Kafli 11
THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
The manager of a used-car dealership is very interested in the resale price of used cars. The
manager feels that the age of the car is important in determining the resale value. He collects
data on the age and resale value of 15 cars and runs a regression analysis with the value of the
car (in thousands of dollars) as the dependent variable and the age of the car (in years) as the
independent variable. Unfortunately, the printout had lost some of the results, identified by “A”
through “F”. The partial results left are displayed below.
SUMMARY OUTPUT
Regression Statistics
Multiple R
R Square
Adjusted R Square
Standard Error
Observations
0.442
“A”
0.133
“B”
15.000
ANOVA
df
SS
MS
F
Significance F
Regression
1
44.397
44.397
3.154
0.09914
Residual
13
“C”
14.076
Total
14
227.389
Coefficients
Standard Error
t Stat
P-value
Intercept
“D”
3.835
5.988
0.000
Age
“E”
0.640
–1.776
“F”
1/12
1.
Which of the following is the value of “A”?
A) 0.195
B) 0.805
C) 0.442
D) 0.67
ANSWER:
2.
What is the value of “B”?
A)
B)
C)
D)
3.
1.136
–1.136
0.278
–0.278
What is the approximate value of “F”?
A)
B)
C)
D)
7.
9.35
3.06
9.82
22.96
Calculate the value of “E.”
A)
B)
C)
D)
6.
172.25
162.42
140.03
182.99
Compute the value of “D.”
A)
B)
C)
D)
5.
2.58
6.67
3.75
3.95
What is the value of “C”?
A)
B)
C)
D)
4.
A
0.025
0.05
0.10
0.01
In order to estimate with 95% confidence the expected value of y in a simple linear
regression problem, a random sample of 10 observations is taken. Which of the
following t-table values listed below would be used?
A)
B)
C)
D)
2.228
1.860
1.812
2.306
2/12
THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
A sales manager is interested in determining the relationship between the amount spent on
advertising and total sales. The manager collects data for the past 24 months and runs a
regression of sales on advertising expenditures. The results are presented below but,
unfortunately, some values identified by asterisks are missing.
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.492
R Square
0.242
Adjusted
Square
R
0.208
Standard Error
40.975
Observations
24.000
ANOVA
df
SS
MS
F
Significance F
Regression
1
11809.406
11809.406
7.034
*
Residual
*
*
*
Total
*
*
Coefficients Standard Error
Intercept
Advertising
P-value
*
26.239
4.021
0.001
2.015
*
2.652
0.015
8. What are the degrees of freedom for residuals?
A)
B)
C)
D)
t Stat
21
22
23
24
3/12
9. The value of mean square error is ____.
A)
B)
C)
D)
1678.9
1,554.25
1,493.63
1,407.35
10. The total degrees of freedom is ____.
A)
B)
C)
D)
21
22
23
24
11. Determine the value of residual sum of squares.
A)
B)
C)
D)
10,945.2
11,759.9
10,130.5
36,935.8
12. What is the value of total sum of squares?
A)
B)
C)
D)
48,745.2
46,538.7
50,292.4
52,644.8
13. Determine the regression coefficient of the y-intercept.
A)
B)
C)
D)
112.4
102.3
108.6
105.5
14. Calculate the standard error of estimate.
A)
B)
C)
D)
0.66
0.76
0.85
0.61
4/12
15.
A regression analysis between sales (in $1000) and advertising (in $100) resulted in the
following least squares line: ŷ = 75 + 5x. This implies that if advertising is $800, then
the predicted amount of sales (in dollars) is _____.
A)
B)
C)
D)
16.
$4075
$115,000
$164,000
$179,000
Correlation analysis is used to determine the:
A)
B)
C)
D)
strength of the relationship between x and y.
least squares estimates of the regression parameters.
predicted value of y for a given value of x.
forecast value of a particular dependent variable.
17. In a regression problem, a coefficient of determination 0.90 indicates that:
A)
B)
C)
D)
90% of the y values are positive.
90% of the variation in y can be explained by the regression line.
90% of the x values are equal.
90% of the variation in x can be explained by the regression line.
18. If the regression line ŷ = 3 + 2x has been fitted to the data points (4, 8), (2, 5), and (1, 2),
the residual sum of squares will be ____.
A)
B)
C)
D)
10
15
13
22
5/12
Kafli 12
THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
A loan officer is interested in examining the determinants of the total dollar value of
residential loans made during a month. The officer used Y  0  1 X1  2 X 2  3 X 3   to
model the relationship, where Y is the total dollar value of residential loans in a month (in
millions of dollars), X 1 is the number of loans, X 2 is the interest rate, and X 3 is the dollar
value of expenditures of the bank on advertising (in thousands of dollars). Using data from the
past 24 months, she obtained the following results: yˆ  5.7  0.189 x1  1.3x2  0.08x3 , sb0 = 3.2,
sb1 = 0.03, sb2 = 0.062, sb3 = 0.17, R 2 = 0.46, and adjusted R 2 = 0.41.
1.
What should the null and alternative hypotheses be for 1 ?
A)
B)
C)
D)
2.
What should the null and alternative hypotheses be for  2 ?
A)
B)
C)
D)
3.
H 0 : 2
H 0 : 2
H 0 : 2
H 0 : 2
 0 and H1 :  2  0
 0 and H1 : 2  0
 0 and H1 :  2  0
 0 and H1 : 2  0
What should the null and alternative hypotheses be for  3 ?
A)
B)
C)
E)
4.
H 0 : 1  0 and H1 : 1  0
H 0 : 1  0 and H1 : 1  0
H 0 : 1  0 and H1 : 1  0
H 0 : 1  0 and H1 : 1  0
H 0 : 3
H 0 : 3
H 0 : 3
H 0 : 3
 0 and H1 : 3  0
 0 and H1 : 3  0
 0 and H1 : 3  0
 0 and H1 : 3  0
How should the loan officer interpret the coefficient on x2 ?
A) For an additional 1.3 percent increase in the interest rate, we would expect the total
dollar value of residential loans to decreases by $1.0 million, assuming that all the
other independent variables in the model are held constant.
B) For an additional percent increase in the interest rate, we would expect the total
dollar value of residential loans to decreases by $1.3 million on average, assuming
that all the other independent variables in the model are held constant.
C) For an additional million dollars in loans, we would expect the interest rate to
decreases by 1.3 percent, assuming that all the other independent variables in the
model are held constant.
D) For an additional $1.3 million in loans, we would expect the interest rate to decrease
by 1.0 percent on average, assuming that all the other independent variables in the
model are held constant.
6/12
5.
How should the loan officer interpret the coefficient on x3 ?
A) For every additional $8,000 spent on advertising, we would expect the total dollar
value of residential loans to increase by $1,000,000 on average, assuming that all
the other independent variables in the model are held constant.
B) For every additional dollar spent on advertising, we would expect the total dollar
value of residential loans to increase by $0.08 million, assuming that all the other
independent variables in the model are held constant.
C) For every additional $80,000 spent on advertising, we would expect the total dollar
value of residential loans to increase by $1,000,000, assuming that all the other
independent variables in the model are held constant.
D) For every additional $1000 spent on advertising, we would expect the total dollar
value of residential loans to increase by $80,000 on average, assuming that all the
other independent variables in the model are held constant.
6.
What would we expect the total dollar value of loans to be in a month where there are 42
loans, the interest rate is 7.5%, and the bank spends $30,000 in advertising?
A)
B)
C)
D)
7.
What is the 95% confidence interval associated with 1 ?
A)
B)
C)
D)
8.
$6.442 million
$6.558 million
$6.288 million
$6.112 million
0.016
0.189
0.189
0.189




0.189
0.016
0.026
0.063
How would we interpret the coefficient of determination R 2 ?
A) Approximately 46% of the time, the dollar value of the loans is determined by these
three variables.
B) Approximately 46% of the observations lie within 1 standard deviation of the
regression line.
C) Approximately 46% of the variation in the total dollar amount of loans can be
explained by the variation in these three variables.
D) Approximately 46% of the total dollar amount of loans is explained by these three
variables.
7/12
THE NEXT TWO QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
A loan officer is interested in examining the determinants of the total dollar value of
residential loans made during a month. She used Y  0  1 X1  2 X 2  3 X 3  4 X 32   to
model the relationship, where Y is the total dollar value of residential loans in a month (in
millions of dollars), X 1 is the number of loans, X 2 is the interest rate, and X 3 is the dollar
value of expenditures of the bank on advertising. (in thousands of dollars). Suppose that by
using data from the past 24 months, she obtained yˆ  3.8  0.23x1  1.31x2  0.032 x3  0.0005x32 .
9.
What do these results suggest about the relationship between the total loan amount and
advertising?
A) As the amount of advertising increases, the total loan amount decreases at a
decreasing rate.
B) As the amount of advertising increases, the total loan amount at first decreases, then
increases.
C) As the amount of advertising increases, the total loan amount increases at an
increasing rate.
D) As the amount of advertising increases, the total loan amount at first increases, then
decreases.
10. What do these results suggest about the relationship between the total loan amount and
number of loans?
A) As the number of loans increases, the total loan amount at first decreases, then
increases.
B) As the number of loans increases, the total loan amount also increases.
C) As the number of loans increases, the total loan amount at first increases, then
decreases.
D) As the number of loans increases, the total loan amount decreases at a decreasing
rate.
8/12
Kafli 13
1.
If the Durbin-Watson statistic has a value close to 0 or 4, which assumption is violated?
A)
B)
C)
D)
2.
normality of the errors
independence of errors
homoscedasticity
variance of errors
Suppose the following scatter plot shows the relationship between X and Y. How might
you model Y?
140000
120000
100000
80000
60000
40000
20000
0
0
A)
B)
C)
D)
3.
60
80
100
120
with dummy variables
with the log normal specification
with dummy variables and interactive terms
with a correction for heteroscedasticity
It will lead to unbiased least squares estimators.
It will lead to biased least squares estimators.
It will lead to biased estimators of the variance.
It will lead to multicollinearity between predictor variables.
If the Durbin-Watson statistic d has values between 0 and d L , this indicates ____.
A)
B)
C)
D)
5.
40
Which of the following is expected to occur in multiple regression analysis if an
important variable is omitted from the list of independent variables?
A)
B)
C)
D)
4.
20
a positive first-order autocorrelation
a negative first-order autocorrelation
no first-order autocorrelation at all
an inconclusive test.
Suppose you are interested in examining the determinants of earnings. You have
information on the age of the individual as well as their level of education: high school
graduate, college graduate or graduate degree. Let Y = earnings, X 1 = age, X 2 = 1 if
9/12
the person has only a high school degree and 0 otherwise, X 3 = 1 if the person has a
college degree and 0 otherwise, X 4 = 1 if the person has a graduate degree and 0
otherwise. Which of the following model specifications would work for this data?
A) Y  0  1 X1  2 X 2  3 X 3
B) Y  0  1 X1   2 X 2  3 X 3   4 X 4
    3   4
C) Y  1 2
X1  X 2  X 3  X 4
D) Y  1  2  3  4  X1  X 2  X 3  X 4
6.
Which of the following regression diagnostic tools is used to study the possible presence
of multicollinearity?
A)
B)
C)
D)
7.
Suppose you want to estimate the model Y  0  1 X1   2 X 2  3 X 3   4 X 4 . However,
you cannot measure X 4 , so you estimate Y  0  1 X1  2 X 2  3 X 3 instead. This is an
example of regression result that will be subject to ____.
A)
B)
C)
D)
8.
autocorrelation.
heteroscedasticity
multicollinearity
specification bias
The Durbin-Watson test is used to detect ____.
A)
B)
C)
D)
9.
heteroscedasticity
residual plot
scatter diagram
correlation matrix
heteroscedasticity
specification bias
autocorrelation
multicollinearity
Suppose that the estimated regression equation of a College of Business graduates is
given by: yˆ  32,000  4,000 x  1,800 D , where y is the starting salary, x is the grade point
average and D is a dummy variable which takes the value of 1 if the student is a finance
major and 0 if not. An accountancy major graduate with a 3.5 grade point average would
have an average starting salary of:
A)
B)
C)
D)
$47,800
$46,000
$37,800
$32,000
10/12
10.
Consider the regression model ŷ  20  8 x1  5 x2  3 x1 x2 .Which combination of x1 and
x 2 , respectively, results in the largest average value of y?
A)
B)
C)
D)
11.
3 and 5
5 and 3
6 and 3
3 and 6
In reference to the Durbin-Watson statistic d and the critical values d L and dU , which
of the following statements is false?
A) If d < d L , we conclude that positive first-order autocorrelation exists
B) If d > dU , we conclude that there is not enough evidence to show that positive
first-order autocorrelation exists
C) If d > 4 - d L , we conclude that there is negative autocorrelation.
D) If d lies in between d L and dU , we conclude that there is no evidence of first-order
autocorrelation.
12.
Suppose that the sample regression equation of a model is yˆ  10  2 x1  3x2  x1 x2 . If
we examine the relationship between x1 and y for four different values of x 2 , we observe
that the:
A.
B.
C.
D.
13.
Suppose that the sample regression equation of a model is yˆ  10  2 x1  3x2  x1 x2 . If
we examine the relationship between x1 and y for four different values of x 2 , we observe
that the:
A.
B.
C.
D.
14.
four equations have different coefficients of x1
four equations produced differ only in the intercept term
coefficient of x 2 remains unchanged
coefficient of x1 remains unchanged
four equations have different coefficients of x1
four equations produced differ only in the intercept term
coefficient of x 2 remains unchanged
coefficient of x1 remains unchanged
The range of the values of the Durbin-Watson statistic, d is ____.
A)
B)
C)
D)
–4  d  4
–2  d  2
0 d 4
0 d 2
11/12
15.
Which of the following is considered one of the most common concerns with time-series
data?
A)
B)
C)
D)
16.
heteroscedasticity
autocorrelation
multicollinearity
specification bias
Consider the following plot of residuals from a regression. This pattern suggests which
of the following problems?
Time
15
10
5
0
-5
0
5
10
15
-10
A)
B)
C)
D)
autocorrelation
specification bias
multicollinearity
heteroscedasticity
12/12
20
25