五、一元线性回归及显著性检验及预测例题(R语言)

题目

程序及结果

1)程序

x<-c(16,23,32,31,37,40,46,48,55,60)
y<-c(13,15,16,17,17,18,19,21,22,24)
A<-data.frame(x,y)
plot(x,y)
lm.reg<-lm(y~x)
abline(lm.reg)
print(lm.reg)

1)结果

Call:
lm(formula = y ~ x)

Coefficients:
(Intercept)            x  
     8.9711       0.2379

2)程序

summary(lm.reg)

2)结果

Call:
lm(formula = y ~ x)

Residuals:
     Min       1Q   Median       3Q      Max 
-0.91258 -0.55828  0.08493  0.59832  0.75740 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)  8.97109    0.67400   13.31 9.70e-07 ***
x            0.23786    0.01645   14.46 5.12e-07 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.6842 on 8 degrees of freedom
Multiple R-squared:  0.9631,	Adjusted R-squared:  0.9585 
F-statistic:   209 on 1 and 8 DF,  p-value: 5.124e-07

3)程序

point<-data.frame(x=45)
lm.pred<-predict(lm.reg,point,interval="prediction",level=0.95)
lm.pred

3)结果

       fit      lwr      upr
1 19.67472 18.00331 21.34613

结果分析