Page 1 of 18 Part A: Multiple Choice (1–11) ______1. Using the “eyeball” method, the regression line = 2+2x has been fitted to the data points (x = 2, y = 1), (x = 3, y = 8), and (x = 4, y = 7). The sum of the squared residuals will be a. 7 b. 19 c. 34 d. 8 ______2. A computer statistical package has included the following quantities in its output: SST = 50, SSR = 35, and SSE = 15. How much of the variation in y is explained by the regression equation? a. 49% b. 70% c. 35% d. 15% ______3. In testing the significance of b, the null hypothesis is generally that a. β = b b. β 0 c. β = 0 d. β = r ______4. Testing whether the slope of the population regression line could be zero is equivalent to testing whether the population _____________ could be zero. a. standard error of estimate c. y-intercept b. prediction interval d. coefficient of correlation ______5. A multiple regression equation includes 4 independent variables, and the coefficient of multiple determination is 0.64. How much of the variation in y is explained by the regression equation? a. 80% b. 16% c. 32% d. 64% ______6. A multiple regression analysis results in the following values for the sum-of-squares terms: SST = 50.0, SSR = 35.0, and SSE = 15.0. The coefficient of multiple determination will be a. = 0.35 b. = 0.30 c. = 0.70 d. = 0.50 ______7. In testing the overall significance of a multiple regression equation in which there are three independent variables, the null hypothesis is a. : b. : c. : d. : ______8. In a multiple regression analysis involving 25 data points and 4 independent variables, the sum-of-squares terms are calculated as SSR = 120, SSE = 80, and SST = 200. In testing the overall significance of the regression equation, the calculated value of the test statistic will be a. F = 1.5 c. F = 5.5 b. F = 2.5 d. F = 7.5 ______9. For a set of 15 data points, a computer statistical package has found the multiple regression equation to be = -23 + 20+ 5 + 25 and has listed the t-ratio for testing the significance of each partial regression coefficient. Using the 0.05 level in testing whether = 20 differs significantly from zero, the critical t values will be a. t = -1.960 and t= +1.960 b. t = -2.132 and t = +2.132 c. t = -2.201 and t = +2.201 d. t = -1.796 and t = +1.796 ______10. Computer analyses typically provide a p-Value for each partial regression coefficient. In the case of , this is the probability that a. = 0 b. = c. the absolute value of could be this large if = 0 d. the absolute value of could be this large if 1 ______11. In the multiple regression equation, = 20,000 + 0.05+ 4500 , is the estimated household income, is the amount of life insurance held by the head of the household, and is a dummy variable ( = 1 if the family owns mutual funds, 0 if it doesn’t). The interpretation of = 4500 is that a. owing mutual funds increases the estimated income by $4500 b. the average value of a mut.

1. Page 1 of 18
Part A: Multiple Choice (1–11)
______1. Using the “eyeball” method, the regression line =
2+2x has been fitted to the data points (x = 2, y = 1), (x = 3, y =
8), and (x = 4, y = 7). The sum of the squared residuals will be
a. 7 b. 19 c. 34 d. 8
______2. A computer statistical package has included the
following quantities in its output: SST = 50, SSR = 35, and SSE
= 15. How much of the variation in y is explained by the
regression equation?
a. 49% b. 70% c. 35% d. 15%
______3. In testing the significance of b, the null hypothesis is
generally that
a. β = b b. β 0 c. β = 0 d. β = r
______4. Testing whether the slope of the population regression
line could be zero is equivalent to testing whether the
population _____________ could be zero.
a. standard error of estimate c. y-intercept
b. prediction interval d. coefficient of
correlation
______5. A multiple regression equation includes 4 independent
variables, and the coefficient of multiple determination is 0.64.
How much of the variation in y is explained by the regression
equation?
a. 80% b. 16% c. 32% d. 64%
______6. A multiple regression analysis results in the following

2. values for the sum-of-squares terms: SST = 50.0, SSR = 35.0,
and SSE = 15.0. The coefficient of multiple determination will
be
a. = 0.35 b. = 0.30 c. = 0.70 d. = 0.50
______7. In testing the overall significance of a multiple
regression equation in which there are three independent
variables, the null hypothesis is
a. :
b. :
c. :
d. :
______8. In a multiple regression analysis involving 25 data
points and 4 independent variables, the sum-of-squares terms
are calculated as SSR = 120, SSE = 80, and SST = 200. In
testing the overall significance of the regression equation, the
calculated value of the test statistic will be
a. F = 1.5 c. F = 5.5
b. F = 2.5 d. F = 7.5
______9. For a set of 15 data points, a computer statistical
package has found the multiple regression equation to be = -23
+ 20+ 5 + 25 and has listed the t-ratio for testing the
significance of each partial regression coefficient. Using the
0.05 level in testing whether = 20 differs significantly from
zero, the critical t values will be
a. t = -1.960 and t= +1.960
b. t = -2.132 and t = +2.132
c. t = -2.201 and t = +2.201
d. t = -1.796 and t = +1.796
______10. Computer analyses typically provide a p-Value for
each partial regression coefficient. In the case of , this is the
probability that
a. = 0

3. b. =
c. the absolute value of could be this large if = 0
d. the absolute value of could be this large if 1
______11. In the multiple regression equation, = 20,000 +
0.05+ 4500 , is the estimated household income, is the amount
of life insurance held by the head of the household, and is a
dummy variable ( = 1 if the family owns mutual funds, 0 if it
doesn’t). The interpretation of = 4500 is that
a. owing mutual funds increases the estimated income by $4500
b. the average value of a mutual funds portfolio is $4500
c. 45% of the persons in the sample own mutual funds
d. the sample size must have been at least n = 4500
Part B: True or False (12-20)
_______ 12. The usual objective of regression analysis is to
predict estimate the value of one variable when the value of
another variable is known.
_______ 13. Correlation analysis is concerned with measuring
the strength of the relationship between two variables.
_______ 14. In the least squares model, the explained sum of
squares is always smaller than the regression sum of squares.
_______ 15. The sample correlation coefficient and the sample
slope will always have the same sign.
_______ 16. An important relationship in regression analysis is
= .

4. _______ 17. If in a regression analysis the explained sum of
squares is 75 and the unexplained sum of square is 25, r2 =
0.33.
_______ 18. When small values of Y tend to be paired with
small values of X, the relationship between X and Y is said to
be inverse.
_______ 19. The probability that the test statistic will fall in the
critical region, given that H0 is true, represents the probability
of making a type II error.
_______ 20. When we reject a true null hypothesis, we commit
a Type I error.
Part C: Answer the following questions (21-26)
21. What is the Null Hypothesis? Explain.
22. What is the Alternative Hypothesis? Explain.

5. 23. Explain how you decide what statement goes into the null
hypothesis and what statement go into the alternative
hypothesis.
24. When should the z-test be used?
25. When should the t-test be used?
26. What is the definition of P-Value?
Part D: Must show all your work step by step in order to receive
the full credit; Excel is not allowed. (27-46)
27. Work on problem number 9 (a-f) on page 7-47

7. 28. Work on problem number 1 (a-e) on page 7-68
29. Work on problem number 2 (a-c) on page 7-68

8. 30. Work on problem number 7 (a-e) on page 7-69

9. 31. Work on problem number 16 (a-b) on page 8-12
;Given that
32. State whether you would reject or fail to reject the null
hypothesis in each of the following cases (two-tailed):
a) P = 0.12 ;
b) P = 0.03 ;

10. c) P = 0.001 ;
d) P = 0.01 ;
33. Consider the following hypothesis test.
Ho: µ = 17
Ha: µ ≠ 17
A sample of 25 gives a sample mean of 14.2 and sample
variation of 25.
a)
At α = 0.05, what is the rejection rule?
b)
Compute the value of the test statistic
c)
What is the p-value?
d)
What is your conclusion?

11. 34. Consider the following hypothesis test.
Ho: μ = 15
Ha: μ ≠ 15
A sample of 50 gives a sample mean of 14.2 and
sample variation of 25.
a)
At α = 0.05, what is the rejection rule?
b)
Compute the value of the test statistic
c)
What is the p-value?
d)
What is your conclusion?
35. Consider the following hypothesis test
Ho: µ ≥ 10

12. Ha: µ <10
A sample of 50 provides a sample mean of 9.46 and sample
variation of 4.
a)
At α = 0.05, what is the rejection rule?
b)
Compute the value of the test statistic
c)
What is the p-value?
d)
What is your conclusion?
36. Fill in the table and find the following answers:
Months on job (x)
Monthly sales (y) thousands of dollars
X2
Y2
XY
1

13. 0.80
2
2.40
4
7.00
5
3.70

14. 8
11.30
9
12.00
12
15.00
41

15. a) Find
b) Find
c) Write the estimated regression equation
d) Interpret
e) Calculate the coefficient of determination
f) Interpret the coefficient of determination

16. 37. Work on problem number 3 (a-d) on page 10-32

17. 38. Please fill in the computer printout and answer the
following questions.
Given that
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.9037
R Square
______

18. Adjusted R Square
______
Standard Error
______
Observations
5
ANOVA
df
SS
MS
F
Significance F
Regression
1
4.9
______
______
0.03535

19. Residual
3
1.1
______
Total
______
______
Coefficients
Standard
Error
t Stat
P-value
Lower95%
Upper 95%
Lower 95.0%
Upper 95.0%
Intercept
-0.1
______
-0.15746
0.88488
-2.12112
1.92112
-2.12112
1.92112
X1
0.7
______
3.65563

20. 0.03535
0.09061
1.30939
______
______
a)
What percent of the variation is explained by the regression
equation?
b)
What is the standard error of regression?
c)
What is the critical value of the F-statistic?
d)
What sample size is used in the print out?
39. The following regression equation was obtained using the
five independent variables.
Given that

21. a)
What percent of the variation is explained by the regression
equation?
b)
What is the standard error of regression?
c)
What is the critical value of the F-statistic?
d)
What sample size is used in the print out?
e)
What is the variance of the slope coefficient of income?
f)
Conduct a global test of hypothesis to determine if any of the
regression coefficients are not zero.
g)
Conduct a test of hypothesis on each of the independent
variables. Would you consider eliminating outlets and bosses?
40. Please use the following computer printout to answer the
following questions:
Coefficients
Std. Error
t-Stat

22. P-value
Intercept
729.8665
169.25751
4.3121659
0.0010099
Price
-10.887
3.4952397
-3.1148078
0.0089406
Advertising
0.0465
0.0176228
2.6386297
0.0216284
ANOVA
df
SS
MS
F
Significance F
Regression
2
12442.8
6221.4
37.56127994
0.00000683
Residual
12
1987.6
165.63333

23. Total
14
14430.4
Se =12.86986 R-sq = 0.862263 R-sq(adj) = 0.8393068
a) Write and interpret the multiple regression equation.
b) Does the model with Price and Advertising contribute to the
prediction of Y? Use a 0.05 significance level.
c) Which independent variable appears to be the best predictor
of sales? Explain.

24. d) What is the number of observations used in this study?
e) Assuming that the coefficient on Advertising has Ha: B1 > 0,
what statistical decision should be made at 5% level.
f) What is the standard error of estimate? Can you use this
statistic to assess the model’s fit? If so, how?
g) What is the coefficient of determination, and what does it tell
you about the regression model?
h) What is the coefficient of determination, adjusted for degrees
of freedom? What do this statistic and the statistic referred to in
part (g) tell you about how well this model fits that data.

25. i) Test the overall utility of the model. What does the p-value of
the test statistic tell you?
41. State whether should be accepted or rejected for , given the
following;
a) = 2.34; df = 2 and 11
b) = 2.52; df = 4 and 20
c) = 4.29; df = 3 and 24
42. Given the following, complete the ANOVA table and make
the correct inference.

26. Source
SS
df
MS
F
Treatments
____
2
3.24
____
Error
____
17
____
Total
40.98
____
ANSWER
a)
In the above ANOVA table, is the factor significant at 5% level
of significant?
b)
What is the number of observations?

27. 43. Given the following, complete the ANOVA table and make
the correct inference.
Source
SS
df
MS
F
Treatments
5
____
205.5
____
Error
____
637
____
Total
25
____
ANSWER
a)
In the above ANOVA table, is the factor significant at 5% level
of significant?
b)

28. What is the number of observations?
44. Given the following, complete the ANOVA table and make
the correct inference.
Source
SS
df
MS
F
Treatments
____
3
____
____
Error
88.8
____
____
Total
435
19
ANSWER
a)
In the above ANOVA table, is the factor significant at 5% level
of significant?

29. b)
What is the number of observations?
45. A metropolitan bus system sampler’s rider counts on one of
its express commuter routes for a week. Use the following data
to establish whether the rider ship is evenly balanced by day of
the week. Let
Day
Monday
Tuesday
Wednesday
Thursday
Friday
Rider Count
10
34
21
57
44
a) Is the χ2 value significant at 5% level of significance?

30. b) Write the conclusion for this question
46. A marketing research firm wished to study the relationship
between wine consumption and whether a person likes to watch
professional tennis on television. One hundred randomly
selected people are asked whether they drink wine and whether
they watch tennis. The following results are obtained:
Watch Tennis
Do not Watch Tennis
Totals
Drink Wine
16
24
40
Do not Drink Wine
4
56
60
Totals
20
80
100
Test the hypothesis that whether people drink wine is
independent of whether people watch tennis. Set α = 0.05

31. a) Is the χ2 value significant at 5% level of significant?
b) Write the conclusion for this question
)
Y
ˆ
Y
(
)
Y
Y
ˆ
(
i
-
+
-
The regression equation is
sales = - 19.7 - 0.00063 outlets + 1.74 cars + 0.410 income +
2.04 age
- 0.034 bosses
Predictor Coef SE Coef T P
Constant -19.672 5.422 -3.63 0.022
outlets -0.000629 0.002638 -0.24 0.823
cars 1.7399 0.5530 3.15 0.035
income 0.40994 0.04385 9.35 0.001

32. age 2.0357 0.8779 2.32 0.081
bosses -0.0344 0.1880 -0.18 0.864
S = 1.507 R-Sq = 99.4% R-Sq(adj) = 98.7%
Analysis of Variance
Source DF SS MS F P
Regression 5 1593.81 318.76 140.36 0.000
Residual Error 4 9.08 2.27
Total 9 1602.89
(Minitab Software)
)
Y
Y
(
i
-