# Problem 15.2
speed=read.table("speed.txt")
speed
names(speed)=c("mpg","mph","V3")
attach(speed)
plot(mph,mpg)
speed.lm=lm(mpg~mph)
summary(speed.lm)
anova(speed.lm)
plot(fitted(speed.lm),resid(speed.lm))

     Coefficients:
     		 Estimate Std. Error t value Pr(>|t|)    
     (Intercept) 12.74637    2.49877   5.101 2.57e-05 ***
     mph          0.03908    0.05312   0.736    0.469    
     
     Residual standard error: 5.666 on 26 degrees of freedom
     Multiple R-Squared: 0.02039,    Adjusted R-squared: -0.01729 
     F-statistic: 0.5411 on 1 and 26 DF,  p-value: 0.4686 
     
     Response: mpg
     	       Df Sum Sq Mean Sq F value Pr(>F)
     mph        1  17.37   17.37  0.5411 0.4686
     Residuals 26 834.63   32.10               

speed.lm2=lm(mpg~mph+I(mph^2))
summary(speed.lm2)
anova(speed.lm2)
plot(mph,mpg)
lines(mph[order(mph)],fitted(speed.lm2)[order(mph)])
plot(fitted(speed.lm2),resid(speed.lm2))
plot(mph,resid(speed.lm2))

     Coefficients:
     		   Estimate Std. Error t value Pr(>|t|)    
     (Intercept) -7.5555495  1.4241091  -5.305 1.69e-05 ***
     mph          1.2716937  0.0757321  16.792 3.99e-15 ***
     I(mph^2)    -0.0145014  0.0008719 -16.633 4.97e-15 ***
     
     Residual standard error: 1.663 on 25 degrees of freedom
     Multiple R-Squared: 0.9188,     Adjusted R-squared: 0.9123 
     F-statistic: 141.5 on 2 and 25 DF,  p-value: 2.338e-14 
     
     Response: mpg
     	       Df Sum Sq Mean Sq  F value    Pr(>F)    
     mph        1  17.37   17.37   6.2775   0.01911 *  
     I(mph^2)   1 765.46  765.46 276.6417 4.973e-15 ***
     Residuals 25  69.17    2.77                       

speed.lm3=lm(mpg~mph+I(mph^2)+I(mph^3)+I(mph^4))
summary(speed.lm3)
anova(speed.lm3)
plot(mph,mpg)
lines(mph[order(mph)],fitted(speed.lm3)[order(mph)])
plot(fitted(speed.lm3),resid(speed.lm3))
plot(mph,resid(speed.lm3))

vote=read.table("vote.txt")
attach(vote)
plot(Dem1980,Dem1984)

vote.lm=lm(Dem1984~Dem1980)
summary(vote.lm)
plot(fitted(vote.lm),resid(vote.lm))

plot(Dem1980,Dem1984,pch=Southern)
vote.lm2=lm(Dem1984~Dem1980+Southern)
summary(vote.lm2)
plot(fitted(vote.lm2),resid(vote.lm2))

     Coefficients:
                 Estimate Std. Error t value Pr(>|t|)    
     (Intercept) 12.09531    2.24456   5.389 2.24e-06 ***
     Dem1980      0.72250    0.05842  12.366  < 2e-16 ***
     Southern    -7.78197    1.04467  -7.449 1.71e-09 ***
     
     Residual standard error: 2.856 on 47 degrees of freedom
     Multiple R-Squared: 0.7688,     Adjusted R-squared: 0.7589 
     F-statistic: 78.13 on 2 and 47 DF,  p-value: 1.134e-15 

vote.lm3=lm(Dem1984~Dem1980*Southern)
summary(vote.lm3)

     Coefficients:
     		      Estimate Std. Error t value Pr(>|t|)    
     (Intercept)       9.94338    2.30167   4.320 8.25e-05 ***
     Dem1980           0.77978    0.06011  12.973  < 2e-16 ***
     Southern          9.52243    7.05922   1.349   0.1840    
     Dem1980:Southern -0.38663    0.15616  -2.476   0.0170 *  
     
     Residual standard error: 2.712 on 46 degrees of freedom
     Multiple R-Squared: 0.796,      Adjusted R-squared: 0.7827 
     F-statistic: 59.82 on 3 and 46 DF,  p-value: 6.548e-16 

plot(Dem1980,Dem1984)
lines(Dem1980[Southern==1],fitted(vote.lm3)[Southern==1])
lines(Dem1980[Southern==0],fitted(vote.lm3)[Southern==0])