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. sleep = 1.47 - 2.52 age + 0.18 age? +0.721 female - 1.005 student - 0.967 female. student (1.02) (0.111) (0.206) (1.003) (0.872) (0.431) n=700, R' = 0.851 (a) How many more minutes of sleep would male students get over female students? [3 marks] (b) What is the initial effect of age on sleep? (5 marks (c) At what point would the effect of age on sleep become zero? [3 marks (d) Is there evidence that the dummy variable female should be included in the model? 15 marks)

Answer 1

a) For a male student:

sleepm = c+0.721*(0) - 1.005 – 0.967 * (0) * 1 c=1.47 – 2.52age +0.18age?

For a female student:

$\Hat{sleep_F}=c +0.721*(1)-1.005 - 0.967 * (1)*1 \\\\ \Hat{sleep_M}-\Hat{sleep_F}=-0.721+0.967=0.246$

Thus a male student sleeps 0.246 more minutes as compared to female students.

b) Initial effect of age on sleep is -2.52.

$\frac{\partial sleep}{\partial age}=-2.52+0.18*2 * age$

So the effect of age on sleep depends on the age.

c) For age to have zero effect on sleep:

-2.52 + 0.36*age=0

This gives: For age= 7, sleep does not depend on age

d) The standard error for dummy "female" is 1.003 which is very high as compared to the coefficient value of 0.721. This makes female an insignificant variable to express any change on sleeping patterns.