3. (25 points). We are interested in the determinants of how much sleep a person

Question

3. (25 points). We are interested in the determinants of how much sleep a person gets. We want to run the following regression where sleep, total work and tw watch are measured in hours per week and age is measured in years. sleep total-work page watch u a. What do you expect the sign of p, to be and why? b. Suppose that you failed to gather data on the number of hours a person watches TV and end up running the following regression. sleep Ao total work Bage +u Will your estimate of B in this case be upward biased, downward biased or unbiased? Why? c. If you include a new variable race in the regression, where race is the racial origin of the person, what effect will it have on your estimate of P,?(Hint: what happens to the mean and variance of when you include an irrelevant variable?) 4. (30 points). We want to learn more about the tradeoff between time spent sleeping and working and to look at other factors affecting sleep. We run a regression using the following model Where sleep is time spent sleeping in minutes per week and totwrk (total work) is time spent working also in minutes per week, edu is years of education, and age is individuals age in years. The regression results are: R-squared Adj R-squared Total 139239836 705 197503.313 Std. Interval] 0.059 -22. E872 a. Write down the estimated equation, and compute and interpret R-squared. b. Interpret the coefficient of edu. c. If we measure sleep in hours instead of minutes and re-run the regression, what would the intercept and the coefficients of totwrk. edu, and age be?

Explanation / Answer

Part-a

Estimated equation is

Sleep=3638.24-0.15 totwrk -11.13 educ + 2.20 age

R-squared is 15784778.6/139239836=0.1134 which means that the regression model(all the predictors taken together) explained only 11.34% of the variations in time spent during sleeping

Part-b

Coefficient of educ is -11.13 which means that corresponding to one year increase in years of education there is on an average a decrease of 11.13 minutes in the sleeping time per week.

Part-c

To convert sleet to hours we have to divide it by 60, so all the coefficients are also divided by 60.

Part-d

new coefficient of educ=-11.13/12=-0.93

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