ECO 578 Final Exam – Using the eyeball method

ECO 578 Final Exam – Using the eyeball method

Subject: Economics    / General Economics
Question
ECO 578 EXAM SPRING 2017 Page 1 of 17
Name: _______________
ID: _______________ Final Exam
Final Exam There are 5 parts:
Part A: Select the correct answer for the following questions (1-10)
Part B: True/False (11-20)
Part C: Fill in the blank and circle your decision (21-25).
Part D:Work Problem (26-38) **Excel is not allowed. &All work must be shown step by step**
Part E: Descriptive Questions (39-40) Two different ways to submit your answer sheet
Use MS-Word to type or PDF to handwrite and place it in the drop-box in ONE FILE. **Excel is not acceptable for this test **Deadline: Tuesday, 2th of May 2017 by 11:59 a.m (Disregard the due date in syllabus) Part A: Multiple Choice (1–10)
______1. Using the “eyeball” method, the regression line ^y = 2+2x has been fitted to the data points (x = 2, y = 2), (x = 3, y = 7), and (x = 4, y = 6). The sum of the squared
residuals will be
a. 7
b. 19
c. 34
d. 21
______2. A computer statistical package has included the following quantities in its output:
SST = 60, SSR = 50, and SSE = 10. How much of the variation in y is explained by the
regression equation?
a.
17.67%
b. 70%
c. 83.33%
d. 20%
______3. 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. coefficient of correlation
b. prediction interval
d. y-intercept
______4. A multiple regression equation includes 4 independent variables, and the
coefficient of multiple determination is 0.81. How much of the variation in y is explained
by the regression equation?
a. 80%
b. 16%
c. 81%
d. 64%
______5. A multiple regression analysis results in the following values for the sum-ofsquares terms: SST = 50.0, SSR = 45.0, and SSE = 5.0. The coefficient of multiple
determination will be ECO 578 EXAM SPRING 2017
a. Page 2 of 17 R2 = 0.35
R 2 b. R2 = 0.30 c. R2 = 0.70 d. = 0.90 ______6. In testing the overall significance of a multiple regression equation in which there
are three independent variables, the null hypothesis is
H0
? 1=? 2=? 3=0
a.
:
b. H0 : ? 1 ? ? 2?? 2 ? ?3 c. H0 : ? 1=? 2=? 3=1 d. H0 : ? 1=? 2=? 3=? ______7. 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 ______8. For a set of 15 data points, a computer statistical package has found the multiple
x
x
x
regression equation to be ^y = -23 + 20 1 + 5 2 + 25 3 and has listed the tratio for testing the significance of each partial regression coefficient. Using the 0.05
b1
level in testing whether
= 20 differs significantly from zero, the critical t values will
be
a.
b.
c.
d. t = -1.960 and t= +1.960
t = -2.132 and t = +2.132
t = -2.201 and t = +2.201
t = -1.796 and t = +1.796 ______9. Computer analyses typically provide a p-Value for each partial regression
b
coefficient. In the case of 1 , this is the probability that
a. ?1 =0 b. b1 = ?1 c. the absolute value of b1 could be this large if ?1 =0 ECO 578 EXAM SPRING 2017
d. the absolute value of Page 3 of 17
b1 could be this large if ?1 ? 1 ______10. The variable about which the investigator wishes to make predictions or estimates
is called the ____.
a . dependent variable
b. unit of association
c. independent variable
d. discrete variable Part B: True or False (11-20)
______ 11. If zero is contained in the 95% confidence interval for b, we may reject Ho: b = 0 at
the 0.05 level of significance.
______ 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 ( Y i?Y )= Y ?Y +(Y i?Y ) .
______ 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: Please fill in the blank and circle your decision (21-25).
21. State whether you would reject or fail to reject the null hypothesis in each of the
following cases (two-tailed): Make a decision. ECO 578 EXAM SPRING 2017 Page 4 of 17 a)
P = 0.12 ; ? =0.05 Decision
Reject / Fail to reject b)
P = 0.03 ; ?=0.05 Decision
Reject / Fail to reject c)
P = 0.001 ; ? =0.01
22. State whether following; ¿ H0 F =computed F Decision
Reject / Fail to reject should be accepted or rejected for ? =0.01 , given the (fill in the blank and circle your decision) ¿
a) F = 2.34; df = 2 and 12 Computed F Critical F Decision ______ _______ Reject / Fail to reject Computed F Critical F Decision ______ ________ Reject / Fail to reject Computed F Critical F Decision ______ _______ Reject / Fail to reject ¿
b) F = 2.52; df = 4 and 20 ¿
c) F = 4.60; df = 3 and 30 23.
Given the following, complete the ANOVA table and make the correct inference.
Using F-value to make a decision. ECO 578 EXAM SPRING 2017 Page 5 of 17 Source SS df MS F Treatments ________ 2 3.24 _______ Error ________ 17 _______ Total 40.98 _______
ANSWER a) State the hypothesis being tested
in this problem?
b) In the above ANOVA table, is the
factor significant at the 5% level?
What is your Conclusion?
c) What is the number of
observations? 24. Given the following, complete the ANOVA table and make the correct inference. Using
F-value to make a decision.
Source SS df MS F _______ 5 205.5 _______ Error 637 _______ _______ Total _______ 25 Treatments ANSWER
a) State the hypothesis being tested
in this problem?
b) In the above ANOVA table, is the
factor significant at the 5% level?
What is your Conclusion?
c) What is the number of
observations? 25. Given the following, complete the ANOVA table and make the correct inference. Using
F-value to make a decision. ECO 578 EXAM SPRING 2017 Page 6 of 17 Source SS df MS F _______ 3 _______ _______ Error 88.8 _______ _______ Total 435 19 Treatments ANSWER
a) State the hypothesis being tested
in this problem?
b) In the above ANOVA table, is the
factor significant at the 5% level?
What is your Conclusion?
c) What is the number of
observations? Part D: Must show all your work step by step in order to receive the full
credit; Excel is not allowed. (26-38) a
) 26. Consider the following hypothesis test.
Ho: µ = 17
Ha: µ ? 17
A sample of 25 gives a sample mean of 14.2 and sample variance of 25.
b
At 5% should the null be rejected?
)
Compute the value of the test statistic c
) What is the p-value? d
) What is your conclusion? ECO 578 EXAM SPRING 2017 Page 7 of 17 a
) 27. Consider the following hypothesis test
Ho: µ ? 10
Ha: µ < 10
A sample of 50 provides a sample mean of 9.46 and sample variance of 4.
b
At 5% should the null be rejected?
)
Compute the value of the test statistic c
) What is the p-value? d
) What is your conclusion? 28. Fill the below table and answer the given questions
Months on
job (x)
1
2
4
5
8
9
12
Total Monthly sales
(y) thousands
of dollars
0.80
2.40
7.00
3.70
11.30
12.00
15.00 X2 Y2 XY (Y ?Y´ ) (Y ?Y´ )2 Y^ (Y ?Y^ ) (Y ?Y^ )2 ECO 578 EXAM SPRING 2017
a)Find b1 Page 8 of 17
b)Find b0 c)Write the equation and interpret it d) Compute R2 and how is it different from adjusted R2. e) Compute the estimated variance of the regression. f)Find Se ECO 578 EXAM SPRING 2017
g) Compute the estimated variance of b1 Page 9 of 17
. h) Compute the standard error of b1 . 29. Work on problem number 3 on page 10-28 and answer the given questions
a. Write the estimated regression equation b. How many branch offices were involved in the study? c. Compute the F statistic and test the significance of the relationship at a .05 level of
significance. ECO 578 EXAM SPRING 2017 Page 10 of 17 d. Predict the annual sales at the Memphis branch office. This branch has 12 sales
persons. 30. For n = 10 data point, the following quantities have been calculated. Answer the given
questions
a)Find b1 ?xy = 400 ?x = 30 ?y = 72 ?x2 = 346 b)Find b0 ?y2 = 1,160 c)Write the equation and interpret it d)Find R2 interpret it e)Find SST f)Find g) Construct the 95% confidence interval for the mean
of y when x = 7 h) Construct the 95% confidence interval for the
individual value of y when x = 7 Se ECO 578 EXAM SPRING 2017 Page 11 of 17 31. The commercial division of a real estate firm is conducting a regression analysis of the
relationship between gross rents (X) and selling price (Y) for apartment building. Data
have been collected on several properties recently sold, and the following output has been
obtained in computer run.
ANOVA
df
Regression
Residual
Total SS
1
8
9 0.798
18.878
19.676 Coefficients
Intercept
1.954
X Variable 1
0.053 Standard Error
1.830
0.092 t Stat
1.068
0.582 Question
Answer
a. How many apartment buildings were in the sample
b. Write the estimated regression equation
c. What’s the sample regression coefficients of b0
d. What’s the sample regression coefficients of b1
e. What’s the value of the estimated variance of the
regression
f. What’s the value of the standard error of the regression
g. What’s the value of the estimated variance of the b1
h. What’s the value of the standard error of the b1 ECO 578 EXAM SPRING 2017 Page 12 of 17 i. Is the result significant when using F statistic to test the
significant of the relationship at a 0.05 level of significance. j. Estimate the selling price of an apartment building with
gross annual rent of $50,000
32. The following regression equation was obtained using the five independent variables.
Given that ?=0.05 a) What percent of the variation is explained by the
regression equation and interpret it c) Write the estimated equation and interpret it e) What sample size is used in the print out? b) What is the standard error of regression? d) What is the critical value of the F-statistic?
Conduct the hypothesis testing to see if it is
significant? f) What is the variance of the slope coefficient of ECO 578 EXAM SPRING 2017 Page 13 of 17
income? g) Assuming that you are using a two-tailed test make a decision using the computed P-value. 33. Use problem 5 on page 15-9 to answer the following questions. (a-d)
a) What is your hypothesis testing b) What is your ?2? c) Is the ? 2 value significant at 5% level? d) Write the conclusion for this question. ECO 578 EXAM SPRING 2017 Page 14 of 17 34. Use problem no.4 on page 15-9 and answer the below questions
a) What is you hypothesis testing b) What is your ? 2 ? c) Is the ?2 value significant at 5% level of significance? d) Write the conclusion for this question. 35. Use the computer printout below to answer the following questions.
Coefficients
729.8665
-10.887
0.0465 Intercept
Price
Advertising Std. Error
169.25751
3.4952397
0.0176228 t-Stat
4.3121659
-3.1148078
2.6386297 P-value
0.0010099
0.0089406
0.0216284 F
37.56127994 Significance F
0.00000683 ANOVA
Regression
Residual
Total df
2
12
14 SS
12442.8
1987.6
14430.4 MS
6221.4
165.63333 ECO 578 EXAM SPRING 2017
Se =12.86986 Page 15 of 17
R-sq = 0.862263 R-sq(adj) = 0.8393068 ?=5 a) Write and interpret the multiple regression equation ? b) Does the model with Price and Advertising contribute to
the prediction of Y? c)
Which independent variable appears to be the best
predictor of sales? Explain. d) What is the number of observations used in this study? e)Find SST Assuming that the coefficient on Advertising has f) What is the standard error of estimate? Can you use this
statistic to assess the model’s fit? If so, how? Ha : b1 > 0, what’s statistical decision ? 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. i) Test the overall utility of the model. What does the p-value of the test statistic tell you? 36. Explain why a 95% confidence interval estimate for the mean value of y at a particular x is
narrower than a 95% confidence interval for an individual y value at the same value of x. ECO 578 EXAM SPRING 2017 37. If 2 R =0.95 , n=11, and Page 16 of 17 ? (Y ?Y´ )2=100, 2 what is S e ? 38. You are given the following information from fitting a multiple regression with three
variables to 30 sample data points:
b1=1.3
b2=10.0
b3 =25.2
S b =0.3
1 S b =2.0 Test the following hypotheses, Use ?=0.05
a) ? 1=0 b) ? 2=0 c) ? 3=0 Part E: Descriptive Questions (39-40) 2 S b =15.0
3 ECO 578 EXAM SPRING 2017
39. Explain the differences between t and F Statistic? 40. Explain why Chi Square is calculated? Page 17 of 17