Final—Form A
Spring 2003
Economics 173
Instructor: Petry
Name_____________
SSN______________
Before beginning the exam, please verify that you have 18 pages with 50 questions in
your exam booklet. You should also have a decision-tree and formula sheet provided by
your TA. Please include your full name, social security number and Net-ID on your
bubble sheets. Good luck!
Use the following information to answer the next eight questions (#1-8).
You are interested in understanding the home run hitting ability of young major league
baseball players. You decide to run a regression with the dependent variable: HRs--Number
of Homeruns Hit by the Player in the Most Recently Completed Major League Season. You
identify three independent variables:
Minor HR--Number of Homeruns the Player Hit in Last Season as a Minor Leaguer.
Age--the player’s age.
Years Pro--Number of Years the Player has been a Professional Ball Player.
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.59256
R Square
0.351128
Adjusted R
Square
0.335172
Standard Error
6.992105
Observations
126
ANOVA
df
Regression
Residual
Total
Intercept
Minor HR
Age
Years Pro
MS
1075.871
48.88953
F
Significance F
1.85592E-11
125
SS
3227.612245
5964.522676
9192.134921
Coefficients
-1.96998
0.665838
0.135728
1.176371
Standard Error
9.547049398
0.087149184
0.524087215
0.670625334
t Stat
-0.20634
7.640212
0.258979
1.75414
P-value
0.836866
5.46E-12
0.796088
0.081917
Lower 95%
-20.86933228
0.493317598
-0.901756157
-0.151200086
3
Upper
95%
16.92938
0.838359
1.173212
2.503942
1. The test statistic for testing the model’s overall significance is:
a.
0.0454
b.
22.006
c.
7.640
d.
0.524
e.
0.671
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2. The degrees of freedom for the test statistic named above is:
a.
3
b.
122
c.
3 and 122
d.
122 and 125
e.
122 and 126
3. The conclusion from the test performed above is:
a.
none of the three independent variables are significant
b.
all three independent variables are significant
c.
the dependent variable is significant
d.
at least one of the independent variables is significant
e.
all of the above
4. Based on the t-tests for individual significance, and at a 5% level of significance, the
variable(s) that DO have a significant impact on homerun hitting ability is (are):
a.
Minor HR
b.
Age
c.
Years Pro
d.
All the above
e.
Both a and c
5. Ignoring the results from any significance tests conducted on the model, the estimated
number of HRs hit by a player who hit 22 HRs in his last season in the minor leagues, is 20
years old and has 3 years of professional ball playing experience is:
a.
19
b.
15
c.
12
d.
10
e.
5
6. Suppose that in this study, you generated a correlation matrix for the 3 independent
variables, as given below. Based SOLELY on this correlation matrix, which of these
problems would you suspect?
Minor HR
Age
Years Pro
a.
b.
c.
d.
e.
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Minor
HR
Age
1
0.035416
-0.03916
1
0.837398
Years
Pro
1
non-normality
autocorrelation
heteroskedasitcity
multicollinearity
none of the above
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7. In order to fix the problem identified in the previous question, you would:
a.
drop either Minor HR or Age from the model
b.
drop either Minor HR or Years Pro from the model
c.
drop either Years Pro or Age from the model
d.
include the log of age in the model
e.
do nothing since there is no problem
8. Assume that it was appropriate to conduct a Durbin-Watson test on the regression output,
and that the DW test statistic was 2.36. The DW critical values are: dL=1.61 and dU=1.74.
What should you conclude from this test?
a.
heteroskedasticity is present
b.
homoskedasticity is present
c.
multicollinearity is present
d.
autocorrelation is present
e.
the test proves inconclusive
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Use the following information to answer the next two questions (#9-10).
In a study of income differentials, data was collected for 100 subjects on their Incomes (in
thousands of dollars), Years of Education, Age, and Number of Children They Had. Then,
the natural log of income was taken as the y-variable, and regressed on the three independent
variables named above. The output is given below:
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.759978
R Square
0.577566
Adjusted R
Square
0.564365
Standard Error
0.264954
Observations
100
ANOVA
df
Regression
Residual
Total
Intercept
Education
Age
Children
3
96
99
SS
9.214115
6.739241
15.95336
Coefficients
2.189232
0.092041
0.001391
-0.01082
Standard
Error
0.156791
0.008131
0.002276
0.020423
MS
3.071372
0.0702
F
43.75147
t Stat
13.9627
11.31922
0.611137
-0.5299
P-value
7.58E-25
2.26E-19
0.542553
0.597402
9. According to this output, for every additional child, the impact on income is
a.
decreases by 0.01082 dollars
b.
decreases by 10.82 dollars
c.
decreases by 0.989 dollars
d.
decreases by 989 dollars
e.
increases by 989 dollars
10. Disregarding any tests on the significance of individual independent variables, the
estimated income, in thousands of dollars, for someone with 17 years of education, 42 years
of age, with 3 children would be:
a.
3.78
b.
3779.9
c.
43.81
d.
24.6
e.
51.12
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11. In a multiple regression model the subjects’ ethnicities are to be represented as
independent variables. All subjects fall into five ethnic groups: Caucasian, AfricanAmerican, Asian, Native-American and Hispanic. How many dummy variables must be
constructed to adequately represent all five groups?
a.
1
b.
2
c.
3
d.
4
e.
5
Use the following information to answer the next two questions (#12-13).
Following is the output from a regression of Used Car Prices on Car Color and Odometer
Reading. Car Color is a qualitative variable, with levels White, Silver and Other Colors, and
is therefore represented in the model via dummy variables.
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.8354822
R Square
0.6980304
Adjusted R Square
0.6885939
Standard Error
142.27105
Observations
100
ANOVA
df
Regression
Residual
Total
Intercept
White
Silver
Odometer
3
96
99
SS
4491749.241
1943140.949
6434890.19
MS
1497250
20241.05
F
73.97095
Coefficients
6350.3231
45.240979
-147.73801
-0.0277698
Standard Error
92.16652879
34.08443045
38.18498973
0.002368579
t Stat
68.90053
1.327321
3.869007
-11.7242
P-value
1.5E-83
0.187551
0.000199
3.14E-20
12. On average, and odometer readings being the same, a White colored car would sell for
how much more (or less) than a Silver colored car?
a.
192.98
b.
-192.98
c.
102.50
d.
-102.50
e.
45.24
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13. According to this model, the estimated average selling price of a car that is of a Color
other than White or Silver (neither White nor Silver), and has an Odometer reading of 27,125
miles would be:
a.
6350.32
b.
5642.31
c.
5597.07
d.
5449.33
e.
4200.91
Use the following information to answer the next five questions (#14-18).
These questions are based on Project 2. You are expected to be able to recall that entire
scenario. Provided below are the ANOVA tables from the full and reduced model
regressions, respectively:
From full model:
ANOVA
df
Regression
Residual
Total
15
284
299
SS
2386035
1875818
4261852
MS
159069
6604.991
F
24.08315
Significance
F
3.63E-42
From reduced model:
ANOVA
df
Regression
Residual
Total
8
291
299
SS
2318693.212
1943159.21
4261852.422
MS
289836.7
6677.523
F
43.40481
Significance
F
2.06E-45
14. Going from the full to the reduced, how many variables get dropped?
a.
6
b.
7
c.
8
d.
9
e.
10
15. In order to test if the variables dropped are significant as a group, which statistical test
should be conducted?
a.
t-test, two sample, assuming equal variances
b.
t-test, two sample, assuming unequal variances
c.
chi square test for variance
d.
F-test for overall significance
e.
Partial F-test
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16. The calculated value of the test statistic for the test referred to above is:
a.
1.227
b.
1.117
c.
1.025
d.
1.457
e.
cannot be calculated due to insufficient information
17. The degrees of freedom for the test statistic calculated above is (are):
a.
6 and 284
b.
7 and 284
c.
6
d.
7
e.
284
18. Given that the relevant critical value for this test is 2.04, your conclusion should be:
a.
fail to reject the null hypothesis, therefore choose the reduced model
b.
fail to reject the null hypothesis, therefore choose the full model
c.
reject the null hypothesis, therefore choose the reduced model
d.
reject the null hypothesis, therefore choose the full model
e.
the test proves inconclusive
19. The range of values that R2 can possibly take is from -1 to 1.
a.
True
b.
False
20. While R2 can go down if irrelevant variable are included in the model, adjusted R2
always goes up upon the inclusion of new variables.
a.
True
b.
False
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Use the following information to answer the next two questions (#21-22).
MON
TUE
WED
THU
FRI
SAT
SUN
35
42
56
46
67
51
39
21. After doing a centered 2 period moving average on this column, the moving averages for
Friday, Saturday and Sunday are (in that order):
a.
50, 53.75, 57.75
b.
53.75, 57.75, 52
c.
57.75, 52, not available
d.
52, not available, not available
e.
67, 51, 39
22. The exponentially smoothed value (use a smoothing constant of 0.4) for Sunday is:
a.
not available
b.
54.07
c.
52.84
d.
47.30
e.
39
Use the following information to answer the next two questions (#23-24).
The following table gives you the actual observations from a time series (y) and the
corresponding residuals obtained after fitting a trend to the series.
Observation
1
2
3
4
5
6
7
8
9
10
Y
6.9
7.6
8.5
11.3
12.7
10.9
11.9
11.6
10.2
11.5
Residuals
-1.89763
-1.59915
-1.10068
1.297798
2.296273
0.094749
0.693224
-0.0083
-1.80982
-0.91135
23. The percent of trend value for period 7 is:
a.
1.06
b.
0.94
c.
17.17
d.
8.25
e.
cannot be calculated from the information provided
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24. After obtaining the percent trends for all periods, you plotted them against time. This
procedure is designed to reveal the presence of which time-series component?
a.
trend
b.
seasonal
c.
cyclical
d.
random
e.
irregular
Use the following information to answer the next five questions (#25-29).
Following is some output you might expect to be generated when dealing with a seasonal
time series. In this case we have quarterly data, for which the trend regression output is given
below:
Intercept
Time
Coefficients
23.67601329
0.310413772
Standard
Error
2.256404591
0.089331913
t Stat
10.4928
3.474836
P-value
3.51E-13
0.001221
Based on this model, percent of trend values were calculated, and an attempt was made to
construct seasonal indices. The results from this initial attempt are given below:
Q1
0.78
Q2
1.01
Q3
0.88
Q4
1.36
25. Making any necessary adjustments to these initial results, the final seasonal index for the
third quarter would be:
a.
0.774
b.
1.002
c.
1.350
d.
0.873
e.
0.88
26. Given that the actual value of the series (y) for period 19, which happens to be a third
quarter, is 23.43, what is the seasonal plus trend based forecast (that is the forecast that
takes into account BOTH the trend and the seasonal components) for that period?
a.
29.57
b.
25.82
c.
20.46
d.
26.03
e.
26.82
27. Relying on all the information above, what should the seasonally adjusted
(deseasonalized) value of the series be for period 19?
a. 29.57
b. 25.83
c. 20.46
d. 26.03
e. 26.84
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The SAME time series discussed above is now analyzed by representing the quarters by
indicator variables. The output is given below:
ANOVA
df
Regression
Residual
Total
Intercept
Time
Q1
Q2
Q3
4
38
42
SS
2438.89821
365.8136645
2804.711874
MS
609.7246
9.626675
F
63.33698
Coefficients
34.6197333
0.30514848
-17.5114879
-10.4739091
-14.3417848
Standard Error
1.291752195
0.038191454
1.356199997
1.355662143
1.356199997
t Stat
26.8006
7.989968
-12.9122
-7.72605
-10.575
P-value
2.76E-26
1.17E-09
1.8E-15
2.62E-09
7.06E-13
28. Given that this is sales data, name the quarter that clearly outperforms ALL other
quarters:
a.
Quarter 1
b.
Quarter 2
c.
Quarter 3
d.
Quarter 4
e.
Cannot be determined from the given information
29. Forecast the sales value for period 20, according to this indicator variable model:
a.
34.62
b.
40.72
c.
26.08
d.
42.10
e.
Cannot be determined from the given information
30. Which of the following statements is FALSE ?
a.
SSE should be used for model selection when it is important to avoid any
large errors.
b.
Autoregressive models are based on regressing a time series on its past values.
c.
In Autoregressive models some observations are lost, more so if the order of
the model is high.
d.
MAD is a criteria for model selection when several forecasting techniques are
available.
e.
When using MAD for model selection, the model with the largest MAD
statistic should be chosen.
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Use the following information to answer the next four questions (#31-34).
Recently a member of the United Nations was sent to Baghdad. He was assigned to compare
the prices that looters are charging for hospital equipment on the black market (population 1)
as compared to the prices that are charged by the regular manufacturers (population 2). The
United Nations representative claims that the black market prices are lower than the regular
market prices. Assume that because of the volatile situation in Baghdad, the looters have a
drastically higher variation in prices as compared to manufacturers.
You take a sample of 50 looted blood pressure cuffs and a sample of 300 blood pressure
cuffs from various regular manufacturers. You find that the average price for the sample of
looted cuffs was $65 with a standard deviation of $20.50 as compared to the $75 charged by
cuff manufacturers with a standard deviation of $3.25.
31. What is the null and alternative hypotheses to test the UN representative’s claim?
a.
Ho: μ2=μ1; H1: μ2<μ1
b.
Ho: μ1-μ2=0; H1: μ1- μ2>0
c.
Ho: μ1-μ2=0; H1: μ1- μ2<0
d.
Ho: μ1-μ2=0; H1: μ1- μ2≠0
e.
Ho: μ1=μ2; H1: μ1≠μ2
32. The test statistic for the test above is:
a.
-3.44
b.
-7.92
c.
-5.39
d.
5.39
e.
unable to determine because the variances are not known and cannot be
assumed equal or not equal.
33. What is the correct formula in Excel to calculate the p-value for the test statistic in the
previous question?
a.
FDIST(abs(test statistic),df1,df2,,300)
b.
TDIST(test statistic,df,2)
c.
FDIST(test statistic,df,50)
d.
NORMSDIST(test statistic)
e.
TDIST(abs(test statistic),df,1)
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34. Which shaded area (designated by the arrow) is the appropriate p-value for the test
designated above?
a.
b.
c.
d.
e.
35. Suppose the United Nations wants to make an inference about the population price of
black-market blood pressure cuffs (population 1 parameter) based upon the sample using
a confidence interval. What is the 95% confidence interval for blood pressure cuff prices
on the black market?
TINV(0.025,49)= 2.311
TINV(0.05,49)= 2.009
TINV(0.025,299)= 2.252
TINV(0.05,300)= 1.968
a.
74.63, 75.37
b.
74.58, 75.42
c.
59.29, 70.71
d.
59.18, 70.82
e.
58.30, 71.70
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36. Suppose the United Nations wants to test the claim that the population variance of blackmarket blood pressure cuff prices is equal to $20. What is the correct test to use?
a.
Pooled-variance t test for the difference of two means
b.
F test for the difference in variances
c.
T-test for a single population mean
d.
Z-test for a single population mean
e.
Chi-square test for a single population variance
37. What sequence of commands are necessary to reach the following menu?
Moving Average
Rank and Percentile
Random Number Generation
Regression
Sampling
t-Test: Paired Two Sample for Means
t-Test: Two Sample Assuming Equal Variances
t-Test: Assuming Unequal Variances
z-Test: Two Sample for Means
a.
b.
c.
d.
e.
OK
Cancel
Help
Data --> Tools --> Descriptive Statistics
Tools--> Data Analysis
Tools --> Descriptive Statistics --> Data Analysis
Descriptive Statistics --> Tools
Regression --> Descriptive Statistics
38. The Central Limit Theorem states:
a.
Only when a random sample is drawn from a normally distributed population
will the sampling distribution of the sample mean be approximately normal
for a sufficiently large sample size.
b.
If a random sample is drawn from any population, the sampling distribution of
the sample mean is approximately normal even with a small sample size.
c.
If a random sample is drawn from any population, the sampling distribution of
the sample mean is approximately normal for a sufficiently large sample size.
d.
It is impossible to go from a sampling distribution to a standardized
distribution regardless of the population distribution.
e.
None of the above
39. Which of the following is FALSE regarding Hypothesis Testing?
a.
When the p-value for the test is less than alpha for the test, the null hypothesis
is always rejected.
b.
The currently accepted hypothesis or the status quo is designated as the null
hypothesis, whereas the claim being tested is the alternative hypothesis.
c.
The equal sign is never in the alternative hypothesis.
d.
The alpha or significance level is associated with a Type I error.
e.
The p-value for a one-tailed test is always equal to the p-value of the twotailed test divided in half.
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40. Mark claims that students majoring in life sciences are particularly “slow” in
understanding statistics and that their final exam grades are lower than a 78. Tonight he
finds out that students in the life sciences scored an average of 81. The p-value for the
two-sided test is .04. What is your conclusion for this test based upon a 5% level of
signficance?
a.
There is insufficient evidence to reject the null hypothesis
b.
Ho: μ>78
c.
H1: μ=78
d.
The null hypothesis is rejected
e.
None of the above
Use the following information to answer the next two questions (#41-42).
Based on the summary regression outputs between the S&P 500 index (the market) and five
individual stocks, and your recollection of Project 1, answer the following two questions.
Theragenics
Intercept
S & P 500
Coefficients
2.321611303
-0.48015053
Standard Error
2.89727262
0.62430997
t Stat
0.801309234
0.769089974
P-value
0.426223
0.444961
CDN
Intercept
S & P 500
Coefficients
-4.5450303
1.289943573
Standard Error
2.22063883
0.4785076
t Stat
-2.04672198
2.695764034
P-value
0.045226
0.009175
Xerox
Intercept
S & P 500
Coefficients
-2.14726773
1.82500000
Standard Error
t Stat
2.17235151
-0.98845317
0.468100 3.8987400000
P-value
0.327037
0.000253
Mattel
Intercept
S & P 500
Coefficients
-0.1667143
0.152880037
Standard Error
1.58542855
0.34163124
t Stat
-0.10515409
0.447500161
P-value
0.916616
0.656181
Walmart
Intercept
S & P 500
Coefficients
1.53009625
-1.0523076
Standard Error
1.04315895
0.22478193
t Stat
1.466791088
4.681460317
P-value
0.147834
1.76E-05
41. Suppose that several large companies are posting their expected earnings tomorrow and
that investors expect the market to go DOWN significantly. Where would you invest your
money, i.e. which stock would you buy?
a.
Theragenics
b.
CDN
c.
Xerox
d.
Mattel
e.
Walmart
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42. Suppose that you want to test whether XEROX stock moves perfectly with the market
(S&P 500 index). Use 5% significance level. What is your test statistic and what is your
conclusion (the sample size for Project 1 was 60)? (t0.025, 59= 2.000, t0.05, 59= 1.671, t0.10, 59=
1.296)?
a.
3.89874, conclude that you cannot reject the claim that Xerox and S&P 500
move perfectly together
b.
3.89874, conclude that Xerox and S&P 500 move perfectly together
c.
1.762444, conclude that you cannot reject the claim that Xerox and S&P 500
move perfectly together
d.
1.762444, conclude that Xerox and S&P 500 move perfectly together
e.
1.762444, conclude that you cannot reject the claim that Xerox and S&P 500
move perfectly together, but at 1% level of significance, you would be able to
conclude that they move together
43. The test statistic for testing whether there is linear relationship between Xerox and Mattel
is? Note: there are 60 observations in the sample
a.
b.
c.
d.
e.
Theragenics
CDN
Beverage
Xerox
Mattel
Wal-Mart
0.076418
0.583686
0.001274
1
4.585059
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CDN
Theragenics Beverage
1
Xerox
Mattel
-0.00642
1
0.340769 0.293372
1
0.074253 0.211244 0.076418
1
-0.04206 0.19027 0.21453 0.142672
Wal-Mart
1
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Use the following information to answer the next two questions (#44-45).
Suppose that you are a big baseball enthusiast and that you like both Sammy Sosa and Barry
Bonds. You are interested in testing whether there is a difference in batting averages between
the two of them. You are given the following summary data where SS indicates Sammy Sosa
and BB indicates Barry Bonds.
x SS  0.341 s SS  0.144 n  15
x BB  0.352 s BB  0.221 n  18
44. First, you have to decide which test to perform. Your initial strategy is to perform an Ftest to see whether variances of the two samples are equal or not. What is the value of your F
statistic?
a.
0.651584
b.
0.424561
c.
0.96875
d.
0.7819
e.
0.509474
45. Given that the upper critical value is F0.025, 14, 17 = 2.752, what would you do to test
whether there is a difference in batting averages between Sammy Sosa and Barry Bonds?
a.
perform a difference in means test assuming equal variances
b.
perform a matched pairs test for difference in means
c.
perform a difference in means test assuming unequal variances
d.
perform a ratio of variances test to check whether variances or two samples
are equal
e.
perform a z test for difference in means
Use the following information to answer the next two questions (#46-47).
It is said that group studying improves your chances of receiving an A on the final exam. To
test this claim, you gather grades from the UIUC students. More specifically, you separate
students who study in groups and the ones who don’t. Out of 1,700 observations, you found
that 800 of them study in groups and that 340 of those got A’s. Out of the people who don’t
study in groups, 345 got A’s.
46. At 5% significance, what is the test statistic and your conclusion? (Z0.025=1.96,
Z0.05=1.645, Z0.1=1.28)
a.
-0.252, students studying in groups don’t have a better chance of getting an A
b.
1.748, students studying in groups don’t have a better chance of getting an A
c.
-0.175, students studying in groups don’t have a better chance of getting an A
d.
1.748, students studying in groups have a better chance of getting an A
e.
-0.252, students studying in groups have a better chance of getting an A
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47. You are given summary data of study time in hours (x) and exam grades out of 100 (y).
n  20
x  10
y  82
 xi yi  16,000  xi2 = 1900
Using the given specifications, predict what is the expected grade of a student who studies 13
hours?
a.
42
b.
4
c.
94
d.
13
e.
81.333
48. Suppose that you ran a regression between watching tv and eating chips, where the
dependent variable is bags of chips eaten during a week and an independent variable is hours
of watching tv during the week. You are given the summary of the regression output below.
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.539579
R Square
Adjusted R
Square
0.26583
Standard Error
Observations
30
ANOVA
df
Regression
Residual
Total
SS
MS
1 94.93884 94.93884
28 231.148 8.255287
29
F
Significance F
Calculate the coefficient of determination and interpret it.
a.
0.2911, 29.11% of variation in hours of tv watching is explained by variation
in the number of bags of chips eaten
b.
2.873, 2.873% of variation in the number of bags of chips eaten is explained
by variation in hours of tv watching
c.
11.5, 11.5% of variation in the number of bags of chips eaten is explained by
variation in hours of tv watching
d.
0.2911, 29.11% of variation in the number of bags of chips eaten is explained
by variation in hours of tv watching
e.
2.873, 2.873%, of variation in the number of bags of chips eaten is explained
by variation in hours of tv watching
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Use the following information to answer the next five questions (#49-50).
You are given the summary output of the regression between age and hours of reading
newspapers during a week. Age is an independent variable, while the Hours of Reading
Newspapers During a Week is a dependent variable.
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.333683
R Square
0.111345
Adjusted R
Square
0.096023
Standard Error
16.66673
Observations
60
ANOVA
df
Regression
Residual
Total
Intercept
AGE
1
58
59
Coefficients
-4.54503
1.289944
SS
MS
2018.665 2018.665
16111.22 277.7797
18129.89
Standard
Error
2.220639
0.478508
t Stat
F
Significance F
0.009175
P-value
0.045226
49. If you want to formally test the validity of the model, which test would you perform and
what would be your test statistic?
a.
F-test, 0.009175
b.
t-test, -2.04672
c.
Z-test, 0.111345
d.
t-test, 1.289944
e.
F-test, 7.267144
50. Suppose you want to test whether variable AGE is a significant variable in the above
model. What is your test statistic and a p-value for that test?
a.
test stat: 7.267144; p-value: 0.045226
b.
test stat: 7.267144; p-value: 0.096023
c.
test stat: 2.695764; p-value: 0.009175
d.
test stat: -2.04672; p-value: 0.045226
e.
test stat: 2.695764; p-value: 0.045226
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Answer Key:
1. B
2. C
3. D
4. A
5. A
6. D
7. C
8. E
9. E
10. C
11. D
12. A
13. C
14. B
15. E
16. D
17. B
18. A
19. B
20. B
21. C
22. D
23. A
24. C
25. D
26. B
27. E
28. D
29. B
30. E
31. C
32. A
33. E
34. E
35. E
36. E
37. B
38. C
39. E
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40. A
41. E
42. C
43. B
44. B
45. A
46. D
47. C
48. D
49. E
50. C
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