chapter 1

Chapter 13: Nonlinear and Multiple Regression33.x − 20a. x = 20 and s x = 10.8012 so x ′ = . For x = 20, x ′ = 010.8012y ˆ = βˆ∗0= .9671. For x = 25, x ′ = . 4629 , so, and23(.4629) − .0176(.4629) + .0062(.4629) = . 9407y ˆ = .9671−.0502.b.⎛ x − 20 ⎞ ⎛ x − 20 ⎞ ⎛ x − 20 ⎞y ˆ = .9671−.0502⎜⎟ − .0176⎜⎟ + .0062⎜⎟⎝10.8012⎠ ⎝10.8012⎠ ⎝10.8012⎠32.00000492 x − .000446058x+ .007290688x+ .96034944 .23.0062t . We reject H o if either ≥ t. 025, −4= t.025,3= 3. 182.0031t ≤ −3.182 . Since 2.00 is neither ≥ 3. 182 nor ≤ −3. 182c. = = 2. 00cubic term should be deleted.d. SSE Σ( − ˆ )= y iy iand the y i' stnor if, we cannot reject H o ; theˆ are the same from the standardized as from theunstandardized model, so SSE, SST, and R 2 will be identical for the two models.e. Σy 2 i= 6. 355538 , = 6. 664Σ iy , so SST = .011410. For the quadratic model R 2 =.987 and for the cubic mo del, R 2 = .994; The two R 2 values are very close, suggestingintuitively that the cubic term is relatively unimportant.34.a. x = 49. 9231x − 49.9231and s x = 41.3652 so for x = 50, x ′ == . 001859 and41.36522µ ˆ = .8733 − .3255(.001859) + .0448(.001859) . 873 .Y⋅50 =b. SST = 1.456923 and SSE = .117521, so R 2 = .919.c.d.⎛ x − 49.9231 ⎞ ⎛ x − 49.9231 ⎞. 8733 − .3255⎜⎟ + .0448⎜⎟⎝ 41.3652 ⎠ ⎝ 41.3652 ⎠21.200887− .01048314 x + .00002618 x .ˆ2ˆ= β∗22s xβ so the estimated sd of ˆβ2is the estimated sd of⎛ 1 ⎞sˆ= (.0319) ⎜ ⎟ = . 00077118 .β 2⎝ 41.3652 ⎠2∗ ˆβ2multiplied by1 :s x.0448e. t = = 1. 40 which is not significant (compared to ± t .025, 9at level .05), so the.0319quadratic term should not be retained.414