Chapter 8 Regression and Correlation 351- The Highway workbook contains data
on highway fatalities per million vehicle
miles from 1945 to 1984 for the United
States and the state of New Mexico.
You’ve been asked to use regression
analysis to analyze and compare the
trend in the fatality rates.
a. Open the Highway workbook from
the Chapter08 folder and save it as
Highway Regression Analysis.
b. Create a scatter plot that shows the
New Mexico and U.S. fatality rates
versus the Year variable. For each
data series, display the linear regres-
sion line, along with the regression
equation and R^2 value. How much of
the variation in highway fatalities is
explained by the linear regression line
for the two data sets? Do the trend
lines appear to be the same? What
problems would you see for this trend
line if it is extended out for many
years into the future?
c. Calculate the regression statistics for
both data sets and create residual
plots for both regressions. Do the re-
sidual plots indicate any possible vio-
lations of the regression assumptions?
d. Since these are time-ordered data, per-
form a runs test on the standardized
residuals for both the New Mexico
and U.S. data. Calculate the Durbin-
Watson test statistic for both sets of
residuals. Does your analysis lead you
to believe that one of the regression
assumptions has been violated?
e. Save your changes to the workbook
and write a report summarizing your
conclusions.
21. The HomeTax workbook contains data
on home prices and property taxes for
houses in Albuquerque, New Mexico,
sold back in 1993. Many factors were
involved in assessing the property tax
for a home during that time. You’ve been
asked to do a general analysis compar-
ing the price of the home to its assessed
property tax.
a. Open the HomeTax workbook from
the Chapter08 folder and save it as
HomeTax Regression Analysis.
b. Create a scatter plot of the tax on each
home versus that home’s price. Add
a trend line to the scatter plot and
include the regression equation and
R^2 value. How much of the variation
in property taxes is explained by the
price of the house?
c. Calculate the regression statistics,
comparing property tax to home
price, and create a plot of the
residuals.
d. Create a Normal plot of the residuals.
Is there anything in the two residual
plots that may violate the regression
assumptions?
e. Create two new variables in the work-
book named log(price) and log(tax)
that contain the Base10 logarithms
of the price and tax data. Redo steps
b through d on these transformed
data. Has the transformation solved any
problems with the regression assump-
tions on the untransformed values?
What problems, if any, still remain?
f. Save your changes to the workbook
and write a report summarizing your
conclusions.