(c) (3 pts) ModelM1can be written asyi|xiind∼ N(x′iβ, σ2),i= 1, . . . ,133,where the coefficientsβ= (β0, . . . , β6) for modelM1are in the order specified by theRoutputabove.Letτdenote the expected difference in test scores between a school in Cedar Rapids with apoverty index of 0.25 and a school in Davenport with a poverty index of 0.5:τ=E[Test|Poverty= 0.25,City=CedarRapids]-E[Test|Poverty= 0.5,City=Davenport].Show thatτ=-0.25β1-β2.
(d) (6 pts) Calculate a 95% confidence interval forτunder modelM1. To do this, you can usethe fact that ifT∼t(126), thenP(T <1.66) =.95,P(T <1.98) =.975.
STAT 331, March 19, 2015, 1:30pm-2:20pmPage 3 of 6