ECO 578 ECO578 Final Exam with Answers
Part A: Multiple Choice (1–11)
______1. Using the “eyeball” method, the regression line = 2+2x has been fitted to the data points (x = 2, y = 1), (x = 3, y = 8), and (x = 4, y = 7). The sum of the squared residuals will be
a. 7b. 19 c. 34d. 8
______2. A computer statistical package has included the following quantities in its output: SST = 50, SSR = 35, and SSE = 15. How much of the variation in y is explained by the regression equation?
a. 49% b. 70%c. 35%d. 15%
______3. In testing the significance of, the null hypothesis is generally that
a. β = b. β 0c. β = 0d. β = r
______4. 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 estimatec. yintercept
b. prediction intervald. coefficient of correlation
______5. A multiple regression equation includes 4 independent variables, and the coefficient of multiple determination is 0.64. How much of the variation in y is explained by the regression equation?
a. 80%b. 16%c. 32%d. 64%
______6. A multiple regression analysis results in the following values for the sumofsquares terms: SST = 50.0, SSR = 35.0, and SSE = 15.0. The coefficient of multiple determination will be
a. = 0.35b. = 0.30c. = 0.70 d. = 0.50
______7. In testing the overall significance of a multiple regression equation in which there are three independent variables, the null hypothesis is
a. :
b. :
c. :
d. :
______8. In a multiple regression analysis involving 25 data points and 4 independent variables, the sumofsquares 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 = 1.5c. F = 5.5
b. F = 2.5d. F = 7.5
______9. For a set of 15 data points, a computer statistical package has found the multiple regression equation to be = 23 + 20+ 5 + 25 and has listed the tratio for testing the significance of each partial regression coefficient. Using the 0.05 level in testing whether = 20 differs significantly from zero, the critical t values will be
a. t = 1.960 and t= +1.960
b. t = 2.132 and t = +2.132
c. t = 2.201 and t = +2.201
d. t = 1.796 and t = +1.796
______10. Computer analyses typically provide a pValue for each partial regression coefficient. In the case of , this is the probability that
a. = 0
b. =
c. the absolute value of could be this large if = 0
d. the absolute value of could be this large if 1
______11. In the multiple regression equation, = 20,000 + 0.05+ 4500 , is the estimated household income, is the amount of life insurance held by the head of the household, and is a dummy variable ( = 1 if the family owns mutual funds, 0 if it doesn’t). The interpretation of = 4500 is that
a. owing mutual funds increases the estimated income by $4500
b. the average value of a mutual funds portfolio is $4500
c. 45% of the persons in the sample own mutual funds
d. the sample size must have been at least n = 4500
Part B: True or False (1220)
_______ 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.
_______ 17. If in a regression analysis the explained sum of squares is 75 and the unexplained sum of square is 25, r^{2} = 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 H_{0} 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.
_____ 


Total 
40.98 
_____ 







ANSWER 

a) What is the hypothesis being tested in this problem? 


b) In the above ANOVA table, is the factor significant at the 5% level? 


c) What is the number of observations? 

24. Given the following, complete the ANOVA table and make the correct inference. Using Fvalue to make a decision.
Source 
SS 
df 
MS 
F 
Treatments 
____ 
5 
205.5 
____ 
Error 
637 
____ 
____ 

Total 
____ 
25 



ANSWER 
a) What is the hypothesis being tested in this problem? 

b) In the above ANOVA table, is the factor significant at the 5% level? 

c) What is the number of observations? 
