Chapter 9 Multiple Regression 391
e. Compare the parameter value for
FRB_Index in the fi rst equation with
that in the second. How are they dif-
ferent? Does your interpretation of the
effect of production on unemploy-
ment change from one regression to
the other?
f. Calculate the correlation between
FRB_Index and Year. How signifi cant
is the correlation?
g. Save your changes to the workbook
and write a report summarizing your
observations.
- The Beer Rating workbook contains rat-
ings from ratebeer.com along with val-
ues of IBU (international bittering units,
a measure of bitterness) and ABV
(alcohol by volume) for 25 beers.
a. Open the Beer Rating workbook from
the Chapter09 folder and save it as
Beer Rating Regression.
b. Create a correlation matrix and
scatterplot matrix for Rating, IBU,
and ABV.
c. Which beer has the highest rating?
The lowest?
d. Describe the relationships among the
three variables. Given how the vari-
ables are related, do the correlations
fully describe the strengths of the re-
lationships? Explain.
e. Regress Rating on IBU and ABV.
Notice that, although both predictors
have strongly signifi cant correlations
with Rating, they do not both have
signifi cant regression coeffi cients.
How do you explain this?
f. Plot the residuals from (e) to check
the assumptions. Which of the as-
sumptions is clearly not satisfi ed?
Why should this be expected based
on (d)?
g. Repeat the multiple regression in (e)
with the square of IBU as a third pre-
dictor. Check the assumptions again.
h. How effective is the regression in (g)?
Interpret the coeffi cients with regard
to statistical signifi cance and sign. In
particular, discuss the coeffi cient for
the square of IBU.
i. Save your changes to the workbook
and then write a report summarizing
your conclusions.
