multiple-reg.R

fit1=lm(mpg~cyl+hp,data=mtcars)
summary(fit1)

## 
## Call:
## lm(formula = mpg ~ cyl + hp, data = mtcars)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -4.4948 -2.4901 -0.1828  1.9777  7.2934 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 36.90833    2.19080  16.847  < 2e-16 ***
## cyl         -2.26469    0.57589  -3.933  0.00048 ***
## hp          -0.01912    0.01500  -1.275  0.21253    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 3.173 on 29 degrees of freedom
## Multiple R-squared:  0.7407, Adjusted R-squared:  0.7228 
## F-statistic: 41.42 on 2 and 29 DF,  p-value: 3.162e-09

hist(fit1$residuals)

plot(mtcars$mpg,fit1$fitted.values)

dim(mtcars)

## [1] 32 11

data1=mtcars[c(1:16),]
fit1_1=lm(mpg~cyl+hp,data=data1)
summary(fit1_1)

## 
## Call:
## lm(formula = mpg ~ cyl + hp, data = data1)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -3.6288 -0.8117  0.5287  0.9580  2.9599 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 29.54400    2.63039  11.232  4.6e-08 ***
## cyl         -0.47767    0.80376  -0.594   0.5625    
## hp          -0.05704    0.02370  -2.407   0.0317 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 2.055 on 13 degrees of freedom
## Multiple R-squared:  0.7872, Adjusted R-squared:  0.7545 
## F-statistic: 24.05 on 2 and 13 DF,  p-value: 4.281e-05

data2=mtcars[c(13:20),]
fit1_2=lm(mpg~cyl+hp,data=data2)
summary(fit1_2)

## 
## Call:
## lm(formula = mpg ~ cyl + hp, data = data2)
## 
## Residuals:
##          Merc 450SL         Merc 450SLC  Cadillac Fleetwood Lincoln Continental 
##              2.4885              0.3885             -3.0348             -2.4841 
##   Chrysler Imperial            Fiat 128         Honda Civic      Toyota Corolla 
##              2.6419              0.4420             -2.3289              1.8869 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 46.46121    5.93709   7.826 0.000546 ***
## cyl         -2.71718    2.20013  -1.235 0.271694    
## hp          -0.05507    0.06077  -0.906 0.406357    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 2.753 on 5 degrees of freedom
## Multiple R-squared:  0.9455, Adjusted R-squared:  0.9237 
## F-statistic: 43.37 on 2 and 5 DF,  p-value: 0.0006934