以每年參觀Lake Keepit的人數為例 數98級乙班 林柏佐 494402345

Variable Dist=Distance Inc=Family Income Size=Family Members Y=Numbers of Vistors

pair

Residuals Plot-SLR

Box-Cox

Transformation fm1<-lm(log(Y+1)~Dist+Inc+Size) 在做轉換時，要注意各係數都必須是正數，因為Y有0，所以我讓其加1，來做regression

Residuals Plot-Transformation

Select Model fm2<-lm(log(Y+1)~Dist+Size) Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 1.613546 0.104927 15.378 < 2e-16 *** Dist -0.014158 0.001071 -13.218 < 2e-16 *** Size 0.084795 0.023403 3.623 0.000353 *** --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Residual standard error: 0.5169 on 247 degrees of freedom Multiple R-squared: 0.4295, Adjusted R-squared: 0.4249 F-statistic: 92.99 on 2 and 247 DF, p-value: < 2.2e-16

Residuals Plot-Select Model

Variance Stable Call: lm(formula = sqrt(Y) ~ Dist + Inc + Size) Residuals: Min 1Q Median 3Q Max -1.6186 -0.4273 0.0727 0.4570 1.6070 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 1.884998 0.184333 10.226 < 2e-16 *** Dist -0.017528 0.001348 -13.000 < 2e-16 *** Inc 0.024612 0.018196 1.353 0.17742 Size 0.104933 0.029553 3.551 0.00046 *** --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Residual standard error: 0.6507 on 246 degrees of freedom Multiple R-squared: 0.424, Adjusted R-squared: 0.417 F-statistic: 60.36 on 3 and 246 DF, p-value: < 2.2e-16

Residuals Plot-Variance Stable

WLS lm(formula = sqrt(Y) ~ Dist + Inc + Size, weights = wi) Residuals: Min 1Q Median 3Q Max -3.1818 -0.8134 0.1118 0.9051 3.2484 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 1.874293 0.181835 10.308 < 2e-16 *** Dist -0.018063 0.001328 -13.599 < 2e-16 *** Inc 0.027104 0.017669 1.534 0.126323#收入太低決定將其拿掉 Size 0.113891 0.029023 3.924 0.000113 *** --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Residual standard error: 1.233 on 246 degrees of freedom Multiple R-squared: 0.4511, Adjusted R-squared: 0.4444 F-statistic: 67.38 on 3 and 246 DF, p-value: < 2.2e-16

Residuals Plot-WLS

WLS+Model Selection Call: lm(formula = sqrt(Y) ~ Dist + Size, weights = wi) Residuals: Min 1Q Median 3Q Max -3.2532 -0.8942 0.1028 0.9767 3.0845 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 2.077797 0.124694 16.663 < 2e-16 *** Dist -0.018099 0.001332 -13.590 < 2e-16 *** Size 0.109893 0.028985 3.791 0.000188 *** --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Residual standard error: 1.236 on 247 degrees of freedom Multiple R-squared: 0.4458, Adjusted R-squared: 0.4413 F-statistic: 99.34 on 2 and 247 DF, p-value: < 2.2e-16

Residuals Plot-WLS+Model Selcetion

結論 最後我選擇 這個model, 但是其實還是有很多要改進，它的R-squared太低，解釋力不夠。或許利用generalized least square可以解決這個問題。

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