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7406_Solution2 - ISyE 7406 Spring-2007 Instructor...

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ISyE 7406, Spring-2007 Instructor: Kwok-Leung Tsui Assignment # 2 (Solution) Question 1: Sample commands in R: Best Subset: regsubset, leaps Ridge Regression: lm.ridge Best Subset R Output: Call: lm(formula = y.train ., data = x.train[, best1$which[9, ]]) Residuals: Min 1Q Median 3Q Max -1.58852 -0.44174 0.01304 0.52613 1.93127 Coefficients: Estimate Std. Error t value Pr( > | t | ) (Intercept) 2.49489 0.09316 26.780 < 2e-16 *** lcavol 0.73971 0.09318 7.938 4.14e-11 *** lweight 0.36670 0.10237 3.582 0.000658 *** Signif. codes: 0 ’***’ 0.001 ’**’ 0.01 ’*’ 0.05 ’.’ 0.1 ’ ’ 1 Residual standard error: 0.7613 on 64 degrees of freedom Multiple R-Squared: 0.6148, Adjusted R-squared: 0.6027 F-statistic: 51.06 on 2 and 64 DF, p-value: 5.54e-14 Cross Validation Results: (may different from the book) Subset size 1 2 3 4 Average Prediction Error 0.7094301 0.6172499 0.6082169 0.5888468 Standard Error 0.1446 0.1564 0.1425 0.1208 Subset size 5 6 7 8 Average Prediction Error 0.6148808 0.5841840 0.5939956 0.6188241 Standard Error 0.1151 0.1033 0.1355 0.1351 Ridge Regression R Output:(may different from the book) Intercept lcavol lweight age lbph svi lcp gleason pgg45 2.47 0.356 0.243 -0.023 0.151 0.212 0.0420 0.049 0.116 For cross-validation, you can refer to the following picture.(may different from the book) 1
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