Page 1 of 18Part A Multiple Choice (1–11)______1. Using.docx
- 1. Page 1 of 18 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. 7 b. 19 c. 34 d. 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 b, the null hypothesis is generally that a. β = b b. β 0 c. β = 0 d. 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 estimate c. y-intercept b. prediction interval d. 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
- 2. 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. = 0.35 b. = 0.30 c. = 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 = 1.5 c. F = 5.5 b. F = 2.5 d. 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
- 3. 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 = .
- 4. _______ 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: Answer the following questions (21-26) 21. What is the Null Hypothesis? Explain. 22. What is the Alternative Hypothesis? Explain.
- 5. 23. Explain how you decide what statement goes into the null hypothesis and what statement go into the alternative hypothesis. 24. When should the z-test be used? 25. When should the t-test be used? 26. What is the definition of P-Value? Part D: Must show all your work step by step in order to receive the full credit; Excel is not allowed. (27-46) 27. Work on problem number 9 (a-f) on page 7-47
- 7. 28. Work on problem number 1 (a-e) on page 7-68 29. Work on problem number 2 (a-c) on page 7-68
- 8. 30. Work on problem number 7 (a-e) on page 7-69
- 9. 31. Work on problem number 16 (a-b) on page 8-12 ;Given that 32. State whether you would reject or fail to reject the null hypothesis in each of the following cases (two-tailed): a) P = 0.12 ; b) P = 0.03 ;
- 10. c) P = 0.001 ; d) P = 0.01 ; 33. Consider the following hypothesis test. Ho: µ = 17 Ha: µ ≠ 17 A sample of 25 gives a sample mean of 14.2 and sample variation of 25. a) At α = 0.05, what is the rejection rule? b) Compute the value of the test statistic c) What is the p-value? d) What is your conclusion?
- 11. 34. Consider the following hypothesis test. Ho: μ = 15 Ha: μ ≠ 15 A sample of 50 gives a sample mean of 14.2 and sample variation of 25. a) At α = 0.05, what is the rejection rule? b) Compute the value of the test statistic c) What is the p-value? d) What is your conclusion? 35. Consider the following hypothesis test Ho: µ ≥ 10
- 12. Ha: µ <10 A sample of 50 provides a sample mean of 9.46 and sample variation of 4. a) At α = 0.05, what is the rejection rule? b) Compute the value of the test statistic c) What is the p-value? d) What is your conclusion? 36. Fill in the table and find the following answers: Months on job (x) Monthly sales (y) thousands of dollars X2 Y2 XY 1
- 15. a) Find b) Find c) Write the estimated regression equation d) Interpret e) Calculate the coefficient of determination f) Interpret the coefficient of determination
- 16. 37. Work on problem number 3 (a-d) on page 10-32
- 17. 38. Please fill in the computer printout and answer the following questions. Given that SUMMARY OUTPUT Regression Statistics Multiple R 0.9037 R Square ______
- 18. Adjusted R Square ______ Standard Error ______ Observations 5 ANOVA df SS MS F Significance F Regression 1 4.9 ______ ______ 0.03535
- 19. Residual 3 1.1 ______ Total ______ ______ Coefficients Standard Error t Stat P-value Lower95% Upper 95% Lower 95.0% Upper 95.0% Intercept -0.1 ______ -0.15746 0.88488 -2.12112 1.92112 -2.12112 1.92112 X1 0.7 ______ 3.65563
- 20. 0.03535 0.09061 1.30939 ______ ______ a) What percent of the variation is explained by the regression equation? b) What is the standard error of regression? c) What is the critical value of the F-statistic? d) What sample size is used in the print out? 39. The following regression equation was obtained using the five independent variables. Given that
- 21. a) What percent of the variation is explained by the regression equation? b) What is the standard error of regression? c) What is the critical value of the F-statistic? d) What sample size is used in the print out? e) What is the variance of the slope coefficient of income? f) Conduct a global test of hypothesis to determine if any of the regression coefficients are not zero. g) Conduct a test of hypothesis on each of the independent variables. Would you consider eliminating outlets and bosses? 40. Please use the following computer printout to answer the following questions: Coefficients Std. Error t-Stat
- 23. Total 14 14430.4 Se =12.86986 R-sq = 0.862263 R-sq(adj) = 0.8393068 a) Write and interpret the multiple regression equation. b) Does the model with Price and Advertising contribute to the prediction of Y? Use a 0.05 significance level. c) Which independent variable appears to be the best predictor of sales? Explain.
- 24. d) What is the number of observations used in this study? e) Assuming that the coefficient on Advertising has Ha: B1 > 0, what statistical decision should be made at 5% level. f) What is the standard error of estimate? Can you use this statistic to assess the model’s fit? If so, how? 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.
- 25. i) Test the overall utility of the model. What does the p-value of the test statistic tell you? 41. State whether should be accepted or rejected for , given the following; a) = 2.34; df = 2 and 11 b) = 2.52; df = 4 and 20 c) = 4.29; df = 3 and 24 42. Given the following, complete the ANOVA table and make the correct inference.
- 26. Source SS df MS F Treatments ____ 2 3.24 ____ Error ____ 17 ____ Total 40.98 ____ ANSWER a) In the above ANOVA table, is the factor significant at 5% level of significant? b) What is the number of observations?
- 27. 43. Given the following, complete the ANOVA table and make the correct inference. Source SS df MS F Treatments 5 ____ 205.5 ____ Error ____ 637 ____ Total 25 ____ ANSWER a) In the above ANOVA table, is the factor significant at 5% level of significant? b)
- 28. What is the number of observations? 44. Given the following, complete the ANOVA table and make the correct inference. Source SS df MS F Treatments ____ 3 ____ ____ Error 88.8 ____ ____ Total 435 19 ANSWER a) In the above ANOVA table, is the factor significant at 5% level of significant?
- 29. b) What is the number of observations? 45. A metropolitan bus system sampler’s rider counts on one of its express commuter routes for a week. Use the following data to establish whether the rider ship is evenly balanced by day of the week. Let Day Monday Tuesday Wednesday Thursday Friday Rider Count 10 34 21 57 44 a) Is the χ2 value significant at 5% level of significance?
- 30. b) Write the conclusion for this question 46. A marketing research firm wished to study the relationship between wine consumption and whether a person likes to watch professional tennis on television. One hundred randomly selected people are asked whether they drink wine and whether they watch tennis. The following results are obtained: Watch Tennis Do not Watch Tennis Totals Drink Wine 16 24 40 Do not Drink Wine 4 56 60 Totals 20 80 100 Test the hypothesis that whether people drink wine is independent of whether people watch tennis. Set α = 0.05
- 31. a) Is the χ2 value significant at 5% level of significant? b) Write the conclusion for this question ) Y ˆ Y ( ) Y Y ˆ ( i - + - The regression equation is sales = - 19.7 - 0.00063 outlets + 1.74 cars + 0.410 income + 2.04 age - 0.034 bosses Predictor Coef SE Coef T P Constant -19.672 5.422 -3.63 0.022 outlets -0.000629 0.002638 -0.24 0.823 cars 1.7399 0.5530 3.15 0.035 income 0.40994 0.04385 9.35 0.001
- 32. age 2.0357 0.8779 2.32 0.081 bosses -0.0344 0.1880 -0.18 0.864 S = 1.507 R-Sq = 99.4% R-Sq(adj) = 98.7% Analysis of Variance Source DF SS MS F P Regression 5 1593.81 318.76 140.36 0.000 Residual Error 4 9.08 2.27 Total 9 1602.89 (Minitab Software) ) Y Y ( i -