The population logit model of the binary dependent variable Y with multiple regressors is

Pr left parenthesis Upper Y equals 1 vertical line Upper X 1 comma Upper X 2 comma ... comma Upper X Subscript k right parenthesis equals Upper F left parenthesis beta 0 plus beta 1 Upper X 1 plus beta 2 Upper X 2 plus ... plus beta Subscript k Baseline Upper X Subscript k right parenthesis equals StartFraction 1 Over 1 plus e Superscript negative left parenthesis beta 0 plus beta 1 Upper X 1 plus beta 2 Upper X 2 plus ... plus beta Super Subscript k Baseline Upper X Super Subscript k right parenthesis EndFraction

Where

Upper X Subscript 1 comma Baseline Upper X 2 comma ... comma Upper X Subscript k

are regressors.

Part 2

The equation below estimates the effect of race on the probability of mortgage denial, holding constant the payment-to-income ratio.

Pr left parenthesis deny equals 1 vertical line Upper P divided by Upper I ratio comma black right parenthesis equals Upper F left parenthesis negative 2.25 plus 2.73 Upper P divided by Upper I ratio plus 0.73 black right parenthesis

(0.17

)

(0.44

)

(0.085

)

Part 3

A black mortgage applicant has a P/I ratio of

0.39

.

What is the predicted probability that his application will be denied?

The predicted probability that his application will be denied is

enter your response here

%.

(Express

your response as a percentage and round to two decimal

places)

Part 4

Suppose that the applicant reduced this ratio to

0.33

.

What effect would this have on his predicted probability of being denied a mortgage?

The predicted probability of being denied a mortgage would

decrease

increase

by

enter your response here

percentage points.

(Round

your response to two decimal

places)

Part 5

A white mortgage applicant has a P/I ratio of

0.36

.

What is the predicted probability that his application will be denied?

The predicted probability that his application will be denied is

enter your response here

%.

(Express

your response as a percentage and round to two decimal

places)

Part 6

Suppose that the applicant reduced this ratio to

0.26

.

What effect would this have on his predicted probability of being denied a mortgage?

The predicted probability of being denied a mortgage would

decrease

increase

by

enter your response here

percentage points.

(Round

your response to two decimal

places)

Part 7

Does the marginal effect of the P/I ratio on the probability of mortgage denial depend on race?

A.

Yes.

B.

No.