Data on
salaries, Y83
and Y84,
for chairs of the 50 largest corporations in Chicago are available. We have
information about their age, number of shares they hold, total revenues and
income. Using a model with percentage increase given from 1983 to 1984
(i.e.,
100*(Y84-Y83)/Y83) as the response, and the remaining 4 variables as
predictors, check for outliers. Do you feel the variances of the raises are
equal? If you feel they are not equal, what transformation could be used to
improve matters? Make appropriate plots and
give your conclusions.
The
data
were collected at an oil refinery on variables affecting the octane rating
of gasoline. The variables are:
A1:
Amount of Material
1
A2:
Amount of Material
2
A3:
Amount of Material
3
A4:
A measure of
manufacturing conditions
rating:
the octane rating
Fit a model with the octane rating as the
response and the other four variables as predictors. Perform a full set of
regression diagnostics. Present the important plots, comment on their
meaning and, where appropriate, indicate what action should be taken. Since
it is easy to produce a very large number of plots, you will need to be
selective. Take care to present examples of each major category of
diagnostic. It is acceptable to just report the outcome of some plots
without actually displaying them, especially if they do not show anything
interesting.
The
data
for this question gives observations on the acceleration (ACC) of different vehicles
along with their weight-to-horsepower ration (WHP),
the speed at which they were traveling (SP),
and the grade (G;
G=0 implies the
road was horizontal).
Run a regression using
ACC as your
dependent variable without making any transformations, and obtain the
partial residual plots.
Obtain a good fitting model by
making whatever changes you think are necessary. Obtain appropriate
plots to verify that you have succeeded.
At least one of the partial
residual plots in part a
appears to show heteroscedascity (i.e., violation of var(ε)=σ2I),
. If you have been successful in
part b, the appearance of any serious heteroscedascity should vanish without your having to weight or
transform the dependent variable. Explain why you think this happens.