NAME: _________________________________
University of Illinois
Econ 173
Final Exam
Summer II, 2001
TEST FORM A
SSN or NETID: __________________________
Teaching Assistant: _______________________
Lab Section Number: _____________________
Lab Time: _____________________________
On the Test Answer Sheet, remember to bubble in your (I) LAST NAME; (II) FIRST NAME INI.; (III)
DATE; (IV) SECTION; (V) NETWORK ID and (VI) version of your exam in TEST FORM. Sign your Test
Answer Sheet at the place provided. Enter your last name and first name as it appears on your Students ID, no nicknames please. This exam booklet along with the Test Answer Sheet will have to be turned in when you complete your exam.
This exam is closed book. All you need is a simple calculator, a pencil and an eraser. You may use the back of this exam booklet as scratch paper. There are 43 questions altogether in this exam. Every question has only one best answer, which you have to choose. All questions are worth the same number of points.
Make sure that your exam booklet has all ___ pages.

The Manager of Armani’s Pizza believes that pizza sales is largely explained by the number of students enrolled at the university where each of his restaurants is located. In addition to the information in the table below, he knows that the covariance between sales and enrollment is 61.2, and the variance of sales is 219.2, and enrollment is 18.8.
Use this information to answer the following two questions.
Restaurant
Sales*
Enrollment*
Armani's Pizza Sales & Student Enrollment
42
23
*Annual figures in thousands
1 2
56
30
3
31
20
4
14
18
5
22
19
1. He estimates the simple linear regression equation above, and finds the coefficient for the independent variable to be: a.
3.255 b.
–38.624 c.
6.884 d.
4.669 e.
None of the above
ANSWER: A
2. The R 2 for this regression is: a.
.909 b.
.612 c.
.388 d.
.868 e.
.953
ANSWER: A
3. In simple linear regression, the following two tests will provide identical answers: a.
the two versions of the chi-squared test for equality of means b.
the t-test and correlation coefficient test c.
the p-value test and the test statistic test d.
the beta test and one minus the alpha test e.
the p-value and the confidence level test
ANSWER: B
2

Your answers to the following 4 questions should be based on the multiple regression output provided below. The data represents an attempt by a real estate agent to determine the sale price for houses in her community. The last three coefficients in the table represent dummy variables for the type of house. Ranch style is the fourth type of house style that the agent is interested in. Unfortunately, the agent’s dog slobbered on the output making a number of the data points impossible to read.
SUMMARY OUTPUT
Regression Statistics
Multiple R
R Square
Adjusted R Square
0.77532
0.601122
Standard Error
Observations 100
ANOVA
Regression
Residual df SS MS F Significance F
82119688412 13686614735 23.35896562 1.17636E-16
93 54491075988 585925548.3
Total 99 136610764400
Intercept
Bedrooms
H Size
Lot Size
I two story1
I side split
Coefficients Standard Error t Stat P-value
29217 14589.05962 2.002665031 0.048124991
-937.692 6893.375444 -0.136028 0.892093159
79.86417 51.51834127 1.550208477 0.124487966
-5.06824 16.54643902 -0.30630394 0.760057916
20486.76 6992.663157 2.929750781 0.004267259
12795.04 7258.699651 1.76271809 0.081233206
I back split 19512.23 7964.973077 2.449754831
0.016167232
100000
0
-100000
0 1 2 3 4 5 6
Bedrooms
4. Based on the output given above, how would you characterize this model, and what course of action is most appropriate? a.
This model represents a good start, but it looks like multicollinearity is a problem. The agent had better plot the residuals against the regression line to check if this problem should be remedied before proceeding further. b.
This model is useless as multicollinearity is obviously a problem. The real estate agent should start over with a completely different set of variables. c.
The output suggests a reasonable fit to the data. There do not appear to be any significant error violations. The agent should get rid of the insignificant variables and the model should be ready to use to make predictions. d.
This is not a very well fitting model. For the number of variables R 2 is low and a number of the independent variables are not significant. e.
None of the above.
ANSWER: E
3

5. What is the value for adjusted R 2 ? a.
39.89% b.
57.54% c.
60.11% d.
42.46% e.
None of the above
ANSWER: B
6. What is the value for the Standard error of the estimate? a.
14589 b.
26432 c.
29217 d.
24206 e.
It is impossible to determine from this output
ANSWER: D
7. Assuming the agent deems the above model appropriate to use, it would be correct to say that: a.
A “two-story” house on average would sell for $20,487 more than a “back split” house. b.
A “ranch” house should on average sell for $12,795 more than a “side split” house. c.
A “back split” house should on average sell for $19,512 more than a “two story” house. d.
A “two story” house and a “side split” house should sell for about the same amount compared to a
“back split” house. e.
None of the above.
ANSWER: E
Use the following data points for the next three questions: 5, 6, 12, 7, 8, 2, 9.
8.
9.
The median is for this data is: a.
8 b.
6.5 c.
The same as the mean d.
The same as the mode e.
Larger than the mode
ANSWER: c
The standard deviation for this data set is: a. half the variance b. 10
10. c. 3.16 d. a measure of the dispersion of the data around its mean e. both c & d
ANSWER: e
The “rule of thumb” indicates that: a. Approximately 98% of the observations should lie within 2 means of the standard deviation b. Approximately 65% of the observations lie within 1 standard deviation of the mean c. Exactly 65% of the observations lie within 2 standard deviations of the mean d. Exactly 98% of the observations lie within 2 standard deviations of the mean e. None of the above
Answer: e
4

The following table is meant to list expected returns and standard deviations for various portfolios of stocks and bonds. You also have the following information: the historical return for bonds has been 9%, with standard deviation of 12%. Returns for the S&P 500 index has been 18%, with a standard deviation of 26%. Assume the correlation coefficient between the two assets is zero. Use this information to answer the following 4 questions.
Investment Proportion
Bonds Stocks
0%
20%
40%
60%
80%
100%
100%
80%
60%
40%
20%
0%
Table of Correlation Coefficients
Portfolio
Expected Return Standard Deviation
GM
GM
1
CATERPILLAR BIOGEN ENRON INTEL
CATERPILLAR 0.218434 1
BIOGEN 0.113032 -0.175108261 1
ENRON 0.341501 0.189219646 0.209297 1
INTEL 0.442635 0.081064863 0.342395 0.293953 1
11. Upon completing the table, the 80% bond, 20% stock portfolio will have an expected return of: a.
b.
c.
d.
16.2%
10.8%
9%
18% answer: b
12. That same portfolio (80%bond 20% stock) will have a standard deviation of: a.
b.
c.
d.
1.2%
4.3%
10.9%
19% answer: c
13. Therefore, from the perspective of risk-management, this (80%, 20%) portfolio is: a.
b.
c.
d.
Better than an all bond (0% stocks) portfolio.
Worse than an all bond portfolio.
Same as an all bond portfolio.
The worst possible.
Answer: a
5

Total
Intercept
TOTAL
HI_ENJOY
AF_AM
NAT
ASIAN
HISP
FEMALE
COLLEGE
WORK
WORK2
UNDER25
14. Again, from the diversification/risk-management angle, the most lucrative combination is: a.
b.
c.
d.
INTEL and ENRON
CATERPILLAR and ENRON
BIOGEN and INTEL
BIOGEN and CATERPILLAR.
Answer:d
Use the tables below to answer the following four questions.
FULL MODEL
Regression Statistics
Multiple R 0.470948536
R Square 0.221792524
Adjusted R Square 0.213128271
Standard Error
Observations
2547.059272
1000
ANOVA
Regression
Residual df SS MS F Significance F
11 1826781276 166071025.1 25.59857344 4.84864E-47
988 6409660803 6487510.934
999 8236442079
Coefficients Standard Error t Stat
43700.85579 345.0928105 126.6350804
P-value
0
106.4565472 21.20842047 5.019541521 6.14146E-07
517.173803 178.8663012 2.891398768 0.003919354
-370.4585954 781.8900104 -0.47379886 0.635748026
-211.6441279 581.352107 -0.364054977 0.71589485
-831.2279845 197.9288103 -4.199631086 2.91494E-05
-605.4712339 411.3955267 -1.471749678 0.141406929
-434.709669 175.7162291 -2.473930104 0.013530693
168.5104031 172.5055797 0.976840305 0.328887333
-32.00957871 64.29083108 -0.497887151 0.618674383
16.26601487 4.264223537 3.814531468 0.000144908
-843.6227371 199.9255261 -4.219684967 2.67156E-05
6

REDUCED MODEL
Regression Statistics
Multiple R 0.467601243
R Square
Adjusted R Square
Standard Error
0.218650922
0.21392978
2545.761722
Observations 1000
ANOVA
Regression
Residual
Total df SS MS F Significance F
6 1800905655 300150942.5 46.3131379 3.77367E-50
993 6435536424 6480902.743
999 8236442079
Intercept
TOTAL
HI_ENJOY
Coefficients Standard Error t Stat
43731.73558 255.1951529 171.3658551
P-value
0
102.5075909 20.89307792 4.906294384 1.08413E-06
502.9148062 177.1019572 2.839690843 0.004607905
ASIAN
FEMALE
-787.2056854 195.3972259 -4.028745453 6.03551E-05
-456.2025095 173.6868534 -2.626580542 0.008757564
WORK2 14.07788712 1.35354551 10.40074901 4.04404E-24
UNDER25 -879.7881838 193.5617931 -4.545257458 6.1623E-06
15. Based on the FULL model given above, and using a 5% significance level, what is your conclusion for the overall significance test of the model? a.
Accept the null, concluding that none of the variables in the model are significant. b.
Reject the null, concluding that none of the variables in the model are significant. c.
Accept the null, concluding that at least one of the variables in the model is significant. d.
Reject the null, concluding that at least one of the variables in the model is significant. e.
Reject the null, concluding that all of the variables in the model are significant.
Answer: D
16. The test statistic for testing the following set of hypotheses is________:
H
0
: β
3
= β
4
= β
6
= β
8
= β
9
= 0
H
1
: at least one β j
≠ 0 a. 0.7977 b. 25.598 c. 46.313 d. –1.83 e. 4.848E-7
Answer: A
7

17. Assuming the p-value of the previous test is .00486, and using a 5% significance level what is your conclusion? a.
Reject the null and use the FULL model for prediction b.
Accept the null and use the FULL model for prediction c.
Reject the null and use the REDUCED model for prediction d.
Accept the null and use the REDUCED model for prediction e.
Cannot tell from the information given.
Answer: A
18. Given a person with the following characteristics, and using the REDUCED model, predict this person’s average SALES.
An Hispanic female who is 31 years old, a college graduate, has 2 years of work experience, scored a 10 on the
TOTAL scale, and enjoys working with customers. a. 44411.97 b. 44859.83 c. 44379.44 d. 44831.68 e. 43980.04
Answer B
19. Suppose that we calculate the four-period moving average of the following time series t 1 2 3 4 5 6 y t
16 28 21 15 26 12
The centered moving average for period 3 is: a.
22.5 b.
21.25 c.
20.50 d.
18.5
ANSWER: b
20. If we want to measure the seasonal variations on stock market performance by quarter, we would need: a.
4 indicator variables b.
3 indicator variables c.
2 indicator variables d.
1 indicator variable
ANSWER: b
21. If summer 1998 sales were $12,600 and the summer seasonal index was 1.20, then the deseasonalized 1998 summer sales value would be: a.
$12,600 b.
$12,601.2 c.
$15,120 d.
$10,500
ANSWER: d
8

The actual and forecast values of a time series are shown below. Use these values to answer the following two questions.
Actual Values y t
Forecast Values F t
2325
2555
2835
3185
3510
2330
2595
2860
3125
3390
22.
23.
The mean absolute deviation (MAD) equals: a.
55 b.
48 c.
20 d.
50 e.
60
Answer: D
The sum of squares for forecast error (SSE) equals: a.
20,200 b.
20,250 c.
19,100 d.
21,500 e.
23,200
Answer: B
24. The following seasonal indexes and trend linear were computed from five year of quarterly sales data.
Trend line:

500

30 t ( t = 1, 2, 3, ……., 20)
Quarter
1
Seasonal Index
1.4
2
3
1.2
0.9
4 0.5
The forecast for the 3 rd quarter of the 6 th year equals: a.
1322 b.
1071 c.
1392 d.
1200 e.
None of the above
Answer: B
25. The following autoregressive model was developed t

200

15 y t

1
Forecast the next value of the time series if the last observation was 8. a.
240 b.
8 c.
–8 d.
335 e.
320
9

Answer: E
26. Forecasts based on trend and seasonality are generated by: a.
identifying and removing the seasonal effect b.
extrapolating the linear trend c.
adjusting the forecasts to the seasonal effect d.
all of the above
ANSWER: d
27. The mean absolute deviation (MAD) and the sum of squares for forecast error (SSE) are the most commonly used measures of forecast accuracy. The model that forecasts the data best will usually have the: a.
lowest MAD and highest SSE b.
highest MAD and lowest SSE c.
lowest MAD and SSE d.
highest MAD and SSE
ANSWER: c
28. Stepwise regression is an iterative procedure that: a.
adds one independent variable at a time b.
deletes one independent variable at a time c.
either a or b d.
both a and b
ANSWER: d
29. In regression analysis, indicator variables allows us to use: a.
quantitative variables b.
qualitative variables c.
only quantitative variables that interact d.
only qualitative variables that interact
ANSWER: b
Use the information below to answer the following two questions. For a sample of 500 college professors, the estimated regression equation is

275

3 x

2 I
30. where y is retirement age, x is pre-retirement annual income (in $1000s), and I is an indicator variable that takes the value of 0 for male professors and 1 for female professors. Assume that your model indicates there is a relationship between y and the two independent variables.
For female professors with pre-retirement income of $70,000, the average age of retirement is: a.
70 b.
63 c.
60 d.
58
ANSWER: b
31. For each additional thousand dollars of pre-retirement income, the average age at retirement for male professors changes by: a.
3 b.
2 c.
–3 d.
–2
ANSWER: c
32. In a regression model involving 50 observations, the following estimated regression model was obtained:
10

y
ˆ 
10 .
5

3 .
2 x
1

5 .
8 x
2

6 .
5 x
3
For this model, SSR = 450 and SSE = 175. The value of MSR is: a.
12.50 b.
275 c.
150 d.
3.804
ANSWER: c
33. In testing the utility of a multiple regression model, a large value of the F -test statistic indicates that: a.
most of the variation in the independent variables is explained by the variation in y b.
most of the variation in y is explained by the regression equation c.
most of the variation in y is unexplained d.
the model provides a poor fit
ANSWER: b
34. If multicollinearity exists among the independent variables included in a multiple regression model, then: a.
regression coefficients will be difficult to interpret b.
standard errors of the regression coefficients for the correlated independent variables will increase c.
multiple coefficient of determination will assume a value close to zero d.
both a and b are correct statements
ANSWER: d
35. In testing whether the means of two normal populations are equal, summary statistics computed for two independent samples are as follows: n
1 n
2


25
25 x
1 x
2

7 .
30 s
1

6 .
80 s
2

1 .
05

1 .
20
Assume that the population variances are equal. Then, the standard error of the sampling distribution of the sample mean difference x
1
 x
2
equal to: a.
.1017 b.
1.2713 c.
.3189 d.
1.1275
ANSWER: c
36. In constructing 95% confidence interval estimate for the difference between the means of two normally distributed populations, where the unknown population variances are assumed not to be equal, summary statistics computed from two independent samples are as follows: n n
1
2


50
42 x x
1
2


175
158 s s
1
2


18
32
.
.
5
4
The upper confidence limit is: a.
19.123 b.
28.212 c.
24.911 d.
5.788
ANSWER: b
11

37. A sample of size 100 selected from one population has 60 successes, and a sample of size 150 selected from a second population has 95 successes. The test statistic for testing the equality of the population proportions equal to: a.
-.5319 b.
.7293 c.
-.419 d.
.2702
ANSWER: a
38. If some natural relationship exists between each pair of observations that provides a logical reason to compare the first observation of sample 1 with the first observation of sample 2, the second observation of sample 1 with the second observation of sample 2, and so on, the samples are referred to as: a.
matched samples b.
independent samples c.
weighted samples d.
random samples
ANSWER: a
39. In testing the null hypothesis H
0
: p
1
 p
2

0 , if H is false, the test could lead to:
0 a.
a Type I error b.
a Type II error c.
either a Type I or a Type II error d.
None of the above
ANSWER: b
40. In a hypothesis test for the population variance, the hypotheses are
H
0
:

2
H
1
:

2

30

30 .
If the sample size is 20 and the test is being carried out at the 5% level of significance, the null hypothesis will be rejected if: a.

2 
30 .
144 b.

2 
10 .
851 c.
d.

2

2

10 .
117

31 .
410
ANSWER: c
41. From a sample of 400 items, 14 are defective. The point estimate of the population proportion defective will be: a.
14 b.
0.035 c.
28.57 d.
.05 - .10
ANSWER: b
42. After calculating the sample size needed to estimate a population proportion to within .04, your statistics professor told you the maximum allowable error must be reduced to just .01. If the original calculation led to a sample size of 800, the sample size will now have to be: a.
800 b.
3200 c.
12,800 d.
6400
ANSWER: c
12