Direction: Select the letter of the most correct response for multiple choice problems. Show work for problems 19 and 20. Show work for non multiple question. 1. In a multiple regression problem involving two independent variables, if b1 is computed to be +2.0, it means that a) the relationship between X1 and Y is significant. b) the estimated average of Y increases by 2 units for each increase of 1 unit of X1, holding X2 constant. c) the estimated average of Y increases by 2 units for each increase of 1 unit of X1, without regard to X2. d) the estimated average of Y is 2 when X1 equals zero. ANSWER: TYPE: MC DIFFICULTY: Easy KEYWORDS: slope, interpretation 2. The coefficient of multiple determination r2Y.12 a) measures the variation around the predicted regression equation. b) measures the proportion of variation in Y that is explained by X1 and X2. c) measures the proportion of variation in Y that is explained by X1 holding X2 constant. d) will have the same sign as b1. ANSWER: TYPE: MC DIFFICULTY: Easy KEYWORDS: coefficient of multiple determination, interpretation 3. In a multiple regression model, the value of the coefficient of multiple determination a) has to fall between -1 and +1. b) has to fall between 0 and +1. c) has to fall between -1 and 0. d) can fall between any pair of real numbers. ANSWER: TYPE: MC DIFFICULTY: Easy KEYWORDS: coefficient of multiple determination, properties 1 4. In a multiple regression model, which of the following is correct regarding the value of the a) b) c) d) r2 ? It can be negative. It has to be positive. It has to be larger than the coefficient of multiple determination. It can be larger than 1. ANSWER: TYPE: MC DIFFICULTY: Moderate KEYWORDS: adjusted r-square, properties TABLE 14-1 A manager of a product sales group believes the number of sales made by an employee (Y) depends on how many years that employee has been with the company (X1) and how he/she scored on a business aptitude test (X2). A random sample of 8 employees provides the following: Employee Y X1 X2 1 100 10 7 2 90 3 10 3 80 8 9 4 70 5 4 5 60 5 8 6 50 7 5 7 40 1 4 8 30 1 1 Use Excel to run regression analysis for the above data and answer the following questions: 5. Referring to Table 14-1, for these data, what is the value for the regression constant, b0? a) 0.998 b) 3.103 c) 4.698 d) 21.293 ANSWER: TYPE: MC DIFFICULTY: Moderate KEYWORDS: intercept, estimation 6. Referring to Table 14-1, for these data, what is the estimated coefficient for the variable representing years an employee has been with the company, b1? a) 0.998 b) 3.103 c) 4.698 d) 21.293 ANSWER: TYPE: MC DIFFICULTY: Moderate 2 KEYWORDS: slope, estimation 7. Referring to Table 14-1, for these data, what is the estimated coefficient for the variable representing scores on the aptitude test, b2? a) 0.998 b) 3.103 c) 4.698 d) 21.293 ANSWER: TYPE: MC DIFFICULTY: Moderate KEYWORDS: slope, estimation 8. Referring to Table 14-1, if an employee who had been with the company 5 years scored a 9 on the aptitude test, what would his estimated expected sales be? a) 79.09 b) 60.88 c) 55.62 d) 17.98 ANSWER: TYPE: MC DIFFICULTY: Moderate KEYWORDS: estimation of mean values TABLE 14-2 A professor of industrial relations believes that an individual's wage rate at a factory (Y) depends on his performance rating (X1) and the number of economics courses the employee successfully completed in college (X2). The professor randomly selects 6 workers and collects the following information: Employee Y ($) X1 X2 1 10 3 0 2 12 1 5 3 15 8 1 4 17 5 8 5 20 7 12 6 25 10 9 Use Excel to run regression analysis for the above data and answer the following questions: 9. Referring to Table 14-2, for these data, what is the value for the regression constant, b0? a) 0.616 b) 1.054 c) 6.932 d) 9.103 ANSWER: TYPE: MC DIFFICULTY: Moderate KEYWORDS: intercept, estimation 3 10. Referring to Table 14-2, for these data, what is the estimated coefficient for performance rating, b1? a) 0.616 b) 1.054 c) 6.932 d) 9.103 ANSWER: TYPE: MC DIFFICULTY: Moderate KEYWORDS: slope, estimation 11. Referring to Table 14-2, for these data, what is the estimated coefficient for the number of economics courses taken, b2? a) 0.616 b) 1.054 c) 6.932 d) 9.103 ANSWER: TYPE: MC DIFFICULTY: Moderate KEYWORDS: slope, estimation 12. Referring to Table 14-2, suppose an employee had never taken an economics course and managed to score a 5 on his performance rating. What is his estimated expected wage rate? a) 10.90 b) 12.20 c) 17.23 d) 25.11 ANSWER: TYPE: MC DIFFICULTY: Moderate KEYWORDS: estimation of mean values 13. Referring to Table 14-2, an employee who took 12 economics courses scores 10 on the performance rating. What is her estimated expected wage rate? a) 10.90 b) 12.20 c) 24.87 d) 25.70 ANSWER: TYPE: MC DIFFICULTY: Moderate KEYWORDS: estimation of mean values 4 14. The variation attributable to factors other than the relationship between the independent variables and the explained variable in a regression analysis is represented by a) regression sum of squares. b) error sum of squares. c) total sum of squares. d) regression mean squares. ANSWER: TYPE: MC DIFFICULTY: Moderate KEYWORDS: sum of squares TABLE 14-3 An economist is interested to see how consumption for an economy (in $ billions) is influenced by gross domestic product ($ billions) and aggregate price (consumer price index). The Microsoft Excel output of this regression is partially reproduced below. SUMMARY OUTPUT Regression Statistics Multiple R 0.991 R Square 0.982 Adjusted R Square 0.976 Standard Error 0.299 Observations 10 ANOVA Regression Residual Total df SS 2 33.4163 7 0.6277 9 34.0440 Coeff Intercept - 0.0861 GDP 0.7654 Price - 0.0006 MS 16.7082 0.0897 StdError t Stat 0.5674 - 0.152 0.0574 13.340 0.0028 - 0.219 F 186.325 Signif F 0.0001 P-value 0.8837 0.0001 0.8330 15. Referring to Table 14-3, when the economist used a simple linear regression model with consumption as the dependent variable and GDP as the independent variable, he obtained an r2 value of 0.971. What additional percentage of the total variation of consumption has been explained by including aggregate prices in the multiple regression? a) 98.2 b) 11.1 c) 2.8 d) 1.1 ANSWER: 5 TYPE: MC DIFFICULTY: Moderate KEYWORDS: coefficient of multiple determination 16. Referring to Table 14-3, the p-value for GDP is a) 0.05 b) 0.01 c) 0.001 d) None of the above. ANSWER: TYPE: MC DIFFICULTY: Easy KEYWORDS: t test on slope, p-value 17. Referring to Table 14-3, the p-value for the aggregated price index is a) 0.05 b) 0.01 c) 0.001 d) None of the above. ANSWER: TYPE: MC DIFFICULTY: Easy KEYWORDS: t test on slope, p-value 18. Referring to Table 14-3, the p-value for the regression model as a whole is a) 0.05 b) 0.01 c) 0.001 d) None of the above. ANSWER: TYPE: MC DIFFICULTY: Easy KEYWORDS: F test for the entire regression, p-value Must show work 19. Referring to Table 14-3, what is the predicted consumption level for an economy with GDP equal to $4 billion and an aggregate price index of 150? a) $1.39 billion b) $2.89 billion c) $4.75 billion d) $9.45 billion 6 ANSWER: TYPE: MC DIFFICULTY: Moderate KEYWORDS: prediction of individual values Must show work 20. Referring to Table 14-3, what is the estimated average consumption level for an economy with GDP equal to $4 billion and an aggregate price index of 150? a) $1.39 billion b) $2.89 billion c) $4.75 billion d) $9.45 billion ANSWER: TYPE: MC DIFFICULTY: Moderate KEYWORDS: estimation of mean values 7