Splus handout:  Transformations and Graphical Diagnostics

> #Data:  brain (g) and body (kg) weights for 62 species of mammals
> wts<-read.table("alr.144",header=T)

> motif()
> par(mfrow=c(3,3))
> plot(wts$body,wts$brain)
> title("Fig 1:  body vs brain weight")


>#Can use the menus for this part:
> wts.lm<-lm(brain~body,wts)
> summary(wts.lm)

Call: lm(formula = brain ~ body, data = wts)
Residuals:
    Min     1Q Median     3Q  Max 
 -810.1 -88.52 -79.64 -13.02 2050

Coefficients:
              Value Std. Error t value Pr(>|t|) 
(Intercept) 91.0039 43.5526     2.0895  0.0409 
       body  0.9665  0.0477    20.2777  0.0000 

Residual standard error: 334.7 on 60 degrees of freedom
Multiple R-Squared: 0.8727 
F-statistic: 411.2 on 1 and 60 degrees of freedom, the p-value is 0 

Correlation of Coefficients:
     (Intercept) 
body -0.2176    


>#Compute the studentized residuals:
>#As far as I can tell, you need to use the "old" lsfit function along
>#with the function "ls.diag" to compute studentized residuals.  You can 
>#also compute the studentized residuals using the formula given in
>#class, but this may result in rounding errors.

#Refit the same model using lsfit.

>wts.lsfit<-lsfit(wts$body,wts$brain)
>ls.print(wts.lsfit)

Residual Standard Error = 334.7199,  Multiple R-Square = 0.8727
N = 62,  F-statistic = 411.1869 on 1 and 60 df, p-value = 0

             coef std.err  t.stat p.value 
Intercept 91.0039 43.5526  2.0895  0.0409
        X  0.9665  0.0477 20.2777  0.0000



> e.star<-ls.diag(wts.lsfit)$stud.res

> #residual plots
> plot(wts$body,e.star)
> title("Figure 2")
> abline(h=0)
> qqnorm(e.star)
> title("Figure 3")
_______________________________________________________________________
> #Try transforming the response
> wts2.lsfit<-lsfit(wts$body,log(wts$brain))
> ls.print(wts2.lsfit)

Residual Standard Error = 2.217,  Multiple R-Square = 0.1923
N = 62,  F-statistic = 14.2827 on 1 and 60 df, p-value = 4e-04

            coef std.err  t.stat p.value 
Intercept 2.9030  0.2885 10.0635   0e+00
        X 0.0012  0.0003  3.7792   4e-04


> e.star<-ls.diag(wts2.lsfit)$stud.res

> plot(wts$body,log(wts$brain))
> title("Fig 4:  body vs log(brain weight)")
> plot(wts$body,e.star)
> title("Figure 5")
> abline(h=0)
> qqnorm(e.star)
> title("Figure 6")
_______________________________________________________________________
> #Try transforming the response and the predictor
> wts3.lsfit<-lsfit(log(wts$body),log(wts$brain))
> ls.print(wts3.lsfit)

Residual Standard Error = 0.6941,  Multiple R-Square = 0.9208
N = 62,  F-statistic = 697.8027 on 1 and 60 df, p-value = 0

            coef std.err  t.stat p.value 
Intercept 2.1345  0.0960 22.2287       0
        X 0.7517  0.0285 26.4160       0


 e.star<-ls.diag(wts3.lsfit)$stud.res

 plot(log(wts$body),log(wts$brain))
 title("Fig 7:  log(body) vs log(brain weight)")

 #residual plots
 plot(log(wts$body),e.star)
 title("Figure 6")
 abline(h=0)
 qqnorm(e.star)
 title("Figure 7")