Multiple Regression: Correction to Data

 The following dataset gives information on makes of cars taken from the
April, 1990 issue of Consumer Reports. In particular, the data frame
"fuel.frame" contains data on mileage, weight of car, engine
displacement and size of car (qualitative, 6 possibilities, saved under
"Type").

 Question: Can we use a regression model to predict mileage from some of
these variables?

 We should begin with some plots to study the relationships among the
variables.

 ISSUE: When we plot Mileage vs. Displacement, something strange appears in
 plots:

 plot(Mileage ~ Disp, fuel.frame)

 It appears that some Displacement values are near 0, which doesn't make any
sense. Let's take a look at a part of the data frame:

> fuel.frame[1:3,]
       row.names Weight  Disp. Mileage     Fuel  Type
1 Eagle.Summit.4   2560   0.97      33 3.030303 Small
2  Ford.Escort.4   2345 114.00      33 3.030303 Small
3 Ford.Festiva.4   1845   0.81      37 2.702703 Small

 We see that these small displacments appear to be off by a factor of around
100 (the 0.97 should be 97, etc.). So we're going to tell R to multiply all
these small displacements by 100 with the following command:

>  Dispnew <- ifelse(fuel.frame$Disp < 10, fuel.frame$Disp*100,
                      fuel.frame$Disp)

 This command is telling R to take any displacement that is less than 10 and
multiply it by 100. If it is greater than or equal to 10, then leave it
alone.

 Now will put this into our data frame:

> fuel.frame <- cbind(fuel.frame, Dispnew)

 Now let's redo our model:

> fuel.fit1new <- lm(Mileage ~ Weight + Dispnew, data = fuel.frame)
> summary(fuel.fit1new)

Call:
lm(formula = Mileage ~ Weight + Dispnew, data = fuel.frame)

Residuals:
    Min      1Q  Median      3Q     Max 
-4.6633 -1.7553 -0.1638  1.9454  5.5482 

Coefficients:
             Estimate Std. Error t value Pr(>|t|)    
(Intercept) 48.039428   2.263134  21.227  < 2e-16 ***
Weight      -0.007927   0.001139  -6.963 3.67e-09 ***
Dispnew     -0.003025   0.010424  -0.290    0.773    
---
Signif. codes:  0 *** 0.001 ** 0.01 * 0.05 . 0.1   1 

Residual standard error: 2.583 on 57 degrees of freedom
Multiple R-squared: 0.7193,     Adjusted R-squared: 0.7094 
F-statistic: 73.02 on 2 and 57 DF,  p-value: < 2.2e-16 











> anova(fuel.fit1new) # NOTE: This adds terms sequentially (first to last)

Analysis of Variance Table

Response: Mileage
          Df Sum Sq Mean Sq  F value Pr(>F)    
Weight     1 973.75  973.75 145.9588 <2e-16 ***
Dispnew    1   0.56    0.56   0.0842 0.7727    
Residuals 57 380.27    6.67                    
---
Signif. codes:  0 *** 0.001 ** 0.01 * 0.05 . 0.1   1 

> par(mfrow=c(3,2))
> plot(fuel.fit1new, which = 1:6) # Gives some summary plots of the fitted model