ECO 578 Fall 2015 Page 1 of 14 Name: _______________________ ID: _______________________ Online Final Exam There are 4 parts: Part A: True/ False (1-20) Part B: Select the correct answer for the following questions (21-40) Part C: Work Problem (41-52) **All work in part C must be shown step by step** Two different ways to submit your answer sheet 1. Scan your answer sheet and place it in ONE FILE at drop-box. (preferable) 2. Use MS-Word and place it in a drop-box. **Excel is not acceptable for this test **Deadline: Monday, December 7, 2015 by noon (CST) **All work in part C must be shown step by step in order to receive credit Part A: True/ False (1-20) _______ 1. The usual objective of regression analysis is to predict estimate the value of one variable when the value of another variable is known. _______ 2. Correlation analysis is concerned with measuring the strength of the relationship between two variables. _______ 3. The term ei in the simple linear regression model indicates the amount of change in Y for a unit change in X. _______ 4. In the sample regression equation y = a + bx, b is the slope of the regression line. _______ 5. The coefficient of determination can assume any value between -1 and +1. _______ 6. In the least squares model, the explained sum of squares is always smaller than the regression sum of squares. _______ 7. The sample correlation coefficient and the sample slope will always have the same sign. _______ 8. Given the sample regression equation y = -3 + 5x, we know that in the sample X and Y are inversely related. _______ 9. Given the sample regression equation y = 5 - 6x, we know that when X = 2, Y = 17. ECO 578 Fall 2015 Page 2 of 14 _______ 10. An important relationship in regression analysis is = (Yi Y ) (Y Y ) (Yi Y ) . _______ 11. Regression analysis is concerned with the form of the relationship among variables, whereas correlation analysis is conc erned with the strength of the relationship. _______ 12. The correlation coefficient indicates the amount of change in Y when X change by one unit. _______ 13. In simple linear regression analysis, when the slope is equal to zero, the independent variable does not explain any of the variability in the dependent variable. _______ 14. One of the purposes of regression analysis is to estimate a mean of the independent variable for given values of the dependent variable. _______ 15. The variable that can be manipulated by the investigator is called the independent variable. _______ 16. When b = 0, X and Y are not related. _______ 17. If zero is contained in the 95% confidence interval for b, we may reject H o: b = 0 at the 0.05 level of significance. _______ 18. If in a regression analysis the explained sum of squares is 75 and the unexplained sum of square is 25, r2 = 0.33. _______ 19. In general, the smaller the dispersion of observed points about a fitted regression line, the larger the value of the coefficient of determination. _______ 20. 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. Part B: Select the correct answer for the following questions (21 - 40) _______ 21. The variable about which the investigator wishes to make predictions or estimates is called the a. dependent variable b. unit of association c. independent variable d. discrete variable _______ 22. In regression analysis, the quantity that gives the amount by which Y changes for a unit change in X is called the a. coefficient of determination b. slope of the regression line c. Y intercept of the regression line d. correlation coefficient _______ 23. In the equation y = b0 +b1 (x), b0 is the a. coefficient of determination b. slope of the regression line c. y intercept of the regression line d. correlation coefficient ECO 578 Fall 2015 Page 3 of 14 _______ 24. In the equation y = b0 + b1 (x), b1 is the a. coefficient of determination b. slope of the regression line c. y intercept of the regression line d. correlation coefficient _______ 25. In regression and correlation analysis, the measure whose values are restricted to the range 0 to 1, inclusive, is the a. coefficient of determination b. slope of the regression line c. y intercept of the regression line d. correlation coefficient _______ 26. In regression and correlation analysis, the measure whose values are restricted to the range -1 to +1, inclusive, is the a. coefficient of determination b. slope of the regression line c. y intercept of the regression line d. correlation coefficient _______ 27. The quantity (Yi Y ) 2 is called the _______________ sum of square. a. least c. total _______ 28. If, in the regression model, between X and Y. a. an inverse c. a direct b. explained d. unexplained b1 = 0, we say there is _____________ linear relationship b. a significant d. no _______ 29. If, in the regression model, b is negative, we say there is _____________ linear relationship between X and Y. a. an inverse b. a significant c. a direct d. no _______ 30. The _______________ sum of square is a measure of the total variability in the observed values of Y that is accounted for by the linear relationship between the observed values of X and Y. a. unexplained b. total c. error d. explained _______ 31. If two variables are not related, we know that ________________. a. their correlation coefficient is equal to zero. b. the variability in one of them cannot be explained by the other. c. the slope of the regression line for the two variables is equal to zero. d. all of the above statements are true. _______ 32. In simple linear regression analysis, if the correlation coefficient is equal to 1.0, ______________. a. the slope is equal to 1.0 b. all the variability in the dependent variable is explained by the independent variable. c. the y intercept is equal to 1.0 d. the relationship between the two variables can be described as a bivariable normal distribution. ECO 578 Fall 2015 Page 4 of 14 _______ 33. The following results were obtained from a simple linear regression analysis. Total sum of square = 5.7640. Unexplained sum of square = 0.2225. The coefficient of determination is ____ a. 0.0402 b. 0.0386 c. 0.9805 d. 0.9614 _______ 34. The following results were obtained as part of a simple linear correlation analysis: Y = 97.98 - 4.33x regression sum of squares = 2680. 27. Error sum of squares = 125.40. Total sum of squares = 2805.67. The sample correlation coefficient is ____ a. -0.9774 b. 0.9553 c. 0.2114 d. 0.0447 ________ 35. The following equation describes the relationship between output and labor input at a sample of work stations in a manufacturing plant: ^ Y =2.35+2.20 X . Suppose, for a selected workstation, the labor input is 5. The predicted output is _____________. a. 4.55 b. 2.35 c. 2.20 d. 13.35 _______ 36. In regression and correlation analysis, the entity on which sets of measurements are taken is called the ______________. a. dependent variable b. independent variable c. variables d. discrete variable _______ 37. The quantity ^ (Y Y )2 a. least c. explained _______ 38. If, in the regression model, relationship between X and Y. a. an inverse c. a significant is called the _____________ sum of squares. b. total d. unexplained b1 is positive, we say there is ____________ linear b. a direct d. no _______ 39. If, as X increase, Y tends to increase, we say there is ____________ linear relationship between X and Y. a. an inverse b. a direct c. a significant d. no _______ 40. The explained sum of squares divided by the total sum of squares yield the _______. a. F statistic b. total mean square c. p value d. coefficient of multiple determination ECO 578 Fall 2015 Page 5 of 14 Part C: Work Problem (41-52) **All work in part C must be shown step by step** 41. Work problem number 13 on page 8-11. (a-c) a) b) c) 42. Use problem number 1 on page 9-18 to answer the following questions (a-e). a) Use Z or T test? And why? b) At = 0.05, what is the rejection rule? ECO 578 Fall 2015 Page 6 of 14 c) Compute the value of the test statistic. d) What is the p-value? e) What is your conclusion? 43. Use problem number 13 on page 9-20 (a-h) a) What is the sample mean b) What is the sample standard deviation c) Use Z or T test? And why? d) What is your hypothesis test e) At = 0.05, what is the rejection rule? f) Compute the value of the test statistic. ECO 578 Fall 2015 Page 7 of 14 g) What is the p-value? h) What is your conclusion? 44. For n=6 data point, the following quantities have been calculated. xy = 400 a)Find x = 40 x2 = 346 y = 76 b0 c)Write the equation b)Find y2 = 1160 b1 2 d)Find r Se e)Find SST f)Find g) Construct the 95% confidence interval for the mean of y when x = 7 h)Construct the 95% confidence interval for the individual value of y when x = 9 ECO 578 Fall 2015 Page 8 of 14 45. The following data was collected which yielded the regression equation: (see the printout) A regression model relating plane travelling. Given X, number of fuel consumed (in gallon) and Y, flying time (1,000 mile) has been developed. Flying Time (y) Fuel Consumed (x) Given data 25.2 23.8 251.2 235.1 27.9 276.5 23.4 248.8 23.4 249.4 22.2 242 22 239.8 The computer output from a regression analysis of the data follows. Please fill in the blank and answer the following questions (a-d). SUMMARY OUTPUT Regression Statistics Multiple R ANOVA 0.877 df R Square ________ Adjusted R Square ________ Regression Standard Error ________ Residual Observations ________ Total SS MS F Significance F 1 18.937 18.937 ______ 0.010 _________ 5.712 ______ 6 24.649 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept -8.859 8.077 -1.097 0.323 _________ 11.904 -29.621 _________ Fuel Consumed (x) 0.132 0.032 4.071 0.010 _________ 0.215 0.049 _________ a) Write the estimated regression equation b) What is the number of observations c) Compute the F statistic and test the significance of the relationship at a .05 level of significance. d) Predict the flying time when the plane consumed 270 Gallons of gas ECO 578 Fall 2015 Page 9 of 14 46. The following regression equation was obtained using the five independent variables. Given that =0.05 a) What percent of the variation is explained by b) What is the standard error of regression? the regression equation? 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? ECO 578 Fall 2015 Page 10 of 14 47. State whether following; H0 should be accepted or rejected for =0.05 , given the F =computed F (fill in the blank and circle your decision) a) F = 2.34; df = 2 and 11 Computed F Critical F Decision ________ Reject / Fail to reject Computed F Critical F Decision ________ Reject / Fail to reject ________ c) F ________ Computed F Decision ________ b) F Critical F ________ Reject / Fail to reject = 2.52; df = 4 and 20 = 4.29; df = 3 and 24 48. Given the following, complete the ANOVA table and make the correct inference. Source SS df MS F Treatments _____ 2 3.24 _____ Error _____ 17 _____ Total 40.98 _____ ANSWER ECO 578 Fall 2015 Page 11 of 14 a) What is your hypothesis? b) In the above ANOVA table, is the factor significant at 5% level of significant? c) What is the number of observations? 49. Given the following, complete the ANOVA table and make the correct inference. Source SS df MS F _____ 2 24.9 _____ Error 22.9 _____ _____ Total _____ 29 Treatments ANSWER a) What is your hypothesis? b)In the above ANOVA table, is the factor significant at 5% level of significant? c)What is the number of observations? 50. Given the following, complete the ANOVA table and make the correct inference. Source SS df MS F _____ 3 _____ _____ Error 1156.56 _____ _____ Total 2202 23 Treatments ANSWER ECO 578 Fall 2015 Page 12 of 14 a)What is your hypothesis? b)In the above ANOVA table, is the factor significant at 5% level of significant? c)What is the number of observations? 51. Use problem 4 on page 15-9 to answer the following questions. (a-d) a) What is you hypothesis testing b) What is your 2? ECO 578 Fall 2015 Page 13 of 14 c) Is the 2 value significant at 5% level of significance? d) Write the conclusion for this question. 52. An ad agency asks each member of a random sample of 60 viewers to indicate which of six television programs he or she prefers. Let =0.05 Progra m Number 1 2 3 4 5 6 Total 5 8 10 12 12 13 60 c) What is you hypothesis testing d) What is your 2? ECO 578 Fall 2015 Page 14 of 14 c) Is the 2 value significant at 5% level of significance? d) Write the conclusion for this