自编R 程序计算判定系数
>x1=rchisq(100,6)
>x2=rnorm(100,2,1)
>err=rnorm(100,0,0.5)
>y=2.5+2*x1+1.5*x2+err
>plot(x1+x2,y,col=4)
>lm(y~x1+x2)
>
fit=lm(y~x1+x2)
>summary(fit)
Call:
lm(formula=y ~x1+x2)
Residuals:
Min 1Q
-1.30115-0.32732Median 0.058363Q 0.26329Max 1.20733
Coefficients:
(Intercept)
x1
x2
---
Signif. codes:0‘***’0.001‘**’0.01‘*’0.05‘.’0.1‘’1Estimate Std. Error t value Pr(>|t|)2.536430.1561016.25
Residual standard error:0.5009on 97degrees of freedom
Multiple R-squared:0.9953, Adjusted R-squared:0.9952F-statistic:1.018e+04on 2and 97DF, p-value:
有上述回归分析可知：判定系数R^2=0.9953调整后的R^2为0.9952下面自己编程进行验证：
>RSS=sum(fit$residuals^2)
>RSS
[1]24.33994
>TSS=var(y)*(length(y)-1)
[1]5131.309
>ESS=TSS-RSS
>ESS
[1]5106.97
>r_squared=ESS/TSS
>r_squared
[1]0.9952566
>adjustedr_squared=1-(1-r_squared)*(length(y)-1)/(length(y)-2)>adjustedr_squared
[1]0.9952082
由此可见0.9952566≈0.9953
0.9952082≈0.9952
则r_squared=MultipleR-squared
adjustedr_squared=Adjusted R-squared
Test
+{RSS=sum(RE)
+TSS=var(Y)*(length(Y)-1)
+ESS=TSS-RSS
+r_squared=ESS/TSS
+return(r_squared)}
>Test(r,y)
自编R 程序计算判定系数
>x1=rchisq(100,6)
>x2=rnorm(100,2,1)
>err=rnorm(100,0,0.5)
>y=2.5+2*x1+1.5*x2+err
>plot(x1+x2,y,col=4)
>lm(y~x1+x2)
>
fit=lm(y~x1+x2)
>summary(fit)
Call:
lm(formula=y ~x1+x2)
Residuals:
Min 1Q
-1.30115-0.32732Median 0.058363Q 0.26329Max 1.20733
Coefficients:
(Intercept)
x1
x2
---
Signif. codes:0‘***’0.001‘**’0.01‘*’0.05‘.’0.1‘’1Estimate Std. Error t value Pr(>|t|)2.536430.1561016.25
Residual standard error:0.5009on 97degrees of freedom
Multiple R-squared:0.9953, Adjusted R-squared:0.9952F-statistic:1.018e+04on 2and 97DF, p-value:
有上述回归分析可知：判定系数R^2=0.9953调整后的R^2为0.9952下面自己编程进行验证：
>RSS=sum(fit$residuals^2)
>RSS
[1]24.33994
>TSS=var(y)*(length(y)-1)
[1]5131.309
>ESS=TSS-RSS
>ESS
[1]5106.97
>r_squared=ESS/TSS
>r_squared
[1]0.9952566
>adjustedr_squared=1-(1-r_squared)*(length(y)-1)/(length(y)-2)>adjustedr_squared
[1]0.9952082
由此可见0.9952566≈0.9953
0.9952082≈0.9952
则r_squared=MultipleR-squared
adjustedr_squared=Adjusted R-squared
Test
+{RSS=sum(RE)
+TSS=var(Y)*(length(Y)-1)
+ESS=TSS-RSS
+r_squared=ESS/TSS
+return(r_squared)}
>Test(r,y)