# MATHEMATICS

A sales manager for an advertising agency believes that there is a relationship between the number of contacts that a sales person makes and the amount of the sales dollars earned. A regression analysis shows the following results:

What is the Y-intercept of the linear equation? A. -12.201 B. 2.195 C. -1.860 D. 12.505

16. A sales manager for an advertising agency believes that there is a relationship between the number of contacts that a sales person makes and the amount of the sales dollars earned. A regression analysis shows the following results:

What is the slope of the linear equation? A. -12.201 B. 2.195 C. -1.860 D. 12.505

17. A sales manager for an advertising agency believes that there is a relationship between the number of contacts that a sales person makes and the amount of the sales dollars earned. A regression analysis shows the following results:

What is the standard error of the slope? A. -0.176 B. 6.560 C. -12.201 D. 12.505 18. A sales manager for an advertising agency believes that there is a relationship between the number of contacts that a sales person makes and the amount of the sales dollars earned. A regression analysis shows the following results:

What is the decision regarding the hypothesis that the slope equals zero? A. Fail to reject the null hypothesis B. Fail to reject the alternative hypothesis C. Reject the null hypothesis D. Reject the alternative hypothesis

19. A sales manager for an advertising agency believes that there is a relationship between the number of contacts that a sales person makes and the amount of the sales dollars earned. A regression ANOVA shows the following results:

What is the value of the standard error of estimate? A. 9.310 B. 8.778 C. 8.328 D. 86.68 20. A sales manager for an advertising agency believes that there is a relationship between the number of contacts that a sales person makes and the amount of the sales dollars earned. A regression ANOVA shows the following results:

What is the value of the coefficient of correlation? A. 0.6317 B. 0.9754 C. 0.9513 D. 9.3104

21. A sales manager for an advertising agency believes that there is a relationship between the number of contacts that a sales person makes and the amount of the sales dollars earned. A regression ANOVA shows the following results:

What is the value of the coefficient of determination? A. 9.3104 B. 0.9754 C. 0.6319 D. 0.9513

22. A sales manager for an advertising agency believes that there is a relationship between the number of contacts that a sales person makes and the amount of the sales dollars earned. A regression analysis shows the following results

= 33.4. = 2814.4. The 95% confidence interval for 30 calls is A. 55.8, 51.5 B. 51.4, 55.9 C. 46.7, 60.6 D. 31.1, 76.2

23. A sales manager for an advertising agency believes that there is a relationship between the number of contacts that a sales person makes and the amount of the sales dollars earned. A regression analysis shows the following results:

= 33.4. = 2814.4. The 95% prediction interval for a particular person making 30 calls is A. 55.8, 51.5 B. 51.4, 55.9 C. 46.7, 60.6 D. 31.1, 76.2

24. A sales manager for an advertising agency believes that there is a relationship between the number of contacts that a sales person makes and the amount of the sales dollars earned. A regression analysis shows the following results:

What is the regression equation? A. = 2.195 – 12.201X B. = -12.201 + 2.195X C. = 12.201 + 2.195X D. = 2.1946 + 12.201X

25. Which of the following is a characteristic of the F-distribution? A. Normally distributed B. Positively skewed C. Negatively skewed D. Equal to the t-distribution

26. In a regression analysis, three independent variables are used in the equation based on a sample of forty observations. What are the degrees of freedom associated with the F-statistic? A. 3 and 39 B. 4 and 40 C. 3 and 36 D. 2 and 39

27. Which statistic is used to test hypotheses about individual regression coefficients? A. t-statistic B. z-statistic C. (chi-square statistic) D. F

28. Which statistic is used to test a global hypothesis about a multiple regression equation? A. t-statistic B. z-statistic C. (chi-square statistic) D. F

29. The coefficient of determination measures the proportion of A. explained variation relative to total variation. B. variation due to the relationship among variables. C. error variation relative to total variation. D. variation due to regression.

30. What happens as the scatter of data values about the regression plane increases? A. Standard error of estimate increases B. R2 increases C. (1 – R2) decreases D. Error sum of squares decreases

31. All other things being held constant, what is the change in the dependent variable for a unit change in the first independent variable for the multiple regression equation: Ŷ = 5.2 + 6.3X1 – 7.1 X2? A. -7.1 B. +6.3 C. +5.2 D. +4.4

32. The best example of a null hypothesis for a global test of a multiple regression model is: A. H0: β1 = β2 = β3 = β4 = 0 B. H0: µ1 = µ2 = µ3 = µ4 = 0 C. H0: β1 = 0 D. If F is greater than 20.00 then reject.

33. The best example of an alternate hypothesis for a global test of a multiple regression model is: A. H1: β1 = β2 = β3 = β4 = 0 B. H1: β1 ≠ β2 ≠ β3 ≠ β4 ≠ 0 C. H1: Not all the β’s are equal to 0 D. If F is less than 20.00 then fail to reject.

34. The best example of a null hypothesis for testing an individual regression coefficient is: A. H0: β1 = β2 = β3 = β4 = 0 B. H0: µ1 = µ2 = µ3 = µ4 = 0 C. H0: β1 = 0 D. H0: β1 ≠ 0

35. In multiple regression analysis, residuals (Y – Ŷ) are used to: A. Provide a global test of a multiple regression model. B. Evaluate multicollinearity. C. Evaluate homoscedasticity. D. Compare two regression coefficients.

36. In multiple regression analysis, residuals (Y – Ŷ) are used to: A. Provide a global test of a multiple regression model. B. Evaluate the assumption of linearity. C. Calculate the variance inflation factor. D. Compare two regression coefficients.

Problem Solving Questions

1. (50 points) A company compared the variance of salaries for employees who have been employed for 5 years or less with employees who have been employed for 10 years or more. They randomly selected 21 employees with 5 years or less experience and 15 employees with 10 years or more experience. The standard deviation for the group with 5 years or less experience was $2,225; the standard deviation for the group with 10 years or more experience is $1,875.

a) What is the F test statistic for the hypothesis test?

b) Using the 0.05 significance level, what is the F critical value for the hypothesis test? c) Using the 0.05 significance level, what is the decision regarding the null hypothesis?

2. (50 points) A bottle cap manufacturer with four machines and six operators’ wants to see if variation in production is due to the machines and/or the operators. ANOVA table follows.

a) What is the critical value of F for the machine treatment effect at the 1% level of significance?

b) What is the critical value of F for the operator block effect at the 1% level of significance? c) What is the mean square for machines? d) What is the mean square for operators? e) What is the mean square for error? f) What is the computed value of F for the machines? g) What is the computed value of F for the operators? h) Test the hypothesis that all operators are equally productive. State your decision in terms of the null hypothesis.

3. (50 points) A company wants to study the effect of an employee’s length of employment on their number of workdays absent. The results of the regression analysis follow.

What is the slope of the linear equation?

What is the Y intercept of the linear equation?

What is the least squares equation?

What is the meaning of a negative slope?

What is the standard error of estimate?

4. (50 points) Twenty-one executives in a large corporation were randomly selected for a study to determine the effect of several factors on annual salary (expressed in $000’s). The factors selected were age, seniority, years of college, number of company divisions they had been exposed to and the level of their responsibility. A regression analysis was performed using a popular spreadsheet program with the following regression output:

Write out the multiple regression equation.

Which independent variable has the most significant effect on annual salary?

What proportion of the total variation in salary is accounted for by the set of independent variables?

Test the hypothesis that the regression coefficient for age is equal to 0 at the 0.05 significance level. Report the degrees of freedom, the test statistic, the critical value, and your decision.