二
1)
x<-c(20,25,30,35,40,45,50,55,60,65)
y<-c(13.2,15.1,16.4,17.1,17.9,18.7,19.6,21.2,22.5,24.3) lm.reg<-lm(y~x);lm.reg summary(lm.reg) Call:
lm(formula = y ~ x) Coefficients:
(Intercept) x 9.121 0.223
> summary(lm.reg) Call:
lm(formula = y ~ x) Residuals:
Min 1Q Median 3Q Max -0.67273 -0.33333 -0.07273 0.34545 0.68182 Coefficients:
Estimate Std. Error t value Pr(>|t|) (Intercept) 9.12121 0.47708 19.12 5.8e-08 *** x 0.22303 0.01063 20.97 2.8e-08 *** ---
Signif. codes:
0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 0.483 on 8 degrees of freedom Multiple R-squared: 0.9821,
Adjusted R-squared: 0.9799
F-statistic: 439.8 on 1 and 8 DF, p-value: 2.805e-08 由上述r语言计算得：回归方程为，y=0.22303+9.12121x 2)
方程的检验: F分布的p值为2.805e-08<0.001, 因此方程是非常 显著的,相关系数的平方R2=0.9821, 表明数据 中98%可由回归方程来描述.
3)
point<-data.frame(x=42)
lm.pred<-predict(lm.reg,point,interval=\lm.pred
fit lwr upr 1 18.48848 17.32034 19.65663 由计算结果得到:
当x =42时,y的预测值为18.48848, 预测区间为[17.32034, 19.65663].