Final—Form A
Summer 2002
Economics 173
Instructor: Petry
Name_____________
SSN______________
Before beginning the exam, please verify that you have 11 pages with 35 questions in your
exam booklet. You should also have a decision-tree and formula sheet provided by your
TAs. Please include your full name, social security number and Net-ID on your bubble
sheets.
Good luck!
Use the following data points to answer questions 1-2.
5, 6, 12, 7, 8, 2, 9.
1.
The median 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
2.
The standard deviation for this data set is:
a. half the variance
b. 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”, or “empirical rule, 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
3.
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Use the following information to answer questions 4-7.
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.
Recall that the portfolio variance formula is: 2(Rp) =w12 21 + w22 22 +2w1w212.
Benefits of Diversification
Investment Proportion
Bonds
Stocks
0%
100%
20%
80%
40%
60%
60%
40%
80%
20%
100%
0%
Portfolio
Expected Return
Standard Deviation
Table of Correlation Coefficients
GM
GM
1
CATERPILLAR 0.218434
BIOGEN
0.113032
ENRON
0.341501
INTEL
0.442635
CATERPILLAR BIOGEN ENRON
1
-0.175108261
0.189219646
0.081064863
INTEL
1
0.209297 1
0.342395 0.293953 1
4.
Upon completing the table, the 80% bond, 20% stock portfolio will have an expected
return of:
a. 16.2%
b. 10.8%
c. 9%
d. 18%
ANSWER: B
5.
That same portfolio (80%bond 20% stock) will have a standard deviation of:
a. 1.2%
b. 4.3%
c. 10.9%
d. 19%
ANSWER: C
6.
Therefore, from the perspective of risk-management, this (80%, 20%) portfolio is:
a.
Better than an all bond (0% stocks) portfolio.
b.
Worse than an all bond portfolio.
c.
Same as an all bond portfolio.
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d.
The worst possible
ANSWER: A
7.
Again, from the diversification/risk-management angle, the most lucrative combination
is:
a. INTEL and ENRON
b. CATERPILLAR and ENRON
c. BIOGEN and INTEL
d. BIOGEN and CATERPILLAR.
ANSWER: D
Use the following two tables to answer questions 8-11.
FULL MODEL
Regression Statistics
Multiple R
0.470948536
R Square
0.221792524
Adjusted R Square
0.213128271
Standard Error
2547.059272
Observations
1000
ANOVA
df
Regression
Residual
Total
Intercept
TOTAL
HI_ENJOY
AF_AM
NAT
ASIAN
HISP
FEMALE
COLLEGE
WORK
WORK2
UNDER25
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988
999
SS
MS
F
Significance F
1826781276 166071025.1 25.59857344 4.84864E-47
6409660803 6487510.934
8236442079
Coefficients Standard Error
43700.85579 345.0928105
106.4565472 21.20842047
517.173803 178.8663012
-370.4585954 781.8900104
-211.6441279
581.352107
-831.2279845 197.9288103
-605.4712339 411.3955267
-434.709669 175.7162291
168.5104031 172.5055797
-32.00957871 64.29083108
16.26601487 4.264223537
-843.6227371 199.9255261
t Stat
126.6350804
5.019541521
2.891398768
-0.47379886
-0.364054977
-4.199631086
-1.471749678
-2.473930104
0.976840305
-0.497887151
3.814531468
-4.219684967
P-value
0
6.14146E-07
0.003919354
0.635748026
0.71589485
2.91494E-05
0.141406929
0.013530693
0.328887333
0.618674383
0.000144908
2.67156E-05
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REDUCED MODEL
Regression Statistics
Multiple R
0.467601243
R Square
0.218650922
Adjusted R Square
0.21392978
Standard Error
2545.761722
Observations
1000
ANOVA
df
Regression
Residual
Total
Intercept
TOTAL
HI_ENJOY
ASIAN
FEMALE
WORK2
UNDER25
6
993
999
SS
MS
1800905655 300150942.5
6435536424 6480902.743
8236442079
Coefficients Standard Error
43731.73558 255.1951529
102.5075909 20.89307792
502.9148062 177.1019572
-787.2056854 195.3972259
-456.2025095 173.6868534
14.07788712
1.35354551
-879.7881838 193.5617931
t Stat
171.3658551
4.906294384
2.839690843
-4.028745453
-2.626580542
10.40074901
-4.545257458
F
Significance F
46.3131379 3.77367E-50
P-value
0
1.08413E-06
0.004607905
6.03551E-05
0.008757564
4.04404E-24
6.1623E-06
8.
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. Do not reject 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. Do not reject 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
9.
The test statistic for testing the following set of hypotheses is based principally upon:
H0: β3 = β4 = β6 = β8 = β9 = 0
H1: at least one βj ≠ 0
a. The relationship between SSRr and SSRf
b. The relationship between SSTr and SSTf
c. The relationship between SSEr and SSTf
d. The relationship between the t-distribution and the F-distribution
e. None of the above
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ANSWER: A
10.
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. Do not reject the null and use the FULL model for prediction
c. Reject the null and use the REDUCED model for prediction
d. Do not reject the null and use the REDUCED model for prediction
e. Cannot tell from the information given.
ANSWER: A
11.
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. 44,411.97
b. 44,859.83
c. 44,379.44
d. 44,831.68
e. 43,980.04
ANSWER: B
12.
Suppose that we calculate the four-period moving average of the following time series
t
yt
1
16
2
28
3
21
4
15
5
26
6
12
The centered moving average for period 3 (that would be in the same row as) is:
a. 22.5
b. 21.25
c. 20.50
d. 18.5
ANSWER: B
13.
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
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14.
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
Use the following table to answer questions 15-16.
Actual Values yt
2325
2555
2835
3185
3510
Forecast
Values
Ft
2330
2595
2860
3125
3390
15.
The mean absolute deviation (MAD) equals:
a. 55
b. 48
c. 20
d. 50
e. 60
ANSWER: D
16.
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
17.
The following seasonal indexes and linear trend were computed from five years of
quarterly sales data.
Trend line: yˆ  500  30t
Quarter
1
2
3
4
(t = 1, 2, 3, ……., 20)
Seasonal Index
1.4
1.2
0.9
0.5
The forecast for the 3rd quarter of the 6th year equals:
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a. 1,322
b. 1,071
c. 1,392
d. 1,200
e. None of the above
Answer: B
18.
The following autoregressive model was developed
yˆ t  200  15 yt 1
Assuming that the values for time periods 20 and 21 were 10 and 8 respectively, what
would you forecast for time-period 22?
a. 240
b. 8
c. –8
d. 335
e. 320
Answer: E
19.
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
20.
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
21.
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
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22.
In a regression model involving 50 observations, the following estimated regression
model was obtained:
yˆ  10.5  3.2 x1  5.8x2  6.5 x3
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
23.
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
24.
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
Use the following information to answer questions 25-26.
Suppose that you are interested in explaining why more accidents occur on one particular stretch
of highway than on a second stretch of highway. You believe that high variation in speeds of
travelers on each highway is the leading cause of accidents in these areas. You are given the
following information:
S1 = 4
n1 = 100
S2 = 3
n2 = 50
25.
In order to test whether the population variances of the speeds on the two stretches of
highway are the same, what would the null hypothesis be?
a. The population variance of highway 1 is greater than the population variance of
highway 2.
b. The population variance of highway 1 is the same as the population variance of
highway 2.
c. The population variance of highway 1 is smaller than the population variance of
highway 2.
d. The population variance of highway 1 is different than the population variance of
highway 2.
e. None of the above.
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ANSWER: B
26.
What is the value of the test statistic for the above test?
a. 1.3333
b. 0.75
c. 1.7777
d. 1.1547
e. not enough information given
ANSWER: A
27.
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:
t0.025, 63 = 1.998
n1  50
x1  175
s1  18.5
z0.025 = 1.96
n2  42
x2  158
s2  32.4
The upper confidence limit is approximately:
a. 19.123
b. 28.28
c. 24.911
d. 28.06
ANSWER: B
28.
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
29.
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
30.
In testing the null hypothesis H 0 : p1  p2  0 , if H 0 is false, the test could lead to:
a. a Type I error
b. a Type II error
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c. either a Type I or a Type II error
d. None of the above
ANSWER: B
31.
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. .14
e. None of the above
ANSWER: B
Use the following output to answer questions 32-35.
SUMMARY OUTPUT
Regression Statistics
Multiple R
R Square
Adjusted R Square
Standard Error
Observations
ANOVA
df
Regression
Residual
Total
Intercept
Vacancy
1
28
29
SS
MS
F
Significance F
94.93883672 94.93884 11.50037 0.002089293
231.1480299 8.255287
326.0868667
Coefficients Standard Error
t Stat
P-value
Lower 95%
Upper 95%
20.63970836
1.14279152 18.06078 5.78E-17 18.29880342 22.9806133
-0.303797797 0.089583649 -3.391219 0.002089 -0.487301789
-0.1202938
32.
The coefficient of determination is:
a. .5396
b. .2911
c. .2658
d. .304
e. none of the above
ANSWER: B
33.
The standard error of the regression is:
a. .08958
b. -.3038
c. 2.8732
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d. 8.2553
e. Impossible to determine with the information given
ANSWER: C
34.
The correlation coefficient between the dependent and independent variable is:
a. 20.6397
b. -.303798
c. .540
d. -.2911
e. None of the above
ANSWER: E
35.
In the graph provided below, it is likely that the analyst was trying to determine:
Residuals
Vacancy Residual Plot
10
0
-10
0
5
10
15
20
25
Vacancy
a. if the error variable is normally distributed
b. if the error variance is constant
c. if there is multicollinearity
d. if there is heteroscedasticity
e. both b and d
ANSWER: E
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