chapter 1

Chapter 13: Nonlinear and Multiple Regression38.a. mean life = 125 + 7.75( 40) + .0950( 1100) −.009( 40)( 1100) = 143. 50b. First, the mean life when x 1 = 30 is equal to125+ 7.75( 30) + .0950x2 −.009( 30) x2= 357.50 −.175x2. So when the loadincreases by 1, the mean life decreases by .175. Second, the mean life when x 1 =40 isequal to 125+ 7.75( 40) + .0950x2 −.009( 40) x2= 435 −.265x2. So when theload increases by 1, the mean life decreases by .265.39.a. For x 1 = 2, x 2 = 8 (remember the units of x 2 are in 1000,s) and x 3 = 1 (since the outlet hasa drive-up window) the average sales arey ˆ = 10.00 −1.22 + 6.8 8 + 15.31 = 77. (i.e., $77,300 ).( ) ( ) ( ) 3b. For x 1 = 3, x 2 = 5, and x 3 = 0 the average sales arey ˆ = 10.00 −1.23 + 6.8 5 + 15.3 0 = 40. (i.e., $40,400 ).( ) ( ) ( ) 4c. When the number of competing outlets (x 1 ) and the number of people within a 1-mileradius (x 2 ) remain fixed, the sales will increase by $15,300 when an outlet has a drive-upwindow.40.ˆY⋅10 ,.5,50, 100=a. µ = 1.52 + .02( 10) −1.40( .5) + .02( 50) − .0006( 100) 1. 96ˆY⋅20 ,.5,50, 30=b. µ = 1.52 + .02( 20) −1.40( .5) + .02( 50) − .0006( 30) 1. 40β 100 ˆ4= −.06c.ˆ4= −.0006;β .x = -- in the model. There would be5x xd. There are no interaction predictors – e.g.,1 4dependence if interaction predictors involving x 4 had been included.2 20.0e. R = 1−= . 490 . For testing0: β1= β2= β3= β4= 039.2one among β 1,...,β4is not zero, the test statistic isrejected if ≥ F .= 2. 7605,4,25H vs. H a : at least.49042RkF =2( 1−R ) ( n−k−1). H o will bef . f = = 6. 0 . Because 6.0≥ 2. 76 , H o is.51025rejected and the model is judged useful (this even though the value of R 2 is not all thatimpressive).416