Note that we could have recalculated the weights but the difference would not be much and the question specified to use the weights from part (b). PROC REG Data=ChromaOut plots=none; Model LogOut=Amt1 Amt5 Amt20; Weight w; Plot Student.*Predicted.; Plot Student.*nqq.; run; Weight: w Analysis of Variance Source DF Sum of Squares Mean Square F Value Pr > F Model 3 1245.56987 415.18996 68612.8 <.0001 Error 16 0.09682 0.00605 Corrected Total 19 1245.66669 Root MSE 0.07779 R-Square 0.9999 Dependent Mean 5.43278 Adj R-Sq 0.9999 Coeff Var 1.43185 Parameter Estimates Variable DF Parameter Estimate Standard Error t Value Pr > |t| Intercept 1 1.95207 0.05182 37.67 <.0001 Amt1 1 1.43833 0.05216 27.58 <.0001 Amt5 1 3.39010 0.05256 64.50 <.0001 Amt20 1 4.87291 0.05204 93.64 <.0001
[4 marks] We note that the parameter estimates are exactly the same in the weighted and unweighted analysis but the standard errors are quite different. The weighted mean squared error is larger than in the unweighted case and so the standard errors in the weighted regression are larger. The R 2 in the weighted regression is almost 100% slightly better than in the unweighted regression. Most importantly, the diagnostic plots for the weighted regression suggest that the variability is now constant and the linearity assumption does not seem violated. There may still be some question about the normality but the weighted studentized residuals are closer to normal than the unweighted. [3 marks]
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