chapter 1

Chapter 13: Nonlinear and Multiple Regression76.a. 80.79b. Yes, p-value = .007 which is less than .01.c. No, p-value = .043 which is less than .05.d. . 14167 ± ( 2.447 )(.03301) = (.0609,.2224)e. µ 6. 3067 , using α = . 05 , the interval isˆy⋅9 , 66 =6.3067 ±22( 2.447) (.4851) + (.162) = ( 5.06,7.56)77.ˆ ˆ ˆ 2a. Estimate = β + β ( 15) + β ( 3.5) = 180 + ( 1)( 15) + ( 10.5)( 3.5) 231. 750 12=2 117.4b. R = 1−= . 9031210.30c. H β = β 0 vs. Ha: either β1or β 0 (or both) . .9032f = = 41. 9 , which0:1 2=greatly exceeds.01,2, 92 ≠.0979F so there appears to be a useful linear relationship.2d.117.4022s = = 13. 044 , s + ( est.st.dev) = 3. 806 , t . 025,9 = 2. 262 . The P.I. is12 − 3229 .5 ± 2.262 3.806 = 220.9,238.1( )( ) ( )2 2 278. The second order model has predictors x1, x2, x3, x1, x2, x3, x1x2, x1x3,x2x3withβ1β , β , β , β , β , β , β ,0:4 5 6 7 8 9=, βcorresponding coefficients2 3 4 5 6 7 8 9. We wish to testH β = β = β = β = β = β 0 vs. the alternative that at least one of these six821.5−5027.1530.9502.71( ) β ' is( )is not zero. The test statistic value is 9−3f =( )= = 1. 1. Since5027.1( )20−101.1 < F 3. 22 , H o cannot be rejected. It doesn’t appear as though any of the. 05,6,10=quadratic or interaction carriers should be included in the model.79. There are obviously several reasonable choices in each case.a. The model with 6 carriers is a defensible choice on all three grounds, as are those with 7and 8 carriers.b. The models with 7, 8, or 9 carriers here merit serious consideration. These models meritconsideration because R 2 , , and CK meet the variable selection criteria given inSection 13.5.kMSE k436