Linear regression

year <- c(2000 ,   2001  ,  2002  ,  2003 ,   2004)
rate <- c(9.34 ,   8.50  ,  7.62  ,  6.93  ,  6.60)
fit <- lm(rate ~ year)
fit
## 
## Call:
## lm(formula = rate ~ year)
## 
## Coefficients:
## (Intercept)         year  
##    1419.208       -0.705
summary(fit)
## 
## Call:
## lm(formula = rate ~ year)
## 
## Residuals:
##      1      2      3      4      5 
##  0.132 -0.003 -0.178 -0.163  0.212 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)   
## (Intercept) 1419.2080   126.9496    11.2   0.0015 **
## year          -0.7050     0.0634   -11.1   0.0016 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.201 on 3 degrees of freedom
## Multiple R-squared:  0.976,  Adjusted R-squared:  0.968 
## F-statistic:  124 on 1 and 3 DF,  p-value: 0.00156
anova(fit)
## Analysis of Variance Table
## 
## Response: rate
##           Df Sum Sq Mean Sq F value Pr(>F)   
## year       1   4.97    4.97     124 0.0016 **
## Residuals  3   0.12    0.04                  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
library(car)
head(Prestige)
##                     education income women prestige census type
## gov.administrators      13.11  12351 11.16     68.8   1113 prof
## general.managers        12.26  25879  4.02     69.1   1130 prof
## accountants             12.77   9271 15.70     63.4   1171 prof
## purchasing.officers     11.42   8865  9.11     56.8   1175 prof
## chemists                14.62   8403 11.68     73.5   2111 prof
## physicists              15.64  11030  5.13     77.6   2113 prof
fit <- lm(prestige ~education +log2(income) +women,data=Prestige)
fit
## 
## Call:
## lm(formula = prestige ~ education + log2(income) + women, data = Prestige)
## 
## Coefficients:
##  (Intercept)     education  log2(income)         women  
##    -110.9658        3.7305        9.3147        0.0469
summary(fit)
## 
## Call:
## lm(formula = prestige ~ education + log2(income) + women, data = Prestige)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -17.364  -4.429  -0.101   4.316  19.179 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  -110.9658    14.8429   -7.48  3.3e-11 ***
## education       3.7305     0.3544   10.53  < 2e-16 ***
## log2(income)    9.3147     1.3265    7.02  2.9e-10 ***
## women           0.0469     0.0299    1.57     0.12    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 7.09 on 98 degrees of freedom
## Multiple R-squared:  0.835,  Adjusted R-squared:  0.83 
## F-statistic:  165 on 3 and 98 DF,  p-value: <2e-16
anova(fit)
## Analysis of Variance Table
## 
## Response: prestige
##              Df Sum Sq Mean Sq F value  Pr(>F)    
## education     1  21608   21608  429.55 < 2e-16 ***
## log2(income)  1   3233    3233   64.28 2.3e-12 ***
## women         1    124     124    2.46    0.12    
## Residuals    98   4930      50                    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1