3. For a sample of 676 individuals, we estimated models to test for a tradeoff between minutes per week spent sleeping (sleep) and minutes per week spent working (fotwrk). We also included education and other variables in the equations. log denotes natural logarithm. For questions i)-v), consider the multiple regression model: log(sleep) B,+, log(totwrk) + B,educ+ Bage+u. (1) i) (4 pts) What signs do you expect for A and B, respectively? Explain. ii) (5 pts) What is the interpretation of ? Of B,? iii) (5 pts) We estimated the equation log(sleep)=8.623-0.073 log(towrk)-0.002educ +0.0009age.n=676, R2 = 0.0806. (0.086) (0.010) (0.002) (0.0005) The numbers in parentheses are standard errors. Is either educ or age individually significant at the 5% level against a two-sided alternative? Please show your work. iv) (6 pts) Are you able to test whether educ and age are jointly significant in equation (1) based on the regression results in part iii)? If yes, carry out the test for the joint hypothesis at the 1% level; if not, say what else you need to know and why. 2/5 v) (5 pts) Assume person A has totwrk=3500, educ 12, age 32 and person B has totwrk 5000, educ 14, age 31. Use the estimated model in part iii) to find the predicted difference in log(sleep) between B and A. vi) (5 pts) Add a quadratic in age to equation (1) and the estimated equation becomes log(sleep)=8.680-0.072 log(totwrk)-0.002educ -0.0024age +0.00004 age. Holding log(totwrk) and educ fixed, at what age is log(sleep) minimized? vii) (5 pts) Suppose the individuals spend each week in three activities: working, sleeping, and leisure. Let wage be hourly wage measured in dollars and leisure be time spent on leisure. Which assumption does the following model violate log(wage) B+Btotwrk+ B,sleep+ B,leisure+u? 4. Use the data in alcohol.dta for this question. These data includes labor market information on 9822 men: employ is a binary variable that equals one if the man has a job and 0 otherwise, abuse is a binary variable that equals one if the man abuses alcohol and 0 otherwise, educ is years of education, famsize is family size. We also have information on some other demographic and background variables. i) (6 pts) How many people in the sample were employed at the time of interview? How many have abused alcohol? How many single-person households are there? ii) (6 pts) Estimate the model employ = B+Babuse + Beduc+ Bfamsize+u by OLS and report the results in equation form. Also report both the usual and heteroskedasticity- robust standard errors in parentheses and brackets, respectively. Is abuse statistically significant at the 5% level against the negative one-sided alternative? Does it matter which standard error is used?