Question

Problem 2 (25 pts). The following multiple regression model is to study the tradeoff between time spent on sleeping and working and to look at other factors affecting sleep: sleep-a-bítoturk + bgeduc-b3age te where sleep and totwork (total work) are measured in minutes per week and educ and age are measured in years The estimated model is as follows. sleep3638.25 0.148 totwrk -11.13 educ + 2.2 age (5.88) (112.28) (0.017) n = 706, R-0.113 The standard error of each coefficient is given in parentheses (a) (5 pts) Interpret the coefficient bi based on the estimated values. (b) (10 pts) Is either educ or age individually significant at the 5% level against a two-sided alternative? Show your steps (c) (5 pts) Dropping educ and age from the equation gives sleep =3586.38-0.151 toturk (38.91) (0.017) n 706, R20.103 Are educ and age jointly significant in the original equation at the 5% level? Show your steps. (d) (5 pts) Suppose that the sleep equation contains heteroskedasticity. What does this mean about the tests conducted in parts (a) and (b)?

Answer 1

Ansac Siven The estimakeis as follas 3638.OG ㅡ 0-148とotemk-11. 13 educ + 2.2 age C2)o.oiT) (S88 (1.4S n706, R2 o 113 b) 706-4 , 702 tao-tailed とest at 5% leel. educ 131.8929 e fail to heieck t l hefathesis ak se su level tage Age is also slakisicaiy nsgnifrant at the sx level. -/-5172 Also, 2.20人4S nicant at c) sleef 67iven 3586.38-0-S} btwrk

e coukl to compule the R2. m statistic fen kink significance 3.972 The citical value is the F ohlained ith a denominakosn Thenefone, educ and age ae jcintly signigcanl al the 5% lev! educ and age ase Jointly Signi위 ant atte 27. led) 2702 i e3.00 CIn fact, the p value s aboul 9, and so dThe l and F stalistics that ae used assune homo skedasticity. Ie thesis hetenoskedasticily in e quationthe id