The population logit model of the binary dependent variable Y with multiple regressors is Pr left parenthesis
Question:
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 Start Fraction 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 End Fraction
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.
College Mathematics For Business Economics, Life Sciences, And Social Sciences
ISBN: 978-0134674148
14th Edition
Authors: Raymond Barnett, Michael Ziegler, Karl Byleen, Christopher Stocker