 # ECO 578 ECO578 Final Exam with Answers

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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. y-intercept

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 sum-of-squares 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 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 = 1.5c. 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 t-ratio 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 p-Value 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 (12-20)

_______ 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, 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.

 _____ 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 F-value 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?

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