Question

A GRETL data set was used to estimate the following models to predict the probability of getting accepted into UCSD medical school.

The following SRF's were estimated :

LPM: Accept = -0.40 + 0.35(GPA) + -0.10(Female)

Logit: Accept = -4.00 + 1.50(GPA) + -0.40(Female),

where Accept = 1 if accepted , GPA (0-4) and Female = 1 for female.

2. Answer the following questions about the Logit model.

Round off to two decimal places.

a. What is the probability of a female with a 3.0 GPA getting accepted?

b. What is the probability of a female with a 4.0 GPA getting accepted?

c. What is the difference between 2a and 2b.

Answer 1

a.

For Logot model, the probability of getting accepted is,

p = 1 / (1 + exp(-(-4.00 + 1.50(GPA) -0.40(Female))))

=>

p = 1 / (1 + exp(4.00 - 1.50(GPA) + 0.40(Female)))

For GPA = 3.0 ,  Female = 1

p = 1 / (1 + exp(4.00 - 1.50 * 3 + 0.40 * 1)) = 0.5249792

b.

For GPA = 4.0 ,  Female = 1

p = 1 / (1 + exp(4.00 - 1.50 * 4 + 0.40 * 1)) = 0.8320184

c

The difference between probability of a female with a 3.0 GPA and 4.0 GPA getting accepted is,

0.8320184 - 0.5249792 =  0.3070392