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1、statistics18 by kellerCHAPTER 18 MULTIPLE REGRESSION SECTIONS 1 - 3 MULTIPLE CHOICE QUESTIONS In the following multiple-choice questions, please circle the correct answer. 1. In a multiple regression analysis, if the model provides a poor fit, this indicates that: a. the sum of squares for error wil
2、l be large b. the standard error of estimate will be large c. the multiple coefficient of determination will be close to zero d. All of the above ANSWER: d 2. In a multiple regression analysis, when there is no linear relationship between each of the independent variables and the dependent variable,
3、 then a. multiple t-tests of the individual coefficients will likely show some are significant b. we will conclude erroneously that the model has some validity c. the chance of erroneously concluding that the model is useful is substantially less with the F-test than with multiple t-tests d. All of
4、the above statements are correct ANSWER: d 677 678 Chapter Eighteen 3. In testing the validity of a multiple regression model, a large value of the F-test statistic indicates that: a. most of the variation in the independent variables is explained by the variation in y b. most of the variation in y
5、is explained by the regression equation c. most of the variation in y is unexplained by the regression equation d. the model provides a poor fit ANSWER: b Which of the following statements regarding multicollinearity is not true? a. It exists in virtually all multiple regression models. b. It is als
6、o called collinearity and intercorrelation. c. It is a condition that exists when the independent variables are highly correlated with the dependent variable. d. It does not affect the F-test of the analysis of variance. ANSWER: c In a multiple regression analysis involving 25 data points, the stand
7、ard error of estimate squared is calculated as se2=1.8 and the sum of squares for error as SSE = 36. Then, the number of the independent variables must be: a. 6 b. 5 c. 4 d. 3 ANSWER: c When the independent variables are correlated with one another in a multiple regression analysis, this condition i
8、s called: a. heteroscedasticity b. homoscedasticity c. multicollinearity d. elasticity ANSWER: c In a multiple regression model, the mean of the probability distribution of the error variable e is assumed to be: a. 1.0 b. 0.0 c. Any value greater than 1 d. k, where k is the number of independent var
9、iables included in the model ANSWER: b 4. 5. 6. 7. Multiple Regression 679 8. The adjusted multiple coefficient of determination is adjusted for the: a. number of regression parameters including the y-intercept b. number of dependent variables and the sample size c. number of independent variables a
10、nd the sample size d. coefficient of correlation and the significance level ANSWER: c In a multiple regression model, the standard deviation of the error variable e is assumed to be: a. constant for all values of the independent variables b. constant for all values of the dependent variable c. 1.0 d
11、. not enough information is given to answer this question ANSWER: a 9. 10. In multiple regression analysis, the ratio MSR/MSE yields the: a. t-test statistic for testing each individual regression coefficient b. F-test statistic for testing the validity of the regression equation c. multiple coeffic
12、ient of determination d. adjusted multiple coefficient of determination ANSWER: b 11. In a multiple regression analysis involving 6 independent variables, the sum of squares are calculated as: Total variation in Y = SSY = 900, SSR = 600 and SSE = 300. Then, the value of the F-test statistic for this
13、 model is: a. 150 b. 100 c. 50 d. None of the above ANSWER: d 12. In order to test the validity of a multiple regression model involving 5 independent variables and 30 observations, the numerator and denominator degrees of freedom for the critical value of F are, respectively, a. 5 and 30 b. 6 and 2
14、9 c. 5 and 24 d. 6 and 25 ANSWER: c 13. In multiple regression models, the values of the error variable e are assumed to be: a. autocorrelated b. dependent of each other c. independent of each other d. always positive ANSWER: c 680 Chapter Eighteen 14. 15. A multiple regression model involves 5 inde
15、pendent variables and a sample of 10 data points. If we want to test the validity of the model at the 5% significance level, the critical value is: a. 6.26 b. 3.33 c. 9.36 d. 4.24 ANSWER: a A multiple regression model involves 10 independent variables and 30 observations. If we want to test at the 5
16、% significance level the parameterb4, the critical value will be: a. 2.093 b. 1.697 c. 2.228 d. 1.729 ANSWER: a In a multiple regression analysis involving k independent variables and n data points, the number of degrees of freedom associated with the sum of squares for error is: a. k-1 b. n-k c. n-
17、1 d. n-k-1 ANSWER: d =8+3x1+5x2-4x3. As x3 increases by A multiple regression model has the form y 16. 17. 18. one unit, with x1 and x2 held constant, the y on average is expected to: a. increase by 1 unit b. increase by 12 units c. decrease by 4 units d. decrease by 16 units ANSWER: c The problem o
18、f multicollinearity arises when the: a. dependent variables are highly correlated with one another b. independent variables are highly correlated with one another c. independent variables are highly correlated with the dependent variable d. None of the above ANSWER: b Multiple Regression 681 19. To
19、test the validity of a multiple regression model, we test the null hypothesis that the regression coefficients are all zero by applying the: a. t-test b. z-test c. F-test d. All of the above ANSWER: c To test the validity of a multiple regression model involving two independent variables, the null h
20、ypothesis is that: a. b0=b1=b2 b. b1=b2=0 c. b1=b2 d. b1b2 ANSWER: b If multicollinearity exists among the independent variables included in a multiple regression model, then: a. regression coefficients will be difficult to interpret b. standard errors of the regression coefficients for the correlat
21、ed independent variables will increase c. multiple coefficient of determination will assume a value close to zero d. both (a) and (b) are correct statements ANSWER: d Which of the following is not true when we add an independent variable to a multiple regression model? a. Adjusted coefficient of det
22、ermination can assume a negative value b. Unadjusted coefficient of determination always increases c. Unadjusted coefficient of determination may increase or decrease d. Adjusted coefficient of determination may increase ANSWER: c =b0+b1x1+b2x2. The coefficient b1 is A multiple regression model has
23、the formyinterpreted as the: a. change in y per unit change in x1 b. change in y per unit change in x1, holding x2constant c. change in y per unit change in x1, when x1 and x2 values are correlated d. change in the average value of y per unit change in x1, holding x2 constant ANSWER: d 20. 21. 22. 2
24、3. 682 Chapter Eighteen 24. A multiple regression analysis involving three independent variables and 25 data points results in a value of 0.769 for the unadjusted multiple coefficient of determination. Then, the adjusted multiple coefficient of determination is: a. 0.385 b. 0.877 c. 0.591 d. 0.736 A
25、NSWER: d The coefficient of multiple determination ranges from: a. 1.0 to b. 0.0 to 1.0 c. 1.0 to k, where k is the number of independent variables in the model d. 1.0 to n, where n is the number of observations in the dependent variable ANSWER: b For a multiple regression model, the following stati
26、stics are given: Total variation in Y = SSY = 500, SSE = 80, and n = 25. Then, the coefficient of determination is: a. 0.84 b. 0.16 c. 0.3125 d. 0.05 ANSWER: a For a multiple regression model the following statistics are given: Total variation in Y = SSY = 250, SSE = 50, k = 4, and n = 20. Then, the
27、 coefficient of determination adjusted for the degrees of freedom is: a. 0.800 b. 0.747 c. 0.840 d. 0.775 ANSWER: b =5.25+2x1+6x2. As x2 increases by one A multiple regression model has the form:yunit, holding x1 constant, then the value of y will increase by: a. 2 units b. 7.25 units c. 6 units on
28、average d. None of the above ANSWER: c 25. 26. 27. 28. Multiple Regression 683 29. The graphical depiction of the equation of a multiple regression model with k independent variables (k 1) is referred to as: a. a straight line b. response variable c. response surface d. a plane only when k = 3 ANSWE
29、R: c A multiple regression model has: a. only one independent variable b. only two independent variables c. more than one independent variable d. more than one dependent variable ANSWER: c If all the points for a multiple regression model with two independent variables were on the regression plane,
30、then the multiple coefficient of determination would equal: a. 0 b. 1 c. 2, since there are two independent variables d. any number between 0 and 2 ANSWER: b If none of the data points for a multiple regression model with two independent variables were on the regression plane, then the multiple coef
31、ficient of determination would be: a. 1.0 b. 1.0 c. any number between 1 and 1, inclusive d. any number greater than or equal to zero but smaller than 1 ANSWER: d The multiple coefficient of determination is defined as: a. SSE/SSY b. MSE/MSR c. 1- (SSE/SSY) d. 1- (MSE/MSR) ANSWER: c In a multiple re
32、gression model, the following statistics are given: SSE = 100,R2=0.995, k = 5, and n = 15. Then, the multiple coefficient of determination adjusted for degrees of freedom is: a. 0.955 b. 0.930 c. 0.900 d. 0.855 ANSWER: b 30. 31. 32. 33. 34. 684 Chapter Eighteen 35. 36. In a multiple regression model
33、, the error variable e is assumed to have a mean of: a. 1.0 b. 0.0 c. 1.0 d. Any value smaller than 1.0 ANSWER: b =2-3x1+4x2+5x3, a unit increase in For the following multiple regression model: yx1, holding x2 and x3 constant, results in: a. an increase of 3 units in the value of y b. a decrease of
34、3 units in the value of y c. a decrease of 3 units on average in the value of y d. an increase of 8 units in the value of y ANSWER: c 37. 38. In a multiple regression model, the probability distribution of the error variable e is assumed to be: a. normal b. nonnormal c. positively skewed d. negative
35、ly skewed ANSWER: a Which of the following measures can be used to assess the multiple regression models fit? a. sum of squares for error b. sum of squares for regression c. standard error of estimate d. single t-test ANSWER: c 39. In a multiple regression analysis involving 40 observations and 5 in
36、dependent variables, the following statistics are given: Total variation in Y = SSY = 350 and SSE = 50. Then, the multiple coefficient of determination is: a. 0.8408 b. 0.8571 c. 0.8469 d. 0.8529 ANSWER: b Multiple Regression 685 40. In a multiple regression analysis involving 20 observations and 5
37、independent variables, the following statistics are given: Total variation in Y = SSY = 250 and SSE = 35. The multiple coefficient of determination adjusted for degrees of freedom is: a. 0.810 b. 0.860 c. 0.835 d. 0.831 ANSWER: a In testing the validity of a multiple regression model involving 10 in
38、dependent variables and 100 observations, the numerator and denominator degrees of freedom for the critical value of F will be, respectively, a. 9 and 90 b. 10 and 100 c. 9 and 10 d. 10 and 89 ANSWER: d In multiple regression analysis involving 10 independent variables and 100 observations, the crit
39、ical value of t for testing individual coefficients in the model will have: a. 100 degrees of freedom b. 10 degrees of freedom c. 89 degrees of freedom d. 9 degrees of freedom ANSWER: c For a multiple regression model, a. SSY = SSR SSE b. SSE = SSR SSY c. SSR = SSE SSY d. SSY = SSE + SSR ANSWER: d I
40、n a regression model involving 50 observations, the following estimated regression =10.5+3.2x1+5.8x2+6.5x3. For this model, the following model was obtained: ystatistics are given: SSR = 450 and SSE = 175. Then, the value of MSR is: a. 12.50 b. 275 c. 150 d. 3.804 ANSWER: c 41. 42. 43. 44. 686 Chapt
41、er Eighteen 45. 46. In a regression model involving 30 observations, the following estimated regression =60+2.8x1+1.2x2-x3. For this model, the following statistics model was obtained: ywere given: Total variation in Y = SSY = 800 and SSE = 200. Then, the value of the F statistic for testing the val
42、idity of this model is: a. 26.00 b. 7.69 c. 3.38 d. 0.039 ANSWER: a Most statistical software provide p-value for testing each coefficient in the multiple regression model. In the case of b2, this represents the probability that: a. b2=0 b. b2=0 c. |b2| could be this large if b2=0 d. |b2| could be t
43、his large if b20 ANSWER: c In a regression model involving 60 observations, the following estimated regression =51.4+0.70x1+0.679x2-0.378x3, and the following statistics model was obtained: ywere given: SSY = 119,724 and SSR = 29,029.72. Then, the value of MSE is: a. 1619.541 b. 9676.572 c. 1995.400
44、 d. 5020.235 ANSWER: a In testing the validity of a multiple regression model in which there are four independent variables, the null hypothesis is: a. H0:b1=b2=b3=b4=1 b. H0:b0=b1=b2=b3=b4 c. H0:b1=b2=b3=b4=0 d. H0:b0=b1=b2=b3=b40 ANSWER: c 47. 48. Multiple Regression 687 49. 50. For a set of 20 da
45、ta points, a statistical software listed the estimated multiple regression =-8.61+22x1+7x2+28x3, and also has listed the t statistic for testing equation as ythe significance of each regression coefficient. Using the 5% significance level for testing whether b2=7 differs significantly from zero, the
46、 critical region will be that the absolute value of t is greater than or equal to: a. 1.746 b. 2.120 c. 1.337 d. 1.333 ANSWER: b =75+25x1-15x2+10x3, if x2 were to increase by For the multiple regression model:y5, holding x1 and x3 constant, the value of y will: a. increase by 5 b. increase by 75 c. decrease on average by 5 d. decrease on average by 75 ANSWER: d 51. 52. In a multiple regression analysis, there are 20 data points and 4 independent
