Question

Suppose the following linear probability model
Y = 0.708 + 0.201M, n=1,989, R²=.049.
(0.018) (0.020)
Where y=1 if mortgage approved, M=1 if men, etc.
1. What is the probability of mortgage approval for a typical male applicant?
2. What is the probability of mortgage approval for a typical female applicant?
3. Is the discrimination based on gender significant?
4. What are the problems of this model?
5. What other variables do you think should be added in the model? And if the variables were to be added, what happens to the coefficient of M?

Answer 1

Solution:-

Given data:-

Y = 0.708 + 0.201 M

(0.018) (0.020)

1. What is the probability of mortgage approval for a typical male applicant?

Probability of mortgage approval = 0.708 + 0.201 * 1

Actually Y = 0.708 + 0.201 M and also M = 1 (male applicant)

The probability of mortgage approval for a typical male applicant = 0.909

2. What is the probability of mortgage approval for a typical female applicant?

Probability of mortgage approval = 0.708 + 0.201 * 0

Actually Y = 0.708 + 0.201 M and also M = 1 (female applicant)

The probability of mortgage approval for a typical female applicant = 0.708

3. Is the discrimination based on gender significant?

The distinction between the probabilities of male and female candidates has

The slope coefficient = 0.201

Standard error = 0.020

Null Hypothesis H0: Slope Coefficient of M is 0.

Alternate Hypothesis Ha: Slope Coefficient of M isn't 0.

Test Statistic, t = the slope coefficient / Standard error

The slope coefficient = 0.201

Standard error = 0.020

Test Statistic, t = 10.05

Degree of freedom = n - 2

where n = 1989

Degree of freedom = 1987

At 0.05 level of significance, critical value of Z =1.96

Since the test measurement is more prominent than the basic esteem,

So,we dismiss the invalid speculation and infer that there is noteworthy proof that Slope Coefficient of M isn't 0 and along these lines.

There is huge contrasts in the probabilities of male and female candidates. In this manner we reason that there is huge segregation dependent on gender.

4. What are the problems of this model?

The issues with the model is that there is just a single indicator variable M, which clarifies just 4.9% of the variety of the likelihood of home loan endorsement. R-square of the model is extremely low.

5. What other variables do you think should be added in the model? And if the variables were to be added, what happens to the coefficient of M?

The issues with the model is that there is just a single indicator variable M, which clarifies just 4.9% of the variety of the likelihood of home loan endorsement. R-square of the model is exceptionally low.