chapter 1

Chapter 13: Nonlinear and Multiple Regression68.a.Scatter Plot of Log(edges) vs Log(time)3Log(time2101 2 3 4Log(edgeYes, the scatter plot of the two transformed variables appears quite linear, and thussuggests a linear relationship between the two.b. Letting y denote the variable ‘time’, the regression model for the variables y′ and x′ islog ( y) = y′= α + βx′+ ε ′10. Exponentiating (taking the antilogs of ) both sidesα + β log( x) + ε ′ α β ε′γ 1gives y = 10 = ( 10 )( x ) 10 = γ x ⋅ ε ; i.e., the model isy γ= γ x 10⋅ ε where γ = α 0and γ1= β . This model is often called a “powerfunction” regression model.c. Using the transformed variables y′ and x′ , the necessary sums of squares are( 42.4)( 21.69)Sx′y′= 68 .640 −= 11.1615 and162( 42.4)S 11.1615Sx′x′= 126.34 − = 13.98 . Therefore ˆ1 x′y′β = = . 7983916S 13.98=21.69 ⎛ 42.4 ⎞ˆ0⎜ ⎟16 ⎝ 16 ⎠α −.76011γˆ1 = .7984 and γ = 10 = 10 . 1737β . The estimate of γ1isand = − (.79839) = −.76011is theny ˆ = .1737y = . 1737x0=.7984.7984( 300) 16. 5020x′x′. For x = 300, the predicted value of y is, or about 16.5 seconds.. The estimated power function model431