Question

Suppose we regress y on an intercept and the dummy variable male, which takes the value 1 if the

individual is male and 0 otherwise. We use a sample of 1000 individuals, where half of them are
women. The average values of y for men and women in the sample are 7.5 and 8.5, respectively. Which
of the following statements is true?
a. The estimate of the slope is equal to 7.5.
b. The estimate of the slope is equal to 8.5.
c. The estimate of the slope is equal to -1.
d. The estimate of the slope is equal to 1.
e. None of the above.

Answer 1

The correct answer is option c. In this linear regression scenario with a dummy variable, the estimate of the slope is determined by the difference in the average values of y for men and women, which results in a slope estimate of -1.

Step-by-step explanation:

The question involves identifying the estimate of the slope in a simple linear regression where the dependent variable y is regressed on a dummy variable representing gender. Here, the dummy variable 'male' has a value of 1 if the individual is male and 0 otherwise. With the average values of y for men being 7.5 and for women being 8.5, respectively, we can deduce the slope by observing the change in the average value of y as the dummy variable switches from 0 (women) to 1 (men). The change in y (which is the slope) is 7.5 (male average) - 8.5 (female average), giving us -1.

Hence, the correct option is c. The estimate of the slope is equal to -1.