1) Suppose that you have been asked to estimate a regression model to explain the number of people
jogging a mile or more on the school track to help decide whether to build a second track to handle all the
joggers at SFU. You collect data by living in a press box for the spring term, and you run two possible
explanatory equations:
A : Yˆ  125.0  15.0 X 1  1.0 X 2  1.5 X 3 , R 2  0.75
B : Yˆ  123.0  14.0 X  5.5 X  3.7 X , R 2  0.73
1
2
4
Where Y = the number of joggers on a given day, X1 = inches of rain that day, X2 = hours of sunshine that
day, X3 = the high temperature for that day (in Celsius), and X4 = the number of classes with term papers
due the next day.
a) Which of the two (admittedly hypothetical) equations do your prefer and why?
b) How is it possible to get different estimate signs for the coefficient of the same variable using the
same data?
2) Researchers have looked into driver fatality rates. One in particular concluded that the variance of
driving speed (the extent to which vehicles sharing the same highway drive at dramatically different
speeds) is important in determining fatality rates. As part of this analysis, the following equation was
estimated with data from US states from two different years.
Year 1: Fˆi  ˆ0  0.176Vi  0.0136Ci  7.75H i
R 2 = 0.624, N = 41
Year 2: Fˆi  ˆ0  0.190Vi  0.0071Ci  5.29 H i
R 2 = 0.532, N = 44
Where: Fi = the fatalities on rural interstate highways (per 100 million vehicle miles traveled)
in the i-th state
Vi = the driving speed variance in the i-th state
Ci = driving citations per driver in the i-th state
Hi = hospitals per square mile (adjusted) in the i-th state
a) Think about the intuition behind each variable and develop expected signs for each coefficient. Do the
reported support your expectations?
b) Should we attach much meaning to the differences between the estimated coefficients from the two
years? Why or why not? Under what circumstances might you be concerned about such differences?
c) The equation for the first year has the higher adjusted R2 but which equation has the higher R2?