1. In the following model, we study the tradeoff between time spend sleeping and working and look at other factors affecting sleep: sleep B₁+B,toturk + B₂edu + Bage+u Where sleep and totwrk (total work) are measured in minutes per week and edu and age are measured in years. a. If adults trade off sleep for work, what is the sign of B,? b. What signs do you think B, and B, will have? c. Using data in SLEEP75.RAW, the estimated equation is sleep 3,586.38-.148totwrk -11.13edu +2.20age (112.28) (.017) (5.88) (1.45) n-706, R2-0.113 If someone works five more hours per week, by how many minutes is sleep predicted to fall? Is this a large tradeoff? d. Is either edu or age individually significant at the 5% level against a two-sided alternative? Show your work. e. Dropping edu and age from the equation gives: sleep 3,586.38-.151totwrk (38.91) (.017) n-706, R²=0.103 Are edu and age jointly significant in the original equation at the 5% level? Justify your answer. f. Does including edu an age in the model greatly affect the estimated tradeoff between sleeping and working?