NAME_______________________________________
Econ 2900 Fall 2009
Midterm Part 2
Friday October16th
Question #1 (10points)
A regression analysis was performed in an attempt to predict accountants salary on the basis of years of
experience and gender. The first few lines of the raw data and the associated regression printout are listed below
Gender (X2)
0=Female
1=Male
0
Years
Annual Salary
Experience (X1)
(Y)
5
$44,230
1
0
7
9
$51,150
$60,320
SUMMARY OUTPUT
Regression Statistics
Multiple R
R Square
Adjusted R Square
Standard Error
Observations
0.996686
0.993383
0.991912
1709.481
12
ANOVA
df
Regression
Residual
Total
Intercept
Gender (X2) 0=Female 1=Male
Years Experience (X1)
2
9
11
SS
MS
3.95E+09 1.97E+09
26300913 2922324
3.97E+09
F
Significance F
675.531
1.56E-10
Coefficients Standard Error t Stat
P-value
Lower 95% Upper 95%
23607.52
1434.476 16.45724 5.03E-08
20362.51 26852.53
14683.67
986.969 14.87754 1.21E-07
12450.99 16916.35
4076.498
121.2835 33.61132
9E-11
3802.136 4350.861
Does there appear to be discrimination amongst accountants? Explain
Question #2 (10points)
A professor of economics wanted to develop a multiple regression model to predict the students’ grades in her
fourth-year economics course. She decides that the two most important factors are the student’s grade point average
in the first three years and the student’s major. She proposes the model
y = β0 + β1x1 + β2x2 + β3x3 + ε
where
y
x1
x2
x3
=
=
=
=
=
=
fourth-year economics course mark (out of 100)
G.P.A. in first three years (range 0 to 12)
1 if student’s major is economics
0 if not
1 if student’s major is finance
0 if not
The computer output (based on 100 students) appears below.
THE REGRESSION EQUATION IS
Y = 9.14 + 6.73X1 + 10.42X2 + 5.16X3
PREDICTOR
CONSTANT
X1
X2
X3
COEF
9.14
6.73
10.42
5.16
STDEV
7.10
1.91
4.16
3.93
S = 15.0
R-SQ = 44.2%
T-RATIO
1.29
3.52
2.50
1.31
PVALUE
.2000
.0003
.3600
.0440
ANALYSIS OF VARIANCE
SOURCE
REGRESSION
ERROR
TOTAL
DF
3
96
99
SS
17098
21553
38651
MS
699.3
224.5
F
2.865
SIGNIF-F
.0432
Use the regression coefficients to rank the students according to how well you expect them to
perform in a 4th year econ class. Comment on how accurate this prediction will be.
Question # 3 (35points)
The human resources (HR) director for a large company that produces highly technical industrial
instrumentation devices is interested in using regression modeling to help in making recruiting
decisions concerning sales managers. The company has 45 sales regions, each headed by a sales
manager. Many of the sales managers have degrees in electrical engineering, and due to the technical
nature of the product line, several company officials believe that only applicants with degrees in
electrical engineering should be considered. At the time of their application, candidates are asked to
take the Strong-Campbell Interest Inventory Test and the Wonderlic Personnel Test. Due to the time
and money involved with the testing, some discussion has taken place about dropping one or both of
the tests. To start, the HR director gathered information on each of the 45 current sales managers,
including years of selling experience, electrical engineering background, and the scores from both the
Wonderlic and Strong-Campbell tests. The dependent variable was “sales index” score, which is the
ratio of the regions’ actual sales divided by the target sales. The target values are constructed each
year by upper management, in consultation with the sales managers, and are based on past
performance and market potential within each region. The variables included are
Sales – Ratio of yearly sales divided by the target sales value for that region. The
target values were mutually agreed-upon “realistic expectations”.
Wonder – Score from the Wonderlic Personnel Test. The higher the score, the
higher the applicant’s perceived ability to manage.
SC -- Score on the Strong-Campbell Interest Inventory Test. The higher the
score, the higher the applicant’s perceived interest in sales.
Experience – Number of years of selling experience prior to becoming a sales
manager.
Engineer – Dummy variable that equals 1 if the sales manager has a degree in
electrical engineering and 0 otherwise.
An example of the first few lines of the data are listed below, the regression results are on the following
page.
Manager #
1
2
3
.
.
.
44
45
Sales
96
90
113
.
.
.
101
95
Wonder
27
35
30
.
.
.
33
27
SC
42
46
55
.
.
.
50
54
Experience
5
8
8
.
.
.
9
4
Engineer
1
1
0
.
.
.
0
1
Yes
Yes
No
.
.
.
No
Yes
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.77021321
R Square
0.59322838
Adjusted R Square 0.55255122
Standard Error
11.7420288
Observations
45
ANOVA
df
Regression
Residual
Total
4
40
44
SS
8042.99042
5515.00958
13558
Intercept
Wonder
SC
Experience
Engineer
Coefficients
25.7683409
-0.0134104
1.35141645
0.16815638
7.27470818
Standard
Error
13.95370291
0.404976302
0.19470923
0.528712892
4.101130081
MS
2010.748
137.8752
F
14.583819
t Stat
1.846703
-0.03311
6.94069
0.318049
1.77383
P-value
0.0721979
0.9737483
2.268E-08
0.7521027
0.0837043
Test to see if the model is useful use alpha =.01.
Significance F
xxxx
Use the regression printout to help the Human resources director interpret the results.