288 Chapter 9 Correlation and Regression
9.26 Make up your own example along the lines of the “smoking versus life expectancy” exam-
ple given on pp. 262–263 to illustrate the relationship between and accountable variation.
9.27 Moore and McCabe (1989) found some interesting data on the consumption of alcohol and
tobacco that illustrate an important statistical concept. Their data, taken from the Family
Expenditure Survey of the British Department of Employment, follow. The dependent vari-
ables are the average weekly household expenditures for alcohol and tobacco in 11 regions
of Great Britain.
Region Alcohol Tobacco
North 6.47 4.03
Yorkshire 6.13 3.76
Northeast 6.19 3.77
East Midlands 4.89 3.34
West Midlands 5.63 3.47
East Anglia 4.52 2.92
Southeast 5.89 3.20
Southwest 4.79 2.71
Wales 5.27 3.53
Scotland 6.08 4.51
Northern Ireland 4.02 4.56
a. What is the relationship between these two variables?
b. Popular stereotypes have the Irish as heavy drinkers. Do the data support that belief?
c. What effect does the inclusion of Northern Ireland have on our results? (A scatterplot
would be helpful.)
9.28 Using the data from Mireault (1990) in the file Mireault.dat, at http://www.uvm.edu/~dhowell/
methods7//DataFiles/DataSets.html is there a relationship between how well a student per-
forms in college (as assessed by GPA) and that student’s psychological symptoms (as
assessed by GSIT)?
9.29 Using the data referred to in Exercise 9.28,
a. Calculate the correlations among all of the Brief Symptom Inventory subscales. (Hint:
Virtually all statistical programs are able to calculate these correlations in one state-
ment. You don’t have to calculate each one individually.)
b. What does the answer to (a) tell us about the relationships among the separate scales?
9.30 One of the assumptions lying behind our use of regression is the assumption of homogene-
ity of variance in arrays. One way to examine the data for violations of this assumption is to
calculate predicted values of Yand the corresponding residuals (Y 2 ). If you plot the
residuals against the predicted values, you should see a more or less random collection of
points. The vertical dispersion should not increase or decrease systematically as you move
from right to left, nor should there be any other apparent pattern. Create the scatterplot for
the data from Cancer.dat at the Web site for this book. Most computer packages let you re-
quest this plot. If not, you can easily generate the appropriate variables by first determining
the regression equation and then feeding that equation back into the program in a “compute
statement” (e.g., “set Pred 5 0.256*GSIT 1 4.65,” and “set Resid 5 TotBPT 2 Pred”).
9.31 The following data represent the actual heights and weights referred to earlier for male col-
lege students.
a. Make a scatterplot of the data.
b. Calculate the regression equation of weight predicted from height for these data. Interpret
the slope and the intercept.YNr^2