# 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)
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) 13.09754    2.40000   5.457 1.77e-06 ***
     Dem1980      0.69015    0.06204  11.124 9.22e-15 ***
     Southern    -7.24735    1.13936  -6.361 7.64e-08 ***
     
     Residual standard error: 3.092 on 47 degrees of freedom
     Multiple R-Squared: 0.729,      Adjusted R-squared: 0.7175 
     F-statistic: 63.23 on 2 and 47 DF,  p-value: 4.711e-14 

vote.lm3_lm(Dem1984~Dem1980*Southern)
summary(vote.lm3)

     Coefficients:
     		      Estimate Std. Error t value Pr(>|t|)    
     (Intercept)      11.24824    2.50360   4.493 4.71e-05 ***
     Dem1980           0.73904    0.06492  11.384 5.64e-15 ***
     Southern          8.19964    7.79798   1.052   0.2985    
     Dem1980:Southern -0.34524    0.17253  -2.001   0.0513 .  
     
     Residual standard error: 2.998 on 46 degrees of freedom
     Multiple R-Squared: 0.7507,     Adjusted R-squared: 0.7345 
     F-statistic: 46.18 on 3 and 46 DF,  p-value: 6.367e-14