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# HW8_sol - 1 1170 a)r=0.933203 b H 0 = 0 H 1 0 n2 =0.05 15...

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1. 11 70 a) r = 0.933203 b) 0 : 0 = ρ H 0 : 1 H α = 0.05 15 , 2 / 0 15 , 025 . ) 8709 . 0 ( 1 15 933203 . 0 1 2 0 131 . 2 06 . 10 2 α t t t t r n r > = = = = Reject H 0 . c) x y 498081 . 0 72538 . 0 ˆ + = 0 : 1 0 = β H 0 : 1 1 H α = 0.05 15 , 1 , 0 15 , 1 , 05 . 0 543 . 4 16 . 101 f f f f >> = = Reject H 0 . Conclude that the model is significant at α = 0.05. This test and the one in part b) are identical. d) No problems with model assumptions are noted. 50 40 30 20 10 3 2 1 0 -1 -2 x Residual Residuals Versus x (response is y) 25 15 5 3 2 1 0 Fit ed Value Residuals Versus the Fitted Values (response is y)

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2. 11 77 a) Yes, ε β ln ln ln ln 1 0 + + = x y a) No b) Yes, ln ln ln ln 1 0 + + = x y c) Yes, + + = x y 1 1 1 0 3. 11 96 The regression equation is Population = 3549143 + 651828 Count Predictor Coef SE Coef T P Constant 3549143 131986 26.89 0.000 Count 651828 262844 2.48 0.029 S = 183802 R-Sq = 33.9% R-Sq(adj) = 28.4% Analysis of Variance Source DF SS MS F P Regression 1 2.07763E+11 2.07763E+11 6.15 0.029 Residual Error 12 4.05398E+11 33783126799 Total 13 6.13161E+11 2 1 0 -1 -2 3 2 1 0 Normal Score Residual Normal Probability Plot of the Residuals (response is y)
x y 651828 3549143 ˆ + = Yes, the regression is significant at α = 0.05. Care needs to be taken in making cause and effect statements based on a regression analysis. In this case, it is surely not the case that an increase

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HW8_sol - 1 1170 a)r=0.933203 b H 0 = 0 H 1 0 n2 =0.05 15...

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