Question

1. The following is the logit function for a logistic model that predicts whether an employee will be successful or not based on a specific test score(x):    -43.37 + 0.4897x

1. Find the probability of success for an employee who scored a 93 on the test.
2. What is the odds ratio for x? Interpret.

Answer 1

a. Given log(P(S|x)/(1-P(S|x))= -43.37 + 0.4897x, where

P(S|x)=probability of success for test score x. Then

P(S|x)=exp(-43.37 + 0.4897x)/(1+exp(-43.37 + 0.4897x))

Then P(S|x=93)=exp(-43.37 + 0.4897*93)/(1+exp(-43.37 + 0.4897*93))= 0.897716

b. Odds ratio=P(S|x=93)/(1-P(S|x=93))=exp(-43.37 + 0.4897*93)=8.776696

Thus for a one-unit increase in the score, the expected change in log odds is 0.4897.

Since exp(.4897)=1.6318,  we can say for a one-unit increase in test score, about 63% increase in the odds of success is expected .