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NAME:______________________
I.D. # : ______________________
ECONOMICS 2900
Economics and Business Statistics
SPRING, 2005
MIDTERM EXAMINATION
Thursday, February 17 2005
Weight 35%
NOTE : You have 70 mins to complete the exam, budget your time accordingly. Please
answer all questions on this exam booklet. Calculators used must not have the ability to
program alphabetic characters (whole words or sentences) GOOD LUCK
** Please do not mark the tables **
Question # 1 30 marks
The Following data describe U.S. passenger car travel and fuel consumption from 1995 through 1999. The
data represent billions of gallons consumed and billions of miles traveled
Year
1995
1996
1997
1998
1999
Fuel consumed
68.07
69.22
69.87
71.70
73.16
Miles traveled
1438.29
1469.85
1501.82
1549.58
1569.27
Total
Mean
Variance
Covariance
352.02
70.4
4.1
86.78
7528.81
1505.8
2952.7
A) Calculate the regression equation with fuel as your dependant variable and miles traveled as your
independent variable. Interpret the coefficients.
B) Is there enough evidence to suggest that the number of miles traveled is linearly related to fuel
consumption? (use alpha = .10)
C) What is the coefficient of Determination? What does this statistic tell you?
D) Predict with 95% confidence, the amount of fuel consumed for the year 2000 when there were
1600 miles traveled.
Question 2 (25 marks)
The general manager of the Cleveland Indians baseball team is in the process of determining which minorleague players to draft. He is aware that his team needs home-run hitters and would like to find a way to
predict the number of home runs a player will hit. Being an astute statistician, he gathers a random sample
of players and records the number of home runs each player hit in his first two full years as a major-league
player, the number of home runs he hit in his last full year in the minor leagues, his age, and the number of
years of professional baseball. An example of the first few lines of data, along with the initial regression
printout appears below.
Major
HR
Minor
HR
19
23
6
Years
Pro
Age
13
15
4
19
21
22
3
3
5
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.592560205
R Square
0.351127597
Adjusted R Square 0.335171718
Standard Error
6.992104843
Observations
126
ANOVA
Df
Regression
Residual
Total
Intercept
Minor HR
Age
Years Pro
3
122
125
SS
MS
F
Significance F
3227.612245 1075.871 22.00616 1.85592E-11
5964.522676 48.88953
9192.134921
Coefficients Standard Error t Stat
P-value
Lower 95%
-1.969977822 9.547049398 -0.20634 0.836866 -20.86933228
0.665838264 0.087149184 7.640212 5.46E-12 0.493317598
0.135727743 0.524087215 0.258979 0.796088 -0.901756157
1.176370911 0.670625334 1.75414 0.081917 -0.151200086
a.
What is the regression equation? Interpret each of the coefficients.
b.
How well does the model fit?
c.
Test with alpha =.05 if the model is useful. Explain how your test result relates to
“significance F” on the regression printout.
d.
Do each of the independent variables belong in the model? How can you tell?
e.
Predict with 95% confidence the number of home runs in the first two years of a player
who is 25 years old, has played professional baseball for 7 years, and hit 22 home runs in
his last year in the minor leagues.
Question 3 (25 marks)
The administrator of a school board in a large county was analyzing the average mathematics test scores in
the schools under her control. She noticed that there were dramatic differences in scores among the
schools. In an attempt to improve the scores of all the schools, she attempted to determine the factors that
account for the differences. Accordingly, she took a random sample of 40 schools across the county and,
for each, determined the mean test score last year, the percentage of teachers in each school who have at
least one university degree in mathematics, the mean age, and the mean annual income of the mathematics
teachers. An example of the first few lines of data, along with the initial regression printout appears below.
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.5975122
R Square
0.8570209
Adjusted R Square
0.8034393
Standard Error
7.724526
Observations
40
ANOVA
Df
Regression
Residual
Total
Intercept
Math Degree
Age
Income
SS
MS
F
Significance F
3 1192.732105 397.5774 6.663125 0.001076925
36 2148.058895 59.6683
39
3340.791
Coefficients
Standard Error
35.677618 7.278849159
0.2474816 0.069845662
0.2448306 0.185213036
0.1332967 0.152818937
t Stat
4.901547
3.543263
1.321886
0.872253
Correlation matrix:
Test
Score
Test Score
Math Degree
Age
Income
Math
Degree
1
0.506626
1
0.332495 0.076597
0.311981 0.099351
Age
1
0.869752
Income
1
a.
What is the regression model? Do these coefficients make sense?
b.
Overall, does this model fit the data well?
P-value
2.03E-05
0.001115
0.194545
0.388851
Lower 95%
20.91544713
0.1058282
-0.13079835
-0.17663405
Histogram
Frequency
10
5
Frequency
0
Bin
100
residuals
50
0
0
10
20
30
40
Series1
-50
-100
-150
residuals
Observation #
100
80
60
40
20
0
-20 0
-40
-60
-80
-100
-120
100
200
300
400
500
Series1
Predicted
c.
What are the required conditions regarding the error variable? Are these
conditions satisfied? Explain in detail.
d.
What is Multicollinearity? Why is it a problem? Is multicollinearity a problem in
this model? Should we fix multicollinearity when we do find evidence of it?
e.
How would you suggest to make this model better?
Question # 4 20 marks
QUEBEC REFERENDUM VOTE: WAS THERE ELECTORAL FRAUD?*
Quebecers have been debating whether to separate from Canada and form an independent nation. A
referendum was held on October 30, 1995, in which the people of Quebec voted not to separate. The vote
was extremely close, with the “No” side winning by only 52,448 votes. A large number of “No” votes was
cast by the non-Francophone (non-French-speaking) people of Quebec, who make up about 20% of the
population and who very much want to remain Canadians. The remaining 80% are Francophones, a
majority of whom voted “Yes”.
After the votes were counted, it became clear that the tallied vote was much closer than it should have been.
Supporters of the “No” side charged that poll scrutineers, all of whom were appointed by the proseparatist
provincial government, rejected a disproportionate number of ballots in ridings where the percentage of
“Yes” votes was low and where there are large numbers of Allophone (people whose first language is
neither English nor French) and Anglophone (English-speaking) residents. (Electoral laws require the
rejection of ballots that do not appear to be properly marked. They were outraged that in a strong
democracy like Canada, votes would be rigged much like in many nondemocratic countries around the
world.
If, in ridings where there was a low percentage of “Yes” votes there was a high percentage of rejected
ballots, this would be evidence of electoral fraud. Moreover, if in ridings where there were large
percentages of Allophone and/or Anglophone voters, there were high percentages of rejected ballots, this
too would constitute evidence of fraud on the part of the scrutineers and possibly the government.
In order to determine the veracity of the charges, the following variables were recorded for each riding:
Percentage of rejected ballots in referendum
Percentage of “Yes” votes
Percentage of Allophones
Percentage of Anglophones
A multiple regression analysis to determine how the percentages of “yes” votes, Allophones, and
Anglophones were related to the percentage of rejected ballots was performed and is summarized
below
SUMMARY OUTPUT
Regression Statistics
Multiple R
R Square
Adjusted R Square
Standard Error
Observations
0.372093
0.138453
0.117092
0.981088
125
ANOVA
df
Regression
Residual
Total
Intercept
Pct Yes
Pct Allo
Pct Anglo
3
121
124
SS
MS
F
Significance F
18.71651 6.238838 6.481686 0.000418362
116.4665 0.962533
135.183
Coefficients Standard Error t Stat
P-value
1.565643
0.739285 2.11778 0.03624
0.000262
0.012072 0.02169 0.982731
0.036747
0.010332 3.556591 0.000537
-0.00904
0.01299 -0.69592 0.487811
________________________________
* This case is based on “Voting Irregularities in the 1995 Referendum on Quebec Sovereignty,” by Jason
Cawley and Paul Sommers, Chance, Vol. 9, No. 4, Fall 1996. We are grateful to Dr. Paul Sommers,
Middlebury College, for his assistance in writing this case.
Can we infer that electoral fraud took place? If so, how did it manifest itself?