Using 706 observations, a researcher obtains the following fitted models by OLS. sleep 3, 638. 25 . 148 totwrk 11. 13 educ 2. 20 age R2 . 113 112. 28 . 017 5. 88 1. 45 and the restricted regression sleep 3, 586. 38 . 151 totwrk R2 . 103 38. 91 . 016 where standard errors are in parentheses, sleep and totwrk are the minutes spent sleeping and working each week, educ and age are years of education and age also measured in years. Assume the data satisfy S1-S5. a. (6 points) Using the restricted model, can you reject the null that time spent sleeping is not increasing in age. b. (6 points) Test that time spent sleeping doesn't vary with education or age. c. (6 points) Using the restricted model, construct a 95% confidence interval for the coefficient of totwrk using its asymptotic distribution. d. (4 points) Which of the two estimated regressions have a higher value of R2 ? Explain. e. (4 points) Notice that the standard errors for the restricted regression are smaller than those of the unrestricted regression. Could it have been otherwise? Explain. f. (4 points) From the unrestricted model, how many hours