A Multiple Regression Was Performed with 2 Independent Variables and 50 Observations On

Final Exam, Form AEconomics 173Name______

Spring 2002Instructor: PetrySSN______

Exam Instructions: Be sure you have all 17 pages with 47 questions. Select the best answer from those provided. To receive credit for the exam, you must properly fill out your bubble sheets with your name, SSN and net-id. Turn in your signed exam packet with your bubble sheet. GOOD LUCK!

1. The measurements of monthly rainfall in Aspen in 2001 were as follows: 20, 18, 30, 35, 38, 37, 36, 37, 39, 35, 32, 21. What is the mean and the median of the data?

Mean=30, median=31.5
Mean=31.5, median=35
Mean=35, median=35
Mean=32, median=30
Mean=32.5, median=35.5

2. Based on the relationship between the mean and the median in the above question we would conclude that the distribution of the monthly rainfall in Aspen in 2001 is:

Negatively skewed
Positively skewed
Symmetric
Normal
Not enough information to determine the shape of the distribution

3. We collected data from 5 different people on the number of jobs they have had and the change of their salary (in thousand dollars) last year. The results were put in the table below:

Person / # of previous jobs / Change in salary last year
1 / 4 / 6.8
2 / 4 / 4.9
3 / 4 / -2.8
4 / 4 / 1.7
5 / 4 / 9

Based on this sample, which of the following is true?

a.The number of previous jobs and the change in salary are positively correlated

b.The number of previous jobs and the change in salary are negatively correlated

c. The number of previous jobs and the change in salary are not correlated

d. The covariance between the number of jobs and the change in salary is a large positive number

e. The covariance between the number of jobs and the change in salary is a large negative number

4. To estimate the amount of fish that can be harvested in a pond, the mean weight of the fish in the pond must be estimated within +/-1 ounce with 99% confidence. What sample size should be taken if the weight of the fish is normally distributed with ounces? ()

a.166

5. When conducting a hypothesis test, a type II error occurs when

we reject when is false
we fail to reject when is true
we reject when is true
we fail to reject when is false
none of the above

6. Suppose NASA wants to test the claim that the average time an astronaut spends in space is less then 6 days. They took a sample of 100 astronauts and found that the sample mean is 5.8. If we assume that the average time spent in space is normally distributed with , then the p-value of our test statistic is: ()

a.bigger than 0.05

b.smaller than 0.025 but bigger than 0.01

c.smaller than 0.01

smaller than 0.05 but bigger than 0.025
can’t be determined based on this information

7. A widely acclaimed group of international experts found that a 95% confidence interval for the average minutes a married couple spends on the phone per month is [120, 186]. The number of minutes per month is normally distributed with known standard deviation. If we carried out a hypothesis test about and obtained a test statistic of z=3.504, what was our null hypothesis?

()

8. A factory owner wants to prove that the average output of workers in her factory (measured in boxes per hour) is more than 100. She wants to be 95% confident, and takes a sample of 50 workers. The sample mean turns out to be 105, and the sample standard deviation s=15. If the relevant critical value is 1.676, we would

fail to reject and conclude that the average output of workers is less than 100
reject and conclude that the average output of workers is greater than 100
fail to reject and conclude that the average output of workers is greater than 100
reject and conclude that the average output of workers is less than 100
we can’t decide because the test statistic is the same as the critical value

9. Suppose that in the above question we actually knew that the average output is normally distributed with . The result of the same hypothesis test in this case would be:

a.the same as before because the relevant critical value is now bigger than 2.4

b.the same as before because the relevant critical value is now smaller than 1.676

c.fail to reject

reject and conclude that the average output of men is less than 100
There is not enough information to decide.

10. By looking at the rate of return of Intel and the S&P 500 for the last four years, we can conclude that:

Period / S&P 500 / Intel
1 / 6 / 2
2 / 1 / 4
3 / 5 / 1
4 / 2 / 5

a)for every additional unit of return of S&P500, Intel’s return will increase by 0.85 unit.

b)for every additional unit of return of S&P500, Intel’s return will decrease by 0.65 unit.

c)for every additional unit of return of S&P500, Intel’s return will increase by 1.05 unit.

d)for every additional unit of return of S&P500, Intel’s return will decrease by 1.05 unit.

e)for every additional unit of return of S&P500, Intel’s return will increase by 0.25 unit.

11. In the last question, what is the sum of the differences between actual Y’s and the predicted ones?

a)2.8823

b)3.6625

c)1.8952

d)7.1176

e)0

12. Which of the following statements violates the “required conditions” for a regression model:

The distribution of ε looks like chi-square distribution
The standard deviation of ε for high value X’s is the same as low value X’s.
The mean of ε is 2.02: E(ε)=2.02
Errors associated with different values of Y are all independent.

a)I and II

b)I and III

c)III and IV

d)I and II and III

e)II and III and IV

Use the following information to answer questions 13-16.

The regression below shows the relationship between the market return (S&P 500) and the return of the Novell Company.

SUMMARY OUTPUT
Regression Statistics
Multiple R / 0.335274
R Square
Adjusted R Square / 0.097105
Standard Error / 279.2267
Observations / 60
ANOVA
df / SS / MS / F / Significance F
Regression / 1 / 572702 / 572702 / 7.345388 / 0.008828
Residual / 4522119 / 77967.57
Total / 5094821
Coefficients / Standard Error / t Stat / P-value / Lower 95% / Upper 95%
Intercept / -15.3611 / 37.20357 / -0.41289 / 0.681207 / -89.8321 / 59.10988
S & P 500 / 1.810597 / 0.668058 / 2.710238 / 0.008828 / 0.473334 / 3.147859

13. What is the proportion of the variability of the return of the Novell Company explained by the variability in S&P500 returns?

a)0.8876

b)0.1266

c)0.1124

d)0.8733

e)Not enough information to compute

14. What is the value of the statistic for testing the following hypothesis?

Ho: β1 = 1

H1: β1 ≠ 1

a)1.2134

b)2.7102

c)–1.2134

d)–2.7102

e)1.8162

15. What is the p-value for testing whether there is a positive linear relation between the return of the Novell Company and S&P 500:

a)0.0177

b)0.0088

c)0.0044

d)0.9956

e)0.9912

16. What are the residual degrees of freedom and total degrees of freedom respectively?

a)57,59

b)58,60

c)57,58

d)58,59

e)57,60

17. Going from any other line fitted to a series of X and Y to a “Least Squares Regression Line”:

a)SSE increases but SSR decreases

b)Both SSE and SSR decrease

c)SSE decreases but SSR increases

d)SSE increases but SST decreases

e)SSR decreases but SST increases

Use the following information to answer question 18.

Below is the summary of 5 regression outputs for the relationship of the market (S&P 500) and 5 different companies.

EATN / Coefficients / Standard Error / t Stat / P-value
Intercept / 0.02777373 / 0.116423452 / 0.23855784 / 0.812289
S&P / 0.47612071 / 0.20905961 / 2.27743996 / 0.026464
CAT / Coefficients / Standard Error / t Stat / P-value
Intercept / 0.05203058 / 0.146670497 / 0.35474469 / 0.724068
S&P / 0.7339081 / 0.263373712 / 2.78656548 / 0.007188
GM / Coefficients / Standard Error / t Stat / P-value
Intercept / -0.0579397 / 0.149770652 / -0.3868561 / 0.700279
S&P / 0.91671769 / 0.268940608 / 3.40862503 / 0.001193
COKE / Coefficients / Standard Error / t Stat / P-value
Intercept / -0.0655282 / 0.132785514 / -0.493489 / 0.623531
S&P / 0.88480059 / 0.238440685 / 3.71077859 / 0.000465
NOVELL / Coefficients / Standard Error / t Stat / P-value
Intercept / -0.1536111 / 0.372035737 / -0.4128933 / 0.681207
S&P / 1.81059653 / 0.668058235 / 2.71023757 / 0.008828

18. Which company or companies do you suggest for an aggressive investment assuming the market is expected to rise?

a)50% CAT and 50% EATN

b)EATN

c)50% GM and 50% CAT

d)NOVELL

e)COKE

19. According to the following correlation matrix, which companies would you select as a pair to minimize your risk?

EATN / CAT / GM / COKE / NOVELL
EATN / 1
CAT / 0.62617225 / 1
GM / 0.21937638 / 0.218434208 / 1
COKE / 0.13324676 / 0.141381763 / 0.05954184 / 1
NOVELL / -0.0018949 / 0.050441165 / 0.33289566 / -0.16053 / 1

a)EATN and NOVELL

b)CAT and COKE

c)EATN and CAT

d)GM and COKE

e)COKE and NOVELL

20. A random sample of 40 observations was taken out of a normal population. The sample variance turned out to be 11. Test the claim that the population variance is less than 15 knowing that χ2.95, 39= 25.7 and χ2.05, 39= 54.57. Your conclusion using a 5% significance level is:

a)Reject the null hypothesis and conclude that σ215

b)Fail to reject the null hypothesis and conclude that there is insufficient evidence to claim that σ215

c)Fail to reject the null hypothesis and conclude that there is insufficient evidence to claim that σ215

d)Reject the null hypothesis and conclude that σ215

e)There is insufficient evidence to conclude anything

21. Given that =.2 and n=250, estimate the 95% confidence interval for p.

Z0.025=1.96, Z0.05=1.645

a)[0.165 0.235]

b)[0.150 0.250]

c)[0.175 0.225]

d)[0.003 0.397]

e)[0.103 0.297]

22. To test whether more than 20% of the UIUC students think that the US soccer team will win 50% or more of their games at the upcoming World Cup 2002 in Japan and South Korea, your null hypothesis would be:

a)H0: p0.50

b)H0: p20

c)H0: p0.20

d)H0: p =0.50

e)H0: p0.20

23. If you need to estimate the proportion of the UIUC students who will watch the 2002 World Cup this summer within .04 units with 90% confidence, how big of a sample do you need given that Z0.05=1.645, Z0.10=1.28.

a)21

b)406

c)422

d)752

e)423

Use the following information to answer questions 24-25.

Suppose Kraft Foods only produces regular butter, fat-reduced butter, fat-free butter and margarine. The management will terminate production of any product whose proportion of the total sales volume is less than 10%. Assuming people buy only one of the 4, a survey of 400 people was conducted and the responses are:

The Number of Consumers of Each Product

Regular butter: / 80
Fat-reduced butter: / 100
Fat-free butter: / 200
Margarine: / 20

24. To make the correct decision, management should construct the following null and the alternative hypotheses:

a)H0: p0.10 / Ha: p0.10
b)H0: p10 / Ha: p10
c)H0: p0.10 / Ha: p0.10
d)H0: p =0.10 / Ha: p0.10
e)H0: p0.10 / Ha: p0.10

25. Regarding the question above, what would the management’s decision be regarding margarine production given that Z0.05=1.665: (assume 5% significance level)

a)Fail to reject the null hypothesis and discontinue producing margarine

b)Reject the null hypothesis and discontinue producing margarine

c)Fail to reject the null hypothesis and conclude that there is not enough evidence to continue producing margarine

d)Reject the null hypothesis and continue producing margarine

e)Fail to reject the null hypothesis and conclude that there is not enough evidence to discontinue producing margarine.

26. The owner of a travel agency is deciding where to open a new office. She believes that people whose income is over $40,000 will use the agency services. If more than 60% of the households within a radius of 5 miles have an income of $40,000 or more, then the owner will open a new agency in the area. Suppose you have data on all household incomes in the area. What kind of technique would you use to determine whether the agency will enter a given area?

a)Single population quantitative Z-test

b)Single population qualitative t-test

c)Two population difference in proportions

d)Single population quantitative t-test

e)Single population qualitative Z-test

27. Suppose that you want to compare the means of two populations, but you are not sure whether you should use EQUAL or UNEQUAL variances when constructing your test statistic. How do you proceed?

a)construct an F-test and decide whether variances are equal or unequal and proceed with a χ2 - test

b)assume the variances are equal and do a t -test

c)construct an F-test and determine to use unequal variances and do a t - test

d)look at the variances and eyeball whether they are the same or not and then use a χ2 - test

e)construct an F-test and decide whether variances are equal or unequal and proceed with a t-test

Use the following information to answer questions 28-31.

In this regression the dependent variable is salary and the independent variable is work experience.

SUMMARY OUTPUT
Regression Statistics
Multiple R
R Square
Adjusted R Square
Standard Error
Observations / 14
ANOVA
df / SS / MS / F
Regression / 1 / 571.9287593 / 571.9287593
Residual / 12 / 292.1736322 / 24.34780268
Total / 13
Coefficients / Standard Error / T Stat / P-value
Intercept / -7.442922509 / 2.607462884 / -2.854469206 / 0.014501968
Experience / 1.613399136 / 0.332889992 / 0.000400514

28. The coefficient of correlation is equal to_____and the coefficient of determination is equal to______:

0.814 and 0.662
0.662 and 0.814
0.510 and 0.715
0.715 and 0.510
None of the above

29. The P-value for the test for whether there is significant correlation between salary and work experience is equal to:

0.000400514
0.000200257
0.000801028
0.014501968
None of the above

30. The test statistic for testing the significance of the coefficient of work experience in this regression is equal to:

2.855
– 0.847
– 2.866
4.847
None of the above

31. The standard error of the estimate is equal to:

4.934
24.348
292.174
0.333
None of the above

32. The following graph is obtained from a regression analysis. In this regression which of the following could likely be a problem?

Positively autocorrelated errors
Heteroskedasticity
Negatively autocorrelated errors
a and c
b and c

33. The following graph is obtained from a regression analysis. In this regression, which of the following is likely to be a problem?

Positively autocorrelated errors
Heteroskedasticity
Negatively autocorrelated errors
a and c
b and c

34. It has been computed that the 95% confidence interval is [144.4, 154.2] for the average exam score when a student spent 10 hours on average per week studying for the class. The 99% prediction interval for a student who spent 10 hours on average per week studying for the class will be

a. of the same width

b. narrower

c. cannot be determined based on the provided information.

d. wider

e. None of the above

35. Which of the following is only possible in time-series data?

Autocorrelation
Heteroskedasticity
Non-normality of error terms
Multicolinearity
Both A and B

36. The Durbin-Watson test statistic is designed to test _____and it will vary between_____:

Heteroskedasticity, -4 and 4
Autocorrelation, 0 and 4
Non normality assumption, 2 and 4
Multicollinearity, 4 and 0
None of the above

37. The overall significance F-test is used to

a. Test if all independent variables are significant

b. Test if the model explains all the variation in the dependent variable

c. Test if at least one of the independent variables is significant

d. Give the same information as R^2

e. Select between 2 different models

38. A multiple regression was performed with 2 independent variables and 50 observations on time series data. You suspect that the regression error terms may be correlated, therefore violating a key regression assumption. What test would you perform to verify this?

the partial F test
the Durbin-Watson test
the F test for absolute significance
the t-test for individual significance
the t-test for mean difference

39. Upon performing the correct test for the problem above, you got a test statistic equal to 3.15. Your critical values are as follows:

dL = 1.46

dU = 1.63

You would then conclude that:

there is no autocorrelation
there is significant positive autocorrelation
there is significant negative autocorrelation
the model is not significant as a whole
the means of your independent variables are not equal

40. In Project II, you were asked to create a number of variables. The following text is taken directly from the Project II description, and provides the context for this question.

“They believe that employees who foresee a bright future in the company will have better motivation and, hence, will generate in higher sales. So they want to use the three questions about future employment possibilities (ADVNCOK, PROMFAIR and FUTOPPS) as predictors. Rather than including their results separately, they believe that they should form a scale by adding the results of the three questions together to form a Guttman Scale.” For this scale to be reliable,

the multiple R statistic for autocorrelated errors measured across independent variables should be significantly negative
the multiple R statistic for autocorrelated errors measured across independent variables should be significantly positive
the components should be negatively correlated with each other
the components should be positively correlated with each other
both b and d

41. Recall that for Project II, you identified variables that were not individually significant. Then, to see if they might be significant as a group, you performed a partial F-test. Suppose that the test resulted in a rejection of the null hypothesis. Under these circumstances, your FINAL MODEL would be:

the full model
the reduced model
a model with completely new independent variables
used for prediction
both a and d

42. When computing a seven period moving average, the number of observations lost are:

43. The time series of U.S. Gross Domestic Product (GDP), when plotted, reveals many ups and downs, but in general, shows a tendency to increase with time. Such a general tendency is best picked up by:

the cyclical component
the seasonal component
the trend component
the random component
none of the above

Use the following information to answer questions 44-47.

A manufacturer of ski equipment has noticed that there appears to be a seasonal pattern to her sales data. She therefore undertakes the computation of seasonal indices from the quarterly data she has from the 1st quarter of 1996 until the last quarter of 1999. The residuals and the predicted y values from the linear trend model are provided below:

Observation / Predicted Y / Residuals
1 / 92.44852941 / 13.55147
2 / 94.47205882 / -2.47206
3 / 96.49558824 / -31.4956
4 / 98.51911765 / 22.48088
5 / 100.5426471 / 14.45735
6 / 102.5661765 / -2.56618
7 / 104.5897059 / -31.5897
8 / 106.6132353 / 28.38676
9 / 108.6367647 / 5.363235
10 / 110.6602941 / -5.66029
11 / 112.6838235 / -33.6838
12 / 114.7073529 / 25.29265
13 / 116.7308824 / 4.269118
14 / 118.7544118 / -7.75441
15 / 120.7779412 / -38.7779
16 / 122.8014706 / 40.19853

44. The percentage trend for the 3rd quarter of 1997 should be:

114.4%
97.5%
69.8%
126.6%
cannot be computed from the information provided

45. Suppose the seasonal indices the ski equipment manufacturer came up with are:

Q1 = 1.094

Q2 = 0.958

Q3 = 0.688

Q4 = 1.26

Then the seasonally adjusted value of the original series for the 3rd quarter of 1997 should be:

106.105
50.216
196.25
92.87
cannot be computed from the information provided

46. And the seasonally adjusted forecast for the 3rd quarter of 1997 is:

69.17
70.57
71.96
73.35
cannot be computed from the information provided

47. When selecting a model from competing forecasting techniques, a way to choose is on the basis of:

MAD
SSE
DW
Both a and b
None of the above

Answer Key:

1.b25.b

2.a26.e

3.c27.e

4.a28.a

5.d29.a

6.d30.d

7.e31.a

8.b32.c

9.b33.b

10.b34.d

11.e35.a

12.b36.b

13.c37.c

14.a38.b

15.c39.c

16.d40.d

17.c41.e

18.d42.e

19.e43.c

20.b44.c

21.b45.a

22.c46.c

23.e47.d

24.c

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