以每年參觀Lake Keepit的人數為例

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1 以每年參觀Lake Keepit的人數為例
數98級乙班 林柏佐

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

3 pair

4 Residuals Plot-SLR

5 Box-Cox

6 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

7 Residuals Plot-Transformation

8 Select Model fm2<-lm(log(Y+1)~Dist+Size) Coefficients:
Estimate Std. Error t value Pr(>|t|) (Intercept) < 2e-16 *** Dist < 2e-16 *** Size *** --- Signif. codes: 0 ‘***’ ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Residual standard error: on 247 degrees of freedom Multiple R-squared: , Adjusted R-squared: F-statistic: on 2 and 247 DF, p-value: < 2.2e-16

9 Residuals Plot-Select Model

10 Variance Stable Call: lm(formula = sqrt(Y) ~ Dist + Inc + Size)
Residuals: Min Q Median Q Max Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) < 2e-16 *** Dist < 2e-16 *** Inc Size *** --- Signif. codes: 0 ‘***’ ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Residual standard error: on 246 degrees of freedom Multiple R-squared: 0.424, Adjusted R-squared: 0.417 F-statistic: on 3 and 246 DF, p-value: < 2.2e-16

11 Residuals Plot-Variance Stable

12 WLS lm(formula = sqrt(Y) ~ Dist + Inc + Size, weights = wi) Residuals:
Min Q Median Q Max Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) < 2e-16 *** Dist < 2e-16 *** Inc #收入太低決定將其拿掉 Size *** --- Signif. codes: 0 ‘***’ ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Residual standard error: on 246 degrees of freedom Multiple R-squared: , Adjusted R-squared: F-statistic: on 3 and 246 DF, p-value: < 2.2e-16

13 Residuals Plot-WLS

14 WLS+Model Selection Call:
lm(formula = sqrt(Y) ~ Dist + Size, weights = wi) Residuals: Min Q Median Q Max Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) < 2e-16 *** Dist < 2e-16 *** Size *** --- Signif. codes: 0 ‘***’ ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Residual standard error: on 247 degrees of freedom Multiple R-squared: , Adjusted R-squared: F-statistic: on 2 and 247 DF, p-value: < 2.2e-16

15 Residuals Plot-WLS+Model Selcetion

16 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。

17 Thanks for your attention.
The End Thanks for your attention.