Question

Question 2 Consider the following estimated equation where sleep is the total weekly minutes spent sleeping, age is a person's age, female is a dummy variable that takes the value of 1 if the person is a female and 0 otherwise, and student is a dummy variable that takes the value of 1 if the person is a student and 0 otherwise. Standard errors are in parentheses. (1.02) sleep - 1.17 - 2.52 age + 0.18 age? +0.721 female - 1.005 student (0.206) n = 700, R' = 0.851 (0.111) (1.000) 0.967 female student (0431) (0.872) (a) How many more minutes of sloep would male students get over female students? |3 marks (b) What is the initial effect of age on sleep? 15 marks (e) At what point would the effect of age on sleep become vero? [3 marks (d) Is there evidence that the dummy variable female should be included in the model? 15 marks

Answer 1

Q2)

(a) Minutes of sleep for male students = 1.47 - 1.005 = 0.465

Minutes of sleep for female students = 1.47 - 1.005 + 0.721 - 0.967 = 0.219

Thus, additional sleep for male students = 0.465 - 0.219 = 0.246

(b) Initial effect of age on sleep = dSleep/dAge

= -2.52 + 2*0.18Age

= -2.52 + 0.36 Age

(c) Effect of age is 0 when we have -2.52 + 2*0.18Age = 0

=> Age = 2.52/0.36 = 7

(d) testing for the signifacance of female.

Test statistic = Estimate/standard error

= 0.721/1.003 = 0.71

Since, 0.71 < 1.645, the Z critical value at 5%, the null hypothesis of no significant effect of females on sleep can not be rejected and thus, there is no evidence to include female in the regression.