In logistic regression,

a. the dependent variable only assumes two continuous values.

b. there are two dependent variables.

c. the dependent variable only assumes two discrete values.

d. there can only be two independent variables

2. A regression model between sales (y in $1000), unit price (x1 in dollars), and television advertisement (x2 in dollars) resulted in the following function:

Ŷ = 7 – 3x1 + 5x2

For this model, SSR = 3500, SSE = 1500, and the sample size is 18. The adjusted multiple coefficient of determination for this problem is

a. .70.

b. .66.

c. .2289.

d. .8367.

3. The following estimated regression equation was developed relating yearly income (y in $1000s) of 30 individuals with their age (x1) and their gender (x2) (0 if male and 1 if female).

Ŷ = 30 + .7x1 + 3x2

Also provided are SST = 1200 and SSE = 384. The multiple coefficient of determination is

a. .68.

b. .42.

c. .32.

d. .50.

4. The following estimated regression equation was developed relating yearly income (y in $1000s) of 30 individuals with their age (x1) and their gender (x2) (0 if male and 1 if female).

Ŷ = 30 + .7x1 + 3x2

Also provided are SST = 1200 and SSE = 384. At the 5% level, the model

a. is not significant.

b. would be significant if the sample size was larger than 30.

c. is significant.

d. has significant individual parameters.

5. How many independent variables are there in the estimated regression model ?

a. 1

b. 2

c. 3

d. 4

6. Which of the following represents the estimated value of the dependent variable(s) in the regression equation ?

7. A measure of identifying the effect of an unusual x value on the regression results is called

a. Cook’s D.

b. odd ratio.

c. unusual regression.

d. Leverage.

8. In a multiple regression model involving 30 observations, the following estimated regression equation was obtained:

Ŷ = 17 + 4x1 – 3x2 + 8x3 + 8x4

For this model, SSR = 700 and SSE = 100. The computed F statistic for testing the significance of the above model is

a. 7.00.

b. 4.00.

c. 50.19.

d. 43.75.

9. Below you are given a partial computer output from a multiple regression analysis based on a sample of 16 observations.

Carry out the test of significance for the parameter β1 at the 1% level. The null hypothesis should

a. be revised to test using F statistic.

b. be tested for β₃ instead.

c. be rejected.

d. not be rejected.

10. Which of the following does the graph of a multiple regression equation resemble?

a. A nonlinear function in two-dimensional space

b. A two-dimensional line

c. A cylinder in three-dimensional space

d. A plane in three-dimensional space

11. A logistic regression equation has what shape?

a. Normal

b. Skewed to the left

c. S shape

d. Skewed to the right

12. The following estimated regression equation was developed relating yearly income (y in $1000s) of 30 individuals with their age (x1) and their gender (x2) (0 if male and 1 if female).

Ŷ = 30 + .7x1 + 3x2

Also provided are SST = 1200 and SSE = 384. The estimated income (in $) of a 30-year-old male is

a. $51,000.

b. $21.

c. $51.

d. $90,000.

13. What values are typically assigned to an indicator variable?

a. there can be any number of dependent variables, but only one independent variable.

b. the multiple coefficient of determination must be larger than 1.

c. the adjusted coefficient of determination can never be negative.

d. there can be several independent variables, but only one dependent variable.

14. Which of the following would indicate the possible presence of multicollinearity in a regression analysis?

a. A significant p-value for a test of overall significance

b.
The F value obtained from the table which is used to test if there is a relationship among the variables at the 5% level equals

c. A small value for the coefficient of determination

d. All of these choices

15. The mathematical equation that explains how the dependent variable y is related to several independent variables x1, x2, …, xp and the error term ε is

a. a multiple regression equation.

b. a multiple regression model.

c. a simple nonlinear regression model.

d. an estimated multiple regression equation.

16. In a multiple regression analysis, SSR = 1000 and SSE = 200. The F statistic for this model is

a. 800.

b. 5.

c. 1200.

d. Not enough information is provided to answer this question

17. In a multiple regression model involving 44 observations, the following estimated regression equation was obtained.

Ŷ = 29 + 18x1 + 43x2 + 87x3

For this model, SSR = 600 and SSE = 400. The computed F statistic for testing the significance of the above model is

a. .667.

b. .600.

c. 1.50.

d. 20.00.

18. In a multiple regression analysis involving 10 independent variables and 81 observations, SST = 120 and SSE = 42. The multiple coefficient of determination is

a. .11.

b. .65.

c. .35.

d. .81.

19. What is the predicted value of y derived from a logistic regression equation with β0 = 0.5, β1 = 0.25, β2 = 1.75, x1 = 5, and x2 = 1?

a. 0.97

b. 0.82

c. 0.94

d. 0.78

20. In a multiple regression model involving 30 observations, the following estimated regression equation was obtained:

Ŷ = 17 + 4x1 – 3x2 + 8x3 + 8x4

For this model, SSR = 700 and SSE = 100. At the 5% level,

a. it can be concluded that the model is significant.

b. there is no evidence that the model is significant.

c. the conclusion is that the slope of x1 is significant.

d. there is evidence that the slope of x2 is significant.

21. Which of the following would indicate the possible presence of multicollinearity in a regression analysis?

a. A significant p-value for a test of overall significance

b. A high correlation between two or more independent variables

c. A small value for the coefficient of determination

d. All of these choices

22. Below you are given a partial computer output from a multiple regression analysis based on a sample of 16 observations.

The F value obtained from the table which is used to test if there is a relationship among the variables at the 5% level equals

a. 19.41.

b. 3.63.

c. 3.41.

d. 3.81.

23. In order to test for the significance of a regression model involving 4 independent variables and 36 observations, the numerator and denominator degrees of freedom (respectively) for the critical value of F are

a. 4 and 32.

b. 4 and 31.

c. 4 and 36.

d. 3 and 35.

24. The following estimated regression equation was developed relating yearly income (y in $1000s) of 30 individuals with their age (x1) and their gender (x2) (0 if male and 1 if female).

Ŷ = 30 + .7x1 + 3x2

Also provided are SST = 1200 and SSE = 384. The test statistic for testing the significance of the model is

a. 1.47.

b. 28.69.

c. .73.

d. 5.22.

25. The following estimated regression equation was developed relating yearly income (y in $1000s) of 30 individuals with their age (x1) and their gender (x2) (0 if male and 1 if female).

Ŷ = 30 + .7x1 + 3x2

Also provided are SST = 1200 and SSE = 384. At the 5% level, the model

a. has significant individual parameters.

b. is significant.

c. is not significant.

d. would be significant if the sample size was larger than 30.

26. A regression model between sales (y in $1000), unit price (x1 in dollars), and television advertisement (x2 in dollars) resulted in the following function:

Ŷ = 7 – 3x1 + 5x2

For this model, SSR = 3500, SSE = 1500, and the sample size is 18. The coefficient of x2 indicates that if television advertisement is increased by $1 (holding the unit price constant), sales are expected to

a. increase by $5000.

b. decrease by $2000.

c. increase by $12,000.

d. increase by $5

27. The adjusted multiple coefficient of determination is adjusted for the

a. number of independent variables.

b. number of equations.

c. sample size.

d. number of dependent variables.

28. Which of the following does the graph of a multiple regression equation resemble?

a. A nonlinear function in two-dimensional space

b. A plane in three-dimensional space

c. A cylinder in three-dimensional space

d. A two-dimensional line

29. In a situation where the dependent variable can assume only one of the two possible discrete values,

a. logistic regression should be applied.

b. there can only be two independent variables.

c. all the independent variables must have values of either zero or one.

d. we must use multiple regression.

30. A regression analysis was performed to determine the relationship between the costs of a product (y), the time to make the product (x1 ), the number of different materials used (x2), and the amount spent on marketing the product (x3). The estimated regression equation is . What is the estimated cost if the time to make the product is 5 hours, the number of different materials used is 4, and the amount spent on marketing is $100?

a. 205.4

b. 185.4

c. 213

d. 83

31. The following estimated regression equation was developed relating yearly income (y in $1000s) of 30 individuals with their age (x1) and their gender (x2) (0 if male and 1 if female).

Ŷ = 30 + .7x1 + 3x2

Also provided are SST = 1200 and SSE = 384. The yearly income (in $) expected of a 24-year-old male individual is

a. $46,800.

b. $49,800.

c. $13,800.

d. $16,800

32. In a multiple regression model, the error term ε is assumed to be a random variable with a mean of

a. zero.

b. 1.

c. any value.

d. -1.

33. The equation which has the form of E(y) = Ŷ = b0 + b1x1 + b2x2 + … + bpxp is

a. a multiple nonlinear regression model.

b. an estimated multiple regression equation.

c. a multiple regression equation.

d. an estimated multiple nonlinear regression equation.

34. In multiple regression analysis, the correlation among the independent variables is termed

a. adjusted coefficient of determination.

b. linearity.

c. adjusted correlation.

d. multicollinearity.

35. The following estimated regression equation was developed relating yearly income (y in $1000s) of 30 individuals with their age (x1) and their gender (x2) (0 if male and 1 if female).

Ŷ = 30 + .7x1 + 3x2

Also provided are SST = 1200 and SSE = 384. The yearly income (in $) expected of a 24-year-old female individual is

a. $19.80.

b. $49,800.

c. $19,800.

d. $49.80.

36. What values are typically assigned to an indicator variable?

a. 0 or 1

b. It depends on the data collected.

c. –1 or 1

d. 1 or 2

37. In regression analysis, the response variable is the

a. intercept.

b. slope of the regression function.

c. independent variable.

d. dependent variable.

38. A regression model in which more than one independent variable is used to predict the dependent variable is called

a. a multiple regression model.

b. an adjusted prediction model.

c. a simple linear regression model.

d. an independent model.

39. A variable that takes on the values of 0 or 1 and is used to incorporate the effect of categorical independent variables in a regression model is called

a. an interaction.

b. a logit variable.

c. a constant variable.

d. a dummy variable.

40. For a multiple regression model, SST = 200 and SSE = 50. The multiple coefficient of determination is

a. .80.

b. .25.

c. .75.

d. .33.

41. The correct relationship between SST, SSR, and SSE is given by

a. n(SST) = p(SSR) + (n – p)(SSE).

b. SSR = SST + SSE.

c. SSE = SSR + SST.

d. SSR = SST – SSE.

42. What type of model is the regression equation ?

a. It is a first-order model with three predictor variables.

b. It is a third-order model with three predictor variables.

c. It is a fourth-order model with one predictor variable.

d. It is a third-order model with one predictor variable.

43. In a regression analysis of a first-order model involving 3 predictor variables and 25 observations, the following estimated regression equation was developed.

Ŷ = 10 – 18x1 + 3x2 + 14x3

Also, the following standard errors and the sum of squares were obtained.

sb1 = 3	sb2 = 6	sb3 = 7
SST = 4800	SSE = 1296

If you want to determine whether or not the coefficients of the independent variables are significant, the critical t value at α = .05 is

a. 2.086.

b. 2.064.

c. 2.080.

d. 2.060

44. In a regression analysis of a first-order model involving 3 predictor variables and 25 observations, the following estimated regression equation was developed.

Ŷ = 10 – 18x1 + 3x2 + 14x3

Also, the following standard errors and the sum of squares were obtained.

sb1 = 3	sb2 = 6	sb3 = 7
SST = 4800	SSE = 1296

The p-value for testing the significance of the regression model is

a. less than .01.

b. between .01 and .025.

c. greater than .10.

d. between .025 and .05.

45. In multiple regression analysis, the general linear model

a. must contain more than two independent variables.

b. can be used to accommodate curvilinear relationships between the independent variables and dependent variable.

c. cannot be used to accommodate curvilinear relationships between dependent variables and independent variables.

d. cannot use the standard multiple regression procedures for estimation and prediction.

46. The following regression model

y = β0 + β1x1 + β2×12 + ε

is known as a

a. second-order model with two predictor variables.

b. second-order model with one predictor variable.

c. simple first-order model with one predictor variable.

d. simple first-order model with two predictor variables.

47. A test used to determine whether or not first-order autocorrelation is present is

a. serial-autocorrelation test.

b. t test.

c. Durbin-Watson Test.

d. chi-square test.

48. Which of the following values remains the same in the regression analysis for both the full and reduced models?

a. SSR

b. SST

c. SSE

d. All of these choices

49. Consider the sample correlation coefficients in the table below.

How much of the variability in time can be explained by boxes?

a. .81%

b. 90.2%

c. 66.2%

d. 81.4%

50. The range of the Durbin-Watson statistic is from

a. -∞ to +∞.

b. 0 to 4.

c. 0 to 1.

d. -1 to 1.

51. In a regression analysis of a first-order model involving 3 predictor variables and 25 observations, the following estimated regression equation was developed.

Ŷ = 10 – 18x1 + 3x2 + 14x3

Also, the following standard errors and the sum of squares were obtained.

sb1 = 3	sb2 = 6	sb3 = 7
SST = 4800	SSE = 1296

If we are interested in testing for the significance of the relationship among the variables (i.e., significance of the model), the critical value of F at α = .05 is

a. 2.78.

b. 2.76.

c. 3.10.

d. 3.07.

52. The following estimated regression equation was developed relating yearly income (y in $1000s) of 30 individuals with their age (x1) and their gender (x2) (0 if male and 1 if female).

Ŷ = 30 + .7x1 + 3x2

Also provided are SST = 1200 and SSE = 384. At the 5% level, the model

a. is significant.

b. is not significant.

c. has significant individual parameters.

d. would be significant if the sample size was larger than 30.

53. The following estimated regression equation was developed relating yearly income (y in $1000s) of 30 individuals with their age (x1) and their gender (x2) (0 if male and 1 if female).

Ŷ = 30 + .7x1 + 3x2

Also provided are SST = 1200 and SSE = 384. If we want to test for the significance of the model, the critical value of F at α = .05 is

a. 2.96.

b. 3.33.

c. 3.35.

d. 3.34.

54. In a multiple regression model involving 44 observations, the following estimated regression equation was obtained.

Ŷ = 29 + 18x1 + 43x2 + 87x3

For this model, SSR = 600 and SSE = 400. MSR for this model is

a. 200.

b. 10.

c. 1000.

d. 43.

55. Below you are given a partial computer output from a multiple regression analysis based on a sample of 16 observations.

Carry out the test of significance for the parameter β1 at the 1% level. The null hypothesis should

a. not be rejected.

b. be rejected.

c. be revised to test using F statistic.

d. be tested for β₃ instead.

56. The mathematical equation that explains how the dependent variable y is related to several independent variables x1, x2, …, xp and the error term ε is

a. an estimated multiple regression equation.

b. a simple nonlinear regression model.

c. a multiple regression model.

d. a multiple regression equation

57. The following estimated regression equation was developed relating yearly income (y in $1000s) of 30 individuals with their age (x1) and their gender (x2) (0 if male and 1 if female).

Ŷ = 30 + .7x1 + 3x2

Also provided are SST = 1200 and SSE = 384. The test statistic for testing the significance of the model is

a. .73.

b. 1.47.

c. 5.22.

d. 28.69.

58. A term used to describe the case when the independent variables in a multiple regression model are correlated is

a. leverage.

b. regression.

c. multicollinearity.

d. correlation.

59. What values are typically assigned to an indicator variable?

a. 1 or 2

b. –1 or 1

c. It depends on the data collected.

d. 0 or 1

60. A regression model involving 4 independent variables and a sample of 15 observations resulted in the following sum of squares.

SSR = 165

SSE = 60

If we want to test for the significance of the model at a .05 level of significance, the critical F value (from the table) is

a. 3.11.

b. 3.48.

c. 3.34.

d. 3.06.

61. he equation which has the form of E(y) = Ŷ = b0 + b1x1 + b2x2 + … + bpxp is

a. a multiple nonlinear regression model.

b. an estimated multiple nonlinear regression equation.

c. a multiple regression equation.

d. an estimated multiple regression equation

62. When autocorrelation is present, which of the following statements is true?

63. Consider the sample correlation coefficients in the table below.

How much of the variability in time can be explained by boxes?

a. 90.2%

b. 81.4%

c. 66.2%

d. .81%

64. All of the following variable selection procedures are heuristics except

a. backward elimination.

b. stepwise regression.

c. forward selection.

d. best-subsets regression.

65. In a regression analysis of a first-order model involving 3 predictor variables and 25 observations, the following estimated regression equation was developed.

Ŷ = 10 – 18x1 + 3x2 + 14x3

Also, the following standard errors and the sum of squares were obtained.

sb1 = 3	sb2 = 6	sb3 = 7
SST = 4800	SSE = 1296

The test statistic for testing the significance of the model is

a. .73.

b. 3.70.

c. 1.37.

d. 18.93.

66. The variable selection procedure that identifies the best regression model, given a specified number of independent variables, is

a. forward selection.

b. backward elimination.

c. best-subsets regression.

d. stepwise regression.

67. The following regression model

y = β0 + β1x1 + β2×12 + ε

is known as a

a. second-order model with one predictor variable.

b. simple first-order model with one predictor variable.

c. simple first-order model with two predictor variables.

d. second-order model with two predictor variables.

68. When autocorrelation is present, one of the assumptions of the regression model is violated and that assumption is

a. the values of the error term ε are independent.

b. the expected value of the error term ε is zero.

c. the values of the error term ε are normally distributed for all values of x.

d. the variance of the error term ε is the same for all values of x

69. In a regression analysis of a first-order model involving 3 predictor variables and 25 observations, the following estimated regression equation was developed.

Ŷ = 10 – 18x1 + 3x2 + 14x3

Also, the following standard errors and the sum of squares were obtained.

sb1 = 3	sb2 = 6	sb3 = 7
SST = 4800	SSE = 1296

The multiple coefficient of determination is

a. .73.

b. .33.

c. .27.

d. .50.

70. In a regression analysis of a first-order model involving 3 predictor variables and 25 observations, the following estimated regression equation was developed.

Ŷ = 10 – 18x1 + 3x2 + 14x3

Also, the following standard errors and the sum of squares were obtained.

sb1 = 3	sb2 = 6	sb3= 7
SST = 4800	SSE = 1296

At the 5% level, the coefficient of x2

a. is significant.

b. cannot be tested, because not enough information is provided.

c. should be estimated again, because it is incorrect in the above equation.

d. is not found to be significant.

71. In multiple regression analysis, the general linear model

a. cannot be used to accommodate curvilinear relationships between dependent variables and independent variables.

b. must contain more than two independent variables.

c. cannot use the standard multiple regression procedures for estimation and prediction.

d. can be used to accommodate curvilinear relationships between the independent variables and dependent variable

72. A regression model between sales (y in $1000), unit price (x1 in dollars), and television advertisement (x2 in dollars) resulted in the following function:

Ŷ = 7 – 3x1 + 5x2

For this model, SSR = 3500, SSE = 1500, and the sample size is 18. The adjusted multiple coefficient of determination for this problem is

a. .70.

b. .66.

c. .8367.

d. .2289.

73. A regression model involved 18 independent variables and 200 observations. The critical value of t for testing the significance of each of the independent variable’s coefficients will have

a. 200 degrees of freedom.

b. 181 degrees of freedom.

c. 199 degrees of freedom.

d. 18 degrees of freedom.

74. The following estimated regression equation was developed relating yearly income (y in $1000s) of 30 individuals with their age (x1) and their gender (x2) (0 if male and 1 if female).

Ŷ = 30 + .7x1 + 3x2

Also provided are SST = 1200 and SSE = 384. If we want to test for the significance of the model, the critical value of F at α = .05 is

a. 3.35.

b. 3.34.

c. 3.33.

d. 2.96.

75. The _______ of an observation is determined by how far the values of the independent variables are from their means.

a. collinearity

b. leverage

c. residual

d. odds ratio

76. In multiple regression analysis, a variable that cannot be measured in numerical terms is called a

a. categorical independent variable.

b. nonmeasurable random variable.

c. dependent variable.

d. constant variable

77. A regression model involving 4 independent variables and a sample of 15 observations resulted in the following sum of squares.

SSR = 165

SSE = 60

If we want to test for the significance of the model at a .05 level of significance, the critical F value (from the table) is

a. 3.11.

b. 3.06.

c. 3.34.

d. 3.48.

78. In a regression model involving more than one independent variable, which of the following tests must be used in order to determine if the relationship between the dependent variable and the set of independent variables is significant?

a. F test

b. chi-square test

c. t test

d. Either a t test or a chi-square test can be used.

79. In a multiple regression model involving 44 observations, the following estimated regression equation was obtained.

Ŷ = 29 + 18x1 + 43x2 + 87x3

For this model, SSR = 600 and SSE = 400. The computed F statistic for testing the significance of the above model is

a. 20.00.

b. .600.

c. .667.

d. 1.50.

80. The following estimated regression equation was developed relating yearly income (y in $1000s) of 30 individuals with their age (x1) and their gender (x2) (0 if male and 1 if female).

Ŷ = 30 + .7x1 + 3x2

Also provided are SST = 1200 and SSE = 384. The yearly income (in $) expected of a 24-year-old female individual is

a. $49,800.

b. $49.80.

c. $19.80.

d. $19,800

81. Below you are given a partial computer output from a multiple regression analysis based on a sample of 16 observations.

Carry out the test to determine if there is a relationship among the variables at the 5% level. The null hypothesis should

a. be rejected.

b. be revised to test for multicollinearity.

c. not be rejected.

d. test for individual significance instead.

82. In multiple regression analysis, the word linear in the term “general linear model” refers to the fact that β0, β1, . . ., βp all have exponents of

a. at least 1.

b. less than 0.

c. 0.

d. 1.

83. The forward selection procedure starts with _____ independent variable(s) in the multiple regression model.

a. no

b. two

c. all

d. one

84. When performing a backward elimination procedure, how is the first variable deleted from the model selected?

a. The variable with the largest coefficient for predicting y is selected first.

b. The variable with the smallest standard deviation is selected first.

c. The variable with the highest p-value for the test H0 : βi = 0 is selected first.

d. The variable with the lowest p-value when testing the significance of the coefficients is selected first.

85. The test statistic for a Durbin–Watson test is d = 1.27 with n = 20 and k = 5. Which of the following conclusions can be made when testing H0: ρ = 0 versus Ha: ρ < 0 at the 1% significance level?

a. There is evidence of negative autocorrelation.

b. There is no evidence of positive autocorrelation.

c. There is no evidence of multicollinearity.

d. There is no evidence of negative autocorrelation.

86. When dealing with the problem of nonconstant variance, the reciprocal transformation means using

a. 1/x as the independent variable instead of x.

b. 1/y as the dependent variable instead of y.

c. y2 as the dependent variable instead of y.

d. x2 as the independent variable instead of x

87. Which of the following is the multiple regression model that would be used to analyze data from a randomized block design with two treatments and four blocks?

88. Which procedure selects independent variables for inclusion in the model one at a time?

a. Forward selection

b. Backward elimination

c. Logarithm-transformed regression

d. Nonlinear regression

89. What is the predicted rate ( ) when temperature (x) is 60 for the regression equation ?

a. 695.68

b. 1506.8

c. 86.8

d. Not enough information is given to compute the predicted rate

90. Serial correlation is

a. the correlation between serial numbers of the independent variables.

b. used to identify the effects of multicollinearity.

c. the same as autocorrelation.

d. the same as leverage

91. Multicollinearity may cause problems if the absolute value of the sample correlation coefficient for two of the independent variables exceeds what value?

a. .7

b. 1

c. .5

d. .05

92. If a categorical variable has k levels, the number of dummy variables required is

a. k + 1.

b. k.

c. 2k.

d. k – 1.

93. In order to test for the significance of a regression model involving 8 independent variables and 121 observations, the numerator and denominator degrees of freedom (respectively) for the critical value of F are

a. 7 and 112.

b. 8 and 121.

c. 8 and 112.

d. 7 and 120

94. A regression analysis involved 17 independent variables and 697 observations. The critical value of t for testing the significance of each of the independent variable’s coefficients will have

a. 696 degrees of freedom.

b. 679 degrees of freedom.

c. 714 degrees of freedom.

d. 16 degrees of freedom.

95. A regression model between sales (y in $1000), unit price (x1 in dollars), and television advertisement (x2 in dollars) resulted in the following function:

Ŷ = 7 – 3x1 + 5x2

For this model, SSR = 3500, SSE = 1500, and the sample size is 18. The multiple coefficient of determination for this problem is

a. .7000.

b. .3040.

c. .2289.

d. .4368.

96. In multiple regression analysis, a variable that cannot be measured in numerical terms is called a

a. nonmeasurable random variable.

b. dependent variable.

c. constant variable.

d. categorical independent variable.

97. Below you are given a partial computer output from a multiple regression analysis based on a sample of 16 observations.

The interpretation of the coefficient of x1 is that

a. a one unit change in x1 will lead to a 3.682 unit decrease in y.

b. The unit of measurement for y is required to interpret the coefficient.

c. a one unit increase in x1 will lead to a 3.682 unit decrease in y when all other variables are held constant.

d. a one unit increase in x1 will lead to a 3.682 unit decrease in x2 when all other variables are held constant.

98. What is the predicted value of y derived from a logistic regression equation with β0 = 0.5, β1 = 0.25, β2 = 1.75, x1 = 5, and x2 = 1?

a. 0.97

b. 0.78

c. 0.94

d. 0.82

99. A measure of goodness of fit for the estimated regression equation is the

a. multicollinearity.

b. multiple coefficient of determination.

c. mean square due to regression.

d. studentized residual

100. The following estimated regression equation was developed relating yearly income (y in $1000s) of 30 individuals with their age (x1) and their gender (x2) (0 if male and 1 if female).

Ŷ = 30 + .7x1 + 3x2

Also provided are SST = 1200 and SSE = 384. If we want to test for the significance of the model, the critical value of F at α = .05 is

a. 3.35.

b. 3.33.

c. 2.96.

d. 3.34

101. Which of the following does the graph of a multiple regression equation resemble?

a. A plane in three-dimensional space

b. A two-dimensional line

c. A nonlinear function in two-dimensional space

d. A cylinder in three-dimensional space

102. A regression model involving 4 independent variables and a sample of 15 observations resulted in the following sum of squares.

SSR = 165

SSE = 60

The test statistic obtained from the information provided is

a. 2.110.

b. 6.875.

c. 5.455.

d. 3.480.

103. A multiple regression analysis was performed to determine the relationship between the satisfaction rating for a new candy bar and the amount of chocolate used and the amount of caramel used. What is the mean value of the satisfaction rating, if the estimated regression equation is , the amount of chocolate (x1 ) used is 0.35 ounce, and the amount of caramel (x2 ) used is 0.15 ounce?

a. 4.235

b. .50

c. 6.73

d. 8.47

104. How many independent variables are there in the estimated regression model ?

a. 1

b. 2

c. 3

d. 4

105. The following estimated regression equation was developed relating yearly income (y in $1000s) of 30 individuals with their age (x1) and their gender (x2) (0 if male and 1 if female).

Ŷ = 30 + .7x1 + 3x2

Also provided are SST = 1200 and SSE = 384. If we want to test for the significance of the model, the critical value of F at α = .05 is

a. 2.96.

b. 3.34.

c. 3.35.

d. 3.33

106. The equation which has the form of E(y) = Ŷ = b0 + b1x1 + b2x2 + … + bpxp is

a. a multiple nonlinear regression model.

b. an estimated multiple regression equation.

c. a multiple regression equation.

d. an estimated multiple nonlinear regression equation.

107. Below you are given a partial computer output from a multiple regression analysis based on a sample of 16 observations.

The interpretation of the coefficient of x1 is that

a. a one unit increase in x1 will lead to a 3.682 unit decrease in y when all other variables are held constant.

b. a one unit increase in x1 will lead to a 3.682 unit decrease in x2 when all other variables are held constant.

c. The unit of measurement for y is required to interpret the coefficient.

d. a one unit change in x1 will lead to a 3.682 unit decrease in y.

108. A logistic regression equation has what shape?

a. Skewed to the right

b. Normal

c. S shape

d. Skewed to the left

109. In a multiple regression model involving 30 observations, the following estimated regression equation was obtained:

Ŷ = 17 + 4x1 – 3x2 + 8x3 + 8x4

For this model, SSR = 700 and SSE = 100. The computed F statistic for testing the significance of the above model is

a. 50.19.

b. 7.00.

c. 43.75.

d. 4.00.

110. The mathematical equation that explains how the dependent variable y is related to several independent variables x1, x2, …, xp and the error term ε is

a. a multiple regression model.

b. a multiple regression equation.

c. an estimated multiple regression equation.

d. a simple nonlinear regression model.

111. If an independent variable is added to a multiple regression model, the R2 value

a. is not affected by the variable added even if it is statistically significant.

b. becomes larger even if the variable added is not statistically significant.

c. becomes larger or smaller depending on the statistical significance of the variable.

d. might or might not become larger even if the variable added is statistically significant.

112. An example of a first-order model with two predictor variables is

a. y = b0 + b1x1 + ε.

b. y = b0 + b1x1 + b2x2 + ε.

c. y = b0 + b1x2 + ε.

d. y2 = b0 + b1x1 + b2x2 + ε.

113. In a stepwise regression, which of the following tests is used to determine whether an independent variable makes a significant contribution to the model?

a. F test

b. Chi-square test

c. z test

d. β test

114. serial correlation is

a. the same as autocorrelation.

b. the same as leverage.

c. the correlation between serial numbers of the independent variables.

d. used to identify the effects of multicollinearity.

115. The correlation in error terms that arises when the error terms at successive points in time are related is termed

a. leverage.

b. autocorrelation.

c. interaction.

d. multicorrelation

116. Which of the following statements about the backward elimination procedure is false?

a. It begins with the regression model found using the forward selection procedure.

b. It does not permit an independent variable to be reentered once it has been removed.

c. It does not guarantee that the best regression model will be found.

d. It is a one-variable-at-a-time procedure

117. A variable such as z, whose value is z = x1x2, is added to a general linear model in order to account for potential effects of two variables x1 and x2 acting together. This type of effect is

a. called interaction.

b. one of the transformation effects.

c. impossible to occur.

d. called multicollinearity effect.

118. In a regression analysis of a first-order model involving 3 predictor variables and 25 observations, the following estimated regression equation was developed.

Ŷ = 10 – 18x1 + 3x2 + 14x3

Also, the following standard errors and the sum of squares were obtained.

sb1 = 3	sb2 = 6	sb3= 7
SST = 4800	SSE = 1296

At the 5% level, the coefficient of x2

a. is not found to be significant.

b. is significant.

c. cannot be tested, because not enough information is provided.

d. should be estimated again, because it is incorrect in the above equation

119. What type of model is the regression equation ?

a. It is a first-order model with three predictor variables.

b. It is a fourth-order model with one predictor variable.

c. It is a third-order model with three predictor variables.

d. It is a third-order model with one predictor variable.

120. In a stepwise regression, which of the following tests is used to determine whether an independent variable makes a significant contribution to the model?

a. Chi-square test

b. β test

c. F test

d. z test

121. In order to use the output from a multiple regression analysis to perform the ANOVA test on the difference among the means of three populations, how many dummy variables are needed to indicate treatments?

a. 1

b. 3

c. 4

d. 2

122. When dealing with the problem of nonconstant variance, the reciprocal transformation means using

a. y2 as the dependent variable instead of y.

b. x2 as the independent variable instead of x.

c. 1/y as the dependent variable instead of y.

d. 1/x as the independent variable instead of x.

123. When autocorrelation is present, one of the assumptions of the regression model is violated and that assumption is

a. .5

b. .05

c. .7

d. 1

124. Which of the following tests is used to determine whether an additional variable makes a significant contribution to a multiple regression model?

a. an F test

b. a chi-square test

c. a t test

d. a z test

125. When autocorrelation is present, one of the assumptions of the regression model is violated and that assumption is

a. the variance of the error term ε is the same for all values of x.

b. the expected value of the error term ε is zero.

c. the values of the error term ε are independent.

d. the values of the error term ε are normally distributed for all values of x.

126. The correlation in error terms that arises when the error terms at successive points in time are related is termed

a. autocorrelation.

b. leverage.

c. interaction.

d. multicorrelation

127. In a regression analysis of a first-order model involving 3 predictor variables and 25 observations, the following estimated regression equation was developed.

Ŷ = 10 – 18x1 + 3x2 + 14x3

Also, the following standard errors and the sum of squares were obtained.

sb1 = 3	sb2 = 6	sb3 = 7
SST = 4800	SSE = 1296

At the 5% level, the coefficient of x1

a. is significant.

b. is not found to be significant.

c. should be estimated again, because it is incorrect in the above equation.

d. cannot be tested, because not enough information is provided

128. When autocorrelation is present, which of the following statements is true?

129. All the independent variables in a multiple regression analysis

a. can be either quantitative or qualitative or both.

b. must assume only positive values.

c. must be quantitative.

d. must be either quantitative or qualitative but not a mix of both.

130. In a regression analysis of a first-order model involving 3 predictor variables and 25 observations, the following estimated regression equation was developed.

Ŷ = 10 – 18x1 + 3x2 + 14x3

Also, the following standard errors and the sum of squares were obtained.

sb1 = 3	sb2 = 6	sb3 = 7
SST = 4800	SSE = 1296

The test statistic for testing the significance of the model is

a. 3.70.

b. 1.37.

c. 18.93.

d. .73.

131. In a regression analysis of a first-order model involving 3 predictor variables and 25 observations, the following estimated regression equation was developed.

Ŷ = 10 – 18x1 + 3x2 + 14x3

Also, the following standard errors and the sum of squares were obtained.

sb1 = 3	sb2 = 6	sb3 = 7
SST = 4800	SSE = 1296

If you want to determine whether or not the coefficients of the independent variables are significant, the critical t value at α = .05 is

a. 2.060.

b. 2.064.

c. 2.080.

d. 2.086.

132. In a stepwise regression, which of the following tests is used to determine whether an independent variable makes a significant contribution to the model?

a. Chi-square test

b. F test

c. β test

d. z test

133. In order to use the output from a multiple regression analysis to perform the ANOVA test on the difference among the means of three populations, how many dummy variables are needed to indicate treatments?

a. 2

b. 3

c. 1

d. 4

134. The forward selection procedure starts with _____ independent variable(s) in the multiple regression model.

a. no

b. two

c. one

d. all

135. Which of the following models is not intrinsically linear?

136. A regression model involved 5 independent variables and 136 observations. The critical value of t for testing the significance of each of the independent variable’s coefficients will have

a. 135 degrees of freedom.

b. 130 degrees of freedom.

c. 121 degrees of freedom.

d. 4 degrees of freedom

137. What is the predicted value of y derived from a logistic regression equation with β0 = 0.5, β1 = 0.25, β2 = 1.75, x1 = 5, and x2 = 1?

a. 0.82

b. 0.94

c. 0.97

d. 0.78

138. A multiple regression model has the estimated form

Ŷ = 7 + 2x1 + 9x2

As x1 increases by 1 unit (holding x2 constant), y is expected to

a. decrease by 2 units.

b. increase by 9 units.

c. decrease by 9 units.

d. increase by 2 units.

139. In a multiple regression model involving 30 observations, the following estimated regression equation was obtained:

Ŷ = 17 + 4x1 – 3x2 + 8x3 + 8x4

For this model, SSR = 700 and SSE = 100. The multiple coefficient of determination for the above model is

a. .125.

b. .934.

c. .144.

d. .875.

140. Using the Durbin-Watson test for negative autocorrelation, we conclude that negative autocorrelation is present if

a. d < dU.

b. d < dL.

c. d > 4 – dL.

d. d < 4 – dU.

141. What is the predicted profit when the number of items made (x1 ) is 2,500, and the number of stores stocking the product (x2 ) is 5, using the estimated regression equation ?

a. 1,345

b. 23,200

c. 8,095

d. 75,595

142. A regression model involving 4 independent variables and a sample of 15 observations resulted in the following sum of squares.

SSR = 165

SSE = 60

The multiple coefficient of determination is

a. .275.

b. .7333.

c. .3636.

d. .5

143. The null hypothesis in the Durbin-Watson test is always that there is

a. negative autocorrelation.

b. no autocorrelation.

c. either positive or negative autocorrelation.

d. positive autocorrelation.

144. In a multiple regression analysis involving 5 independent variables and 30 observations, SSR = 360 and SSE = 40. The multiple coefficient of determination is

a. .90.

b. .25.

c. .15.

d. .80

145. Below you are given a partial computer output from a multiple regression analysis based on a sample of 16 observations.

We want to test whether the parameter β1 is significant. The test statistic equals

a. -1.4.

b. -5.0.

c. 3.6.

d. 1.4.

146. The following model

y = β0 + β1x1 + ε

is referred to as a

a. curvilinear model.

b. simple first-order model with one predictor variable.

c. simple second-order model with one predictor variable.

d. curvilinear model with one predictor variable

147. In a regression analysis of a first-order model involving 3 predictor variables and 25 observations, the following estimated regression equation was developed.

Ŷ = 10 – 18x1 + 3x2 + 14x3

Also, the following standard errors and the sum of squares were obtained.

sb1 = 3	sb2 = 6	sb3 = 7
SST = 4800	SSE = 1296

The test statistic for testing the significance of the model is

a. 1.37.

b. 3.70.

c. 18.93.

d. .73.

148. Which procedure selects independent variables for inclusion in the model one at a time?

a. Logarithm-transformed regression

b. Backward elimination

c. Forward selection

d. Nonlinear regression

149. The joint effect of two independent variables acting together is called

a. transformation.

b. joint regression.

c. autocorrelation.

d. interaction.

150. A regression model between sales (y in $1000), unit price (x1 in dollars), and television advertisement (x2 in dollars) resulted in the following function:

Ŷ = 7 – 3x1 + 5x2

For this model, SSR = 3500, SSE = 1500, and the sample size is 18. To test for the significance of the model, the test statistic F is

a. 17.5.

b. .70.

c. 1.75.

d. 2.33.

151. In a multiple regression model involving 30 observations, the following estimated regression equation was obtained:

Ŷ = 17 + 4x1 – 3x2 + 8x3 + 8x4

For this model, SSR = 700 and SSE = 100. The critical F value at α = .05 is

a. 2.99.

b. 2.53.

c. 2.76.

d. 2.69.

152. The numerical value of the coefficient of determination.

a. is negative if the coefficient of correlation is negative.

b. is always smaller than the coefficient of correlation.

c. can be larger or smaller than the coefficient of correlation.

d. is always larger than the coefficient of correlation

153. A regression analysis involved 6 independent variables and 27 observations. The critical value of t for testing the significance of each of the independent variable’s coefficients will have

a. 27 degrees of freedom.

b. 21 degrees of freedom.

c. 26 degrees of freedom.

d. 20 degrees of freedom.

154. In a regression analysis of a first-order model involving 3 predictor variables and 25 observations, the following estimated regression equation was developed.

Ŷ = 10 – 18x1 + 3x2 + 14x3

Also, the following standard errors and the sum of squares were obtained.

sb1 = 3	sb2 = 6	sb3 = 7
SST = 4800	SSE = 1296

At the .05 level of significance, the coefficient of x3

a. should be estimated again, because it is incorrect in the above equation.

b. cannot be tested, because not enough information is provided.

c. is significant.

d. is not found to be significant.

155. A model in the form of y = β0 + β1z1 + β2z2 + . . . + βpzp + ε, where each independent variable zj (for j = 1, 2, . . ., p) is a function of x1, x2 , …, xk, is known as the

a. pth-order z model.

b. general linear model.

c. general curvilinear model.

d. experimental model.

156. Models in which the parameters have exponents other than 1 are called

a. independent models.

b. autocorrelated models.

c. linear models.

d. nonlinear models.

157. In a multiple regression analysis involving 5 independent variables and 30 observations, SSR = 360 and SSE = 40. The multiple coefficient of determination is

a. .90.

b. .15.

c. .80.

d. .25.

158. In order to test for the significance of a regression model involving 3 independent variables and 47 observations, the numerator and denominator degrees of freedom (respectively) for the critical value of F are

a. 3 and 43.

b. 47 and 3.

c. 2 and 43.

d. 3 and 47.

159. In a multiple regression analysis involving 15 independent variables and 200 observations, SST = 800 and SSE = 240. The multiple coefficient of determination is

a. .192.

b. .300.

c. .500.

d. .700.

160. In a multiple regression model, the variance of the error term ε is assumed to be

a. zero.

b. one.

c. the same for all values of the independent variable.

d. the same for all values of the dependent variable.

161. What is the multiple coefficient of determination for a multiple regression analysis involving 4 independent variables and 240 observations when SST = 870 and SSE = 325?

a. .728

b. .626

c. .374

d. .620

162. A regression analysis involved 8 independent variables and 99 observations. The critical value of t for testing the significance of each of the independent variable’s coefficients will have

a. 90 degrees of freedom.

b. 97 degrees of freedom.

c. 98 degrees of freedom.

d. 7 degrees of freedom.

163. Consider the residual plot from the multiple regression analysis to determine the time required to load a truck given the number of boxes to be loaded and the average weight of the boxes.

How many data points in the residual plot given should be investigated further as potential outliers?

a. 0

b. 1

c. 2

d. 3

164. The ratio of MSR to MSE yields

a. the F statistic.

b. the chi-square statistic.

c. SST.

d. SSR.

165. A random sample of 31 sales charge showed a sample standard deviation of $50. A 90% confidence interval estimate of the population standard deviation is

a. 1596.458 to 4466.679.

b. 39.956 to 66.833.

c. 41.393 to 63.684.

d. 1715.101 to 4055.589.

166. Part of an ANOVA table is shown below.

At a 5% level of significance, if we want to determine whether or not the means of the populations are equal, the conclusion of the test is that

a. not all means are equal.

b. some means will never be equal.

c. some means may be equal.

d. all means are equal.

167. In regression analysis, an outlier is an observation whose

a. mean is zero.

b. mean is larger than the standard deviation.

c. residual is much larger than the rest of the residual values.

d. residual is zero.

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BA6933 Statistics Week 7 Quiz (Chapter 15 and 16)

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