learn Multiple Regression

Click on the graph to create data

In the following exercises, imagine:

Y = post-school wages

X = student quality, measured by SAT scores

Black dots represent private university students

Blue dots represent public university students
Mean Difference vs. Dummy Variable I

Create a data set with two properties:

(i) The Mean Differences methodology shows that the wages (Y) for black group are significantly higher than wages (Y) for the blue group at a 95% level, denoted by two asterisks after the t-stat; and

(ii) The Dummy Variable methodology shows no significant difference between the groups.

Check your answer by clicking the button "Am I right?", and explain in words what is going on.
ANSWER: If you look only at mean differences, you can mistakenly infer that private university membership causes higher wages when, in this example, they are caused by the higher test scores of private university students. This is sometimes referred to as:

1. “Selection bias” (those with higher test scores values “select” private university more frequently),

2. “Omitted variables bias,” (estimators of the effect of private university education on wages may be biased biased if you omit a relevant variable like test scores from your analysis); or

3. “Mistaking correlation for causality: going to a private university is correlated with higher wages, but the causality can run both ways. In this example, not only does private education increase productivity and wages, but also higher productivity individuals are more likely to attend private university (selection bias).

Mean Difference vs. Dummy Variable II

Create a data set with two properties:

(i) The Mean Differences methodology shows that the wages (Y) for black group are NOT significantly higher than wages (Y) for the blue group at a 95% level, denoted by less than two asterisks after the t-stat; and

(ii) The Dummy Variable methodology shows significantly higher than wages (Y) for the black group at a 95% level, denoted by at least two asterisks after the dummy variable t-stat.

Check your answer by clicking "Am I right?," and explain in words what is going on.
ANSWER: If you look only at mean differences, you can mistakenly infer that black group membership does NOT cause higher Y values when, in fact, it does.

Trial and Standard Error: Learn Multiple Regression

Simple
Regression

Differences
Between
Groups

Functional
Forms

Create Data

Black (solid)

Blue (empty)

Estimate Differences

Mean Differences
Dummy Variable
Black (solid) Line
Blue (dashed) Line

	Mean Differences:	Dummy Variable:	Black Line:	Blue Line:
Black-Blue:
Stderr:
t-stat:

© 2023 Luke M. Froeb, Keyuan Jiang & Gray Curtis