problem-3.30

problem-3.30  The slope appears in the output of lm(). The scatterplot shows a linear trend between the transformed variables that is not apparent in a scatterplot of the original variables.
> library(MASS)                 # loads data set and lqs()
> names(Animals)
[1] "body"  "brain"
> plot(log(brain) ~ log(body), data = Animals)
> res = lm(log(brain) ~ log(body), data = Animals)
> res

Call:
lm(formula = log(brain) ~ log(body), data = Animals)

Coefficients:
(Intercept)    log(body)
      2.555        0.496
    
To compare to the output of lqs().
> lqs(log(brain) ~ log(body), data = Animals)
Call:
lqs.formula(formula = log(brain) ~ log(body), data = Animals)

Coefficients:
(Intercept)    log(body)
      1.816        0.776

Scale estimates 0.464 0.463

There are three influential points in the scatterplot of the log-transformed data causing the big change in the slope of the regression line.