chapter 1

Chapter 13: Nonlinear and Multiple Regression30.a. R 2 = 0.853. This means 85.3% of the variation in wheat yield is accounted for by themodel.b. − 135.44± ( 2.201)( 41.97) = ( −227.82,−43.06)c. H : µ = 15000 y⋅2.5; H : µ < 1500a y⋅2 . 5; RR : t ≤ −t= −2.718. 01, 11When x = 2.5, y ˆ =1402.151,402.15−1500t == −1.8353.5Fail to reject H o . The data does not indicatey⋅2. 5µ is less than 1500.22d. 1402.15±( 2.201) ( 136.5 ) + ( 53.5) = ( 1081.3, 1725.0 )31.a. Using Minitab, the regression equation is y = 13.6 + 11.4x - 1.72x 2 .b. Again, using Minitab, the predicted and residual values are:ŷ : 23.327 23.327 29.587 31.814 31.814 31.814 20.317y − ŷ : -.327 1.173 1.587 .914 .186 1.786 -.317Residuals Versus the Fitted Values(response i sy)234Residual10-1y323028262422-220 22 24 26 28 30 32Fitted Value201 2 3 4 5 6xThe residual plot is consistent with a quadratic model (no pattern which would suggestmodification), but it is clear from the scatter plot that the point (6, 20) has had a greatinfluence on the fit – it is the point which forced the fitted quadratic to have a maximumbetween 3 and 4 rather than, for example, continuing to curve slowly upward to amaximum someplace to the right of x = 6.c. From Minitab output, s 2 = MSE = 2.040, and R 2 = 94.7%. The quadratic model thusexplains 94.7% of the variation in the observed y’s , which suggests that the model fitsthe data quite well.412