Name:__________________________
Economics 2900
Midterm Exam
Fall 2007
Tuesday, October 16th 2007
Question # 1
Question # 2
Question # 3
Question # 4
(marks)
(marks)
(marks)
(marks)
_________
_________
_________
_________
Total
(100 marks) _________
1.
Management of a soft-drink bottling company wants to develop a method for allocating delivery costs to customers. Although
one cost clearly relates to travel time within a particular route, another variable cost reflects the time required to unload the cases
of soft drink at the delivery point. A sample of 20 deliveries within a territory was selected. The delivery times and the numbers
of cases delivered were recorded in the delivery.xls file:
=======================================================================
Number Delivery
||
Delivery
of Cases Time
||
Number
Time
Customer
(Minutes)
||Customer of Cases (Minutes)
----------------------------------------------------------------------------------------1
52
32.1
|| 11
161
43.0
2
64
34.8
|| 12
184
49.4
3
73
36.2
|| 13
202
57.2
4
85
37.8
|| 14
218
56.8
5
95
37.8
|| 15
243
60.6
6
103
39.7
|| 16
254
61.2
7
116
38.5
|| 17
267
58.2
8
121
41.9
|| 18
275
63.1
9
143
44.2
|| 19
287
65.6
10
157
47.1
|| 20
298
67.3
======================================================================
Mean (number of cases)=169.9
Mean (delivery time) = 48.625
Covariance (#cases,deliverytime)= 872.5
Standard error of the regression = 1.987
Develop a regression model to predict delivery time, based on the number of cases delivered.
Determine the coefficient of determination, r2 , and explain its meaning in this problem.
At the 0.05 level of significance, is there evidence of a linear relationship between delivery time and the number of cases
delivered?
Construct a 95% prediction interval of the delivery time for a single delivery of 150 cases of soft drink.
Question #2
Develop a model to predict the assessed value (in thousands of dollars), using the size of the houses (in thousands of square feet) and the age of
the houses (in years) from the following table:
===========================================================
Size of House
Assessed
(Thousands of
Age
House
Value ($ 000)
Square Feet)
(Years)
===========================================================
1
184.4
2.00
3.42
2
177.4
1.71
11.50
3
175.7
1.45
8.33
4
185.9
1.76
0.00
5
179.1
1.93
7.42
6
170.4
1.20
32.00
7
175.8
1.55
16.00
8
185.9
1.93
2.00
9
178.5
1.59
1.75
10
179.2
1.50
2.75
11
186.7
1.90
0.00
12
179.3
1.39
0.00
13
174.5
1.54
12.58
14
183.8
1.89
2.75
15
176.8
1.59
7.17
=============================================================
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.90912
R Square
0.826499
Adjusted R Square
0.797583
Standard Error
a.
Observations
2.168166
ANOVA
Regression
Residual
Total
Intercept
size
Age
S
t
a
t
e
t
h
e
15
df
SS
MS
F
268.7247
134.3623
12
56.4113
4.700942
14
325.136
m
u
l
Coefficients
Standard Error
t
i
163.7751
5.407173
p
10.72518
3.014327
l
-0.28425
0.083598
e
W
What is the regression equation?
30.28849
1.05E-12
151.9939
175.5563
3.558069
0.003938
4.157528
17.29284
-3.40024
0.005267
-0.4664
-0.10211
t Stat
28.58201
Significance F
2
P-value
X
Lower 95%
Upper 95%
Predict the mean assessed value for a house that has a size of 1,750 square feet and is 10 years old.
Determine whether there is a significant relationship between assessed value and the two independent variables (size and
age)
Is this model valid? Use alpha =.01
The real estate assessor’s office has been publicly quoted as saying that the age of a house has no bearing on its assessed
value. Based on your regression output do you agree with this statement? Explain.
Question # 3
Many factors determine the attendance at Major League Baseball games. These factors can include when the game is played, the weather, the
opponent, whether the team is having a good season, and whether a marketing promotion is held. Popular promotions during the 2002 season
were the traditional hat days and poster days and the new craze, bobble-heads of star players (T.C. Boyd and T.C. Krehbiel, “An Analysis of the
Effects of Specific Promotion Types on Attendance at Major League Baseball Games,” Mid-American Journal of Business, 2006, 21, pp. 21-32).
The data file baseball.xls includes the following variables for the 2002 Major League Baseball season:
TEAM – Kansas City Royals
ATTENDANCE – Paid attendance for the game
TEMP – High temperature for the day
WIN% -- Team’s winning percentage at the time of the game
OPWIN% -- Opponent team’s winning percentage at the time of the game
WEEKEND – 1 if game played on Friday, Saturday or Sunday; 0 otherwise
PROMOTION – 1 if a promotion was held; 0 if no promotion was held
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.548682
R Square
0.301052
Adjusted R Square
0.253826
Standard Error
6442.446
Observations
80
ANOVA
df
Regression
SS
MS
F
6.374694
5
1.32E+09
2.65E+08
Residual
74
3.07E+09
41505105
Total
79
4.39E+09
Coefficients
Standard Error
Intercept
-3862.48
Temp
51.70313
Win%
Significance F
5.65E-05
Lower 95%
Upper
95%
t Stat
P-value
6180.945
-0.6249
0.533958
-16178.3
8453.321
62.94393
0.821416
0.414048
-73.7154
177.1216
21.10849
16.2338
1.30028
0.19754
-11.2381
53.45505
OpWin%
11.34535
6.461665
1.755793
0.083262
-1.5298
24.2205
Weekend
367.5377
2786.264
0.131911
0.895413
-5184.21
5919.29
Promotion
6927.882
2784.344
2.488156
0.015091
1379.955
12475.81
Write out the regression equation. Do the signs of the coefficients make sense? Explain
Determine whether each independent variable makes a significant contribution to the regression model.
Determine and interpret the adjusted r2 . What does this statistic tell you about the reasons why people attend baseball
games?
How well is the employee in charge of promotions performing?
Do a residual analysis on the results to determine the adequacy of the model.