Deck 15: Multiple Regression

Question 1

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

A) regression.
B) correlation.
C) multicollinearity.
D) leverage.

Answer 1

multicollinearity.

Question 2

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(n)

A) simple nonlinear regression model.
B) multiple regression model.
C) estimated multiple regression equation.
D) multiple regression equation.

Answer 2

multiple regression model.

Question 3

A multiple regression model has

A) only one independent variable.
B) more than one dependent variable.
C) more than one independent variable.
D) at least two dependent variables.

Answer 3

more than one independent variable.

Question 4

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 constant variable.
C) a dummy variable.
D) a logit variable.

Question 5

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

A) the same for all values of the dependent variable.
B) zero.
C) the same for all values of the independent variable.
D) one.

Question 6

In regression analysis, the response variable is the

A) independent variable.
B) dependent variable.
C) slope of the regression function.
D) intercept.

Question 7

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) 47 and 3.
B) 3 and 47.
C) 2 and 43.
D) 3 and 43.

Question 8

In regression analysis, an outlier is an observation whose

A) mean is larger than the standard deviation.
B) residual is zero.
C) mean is zero.
D) residual is much larger than the rest of the residual values.

Question 9

The equation which has the form of E(y) = = b₀ + b₁x₁ + b₂x₂ + ... + b_px_p is a(n)

A) estimated multiple nonlinear regression equation.
B) multiple nonlinear regression model.
C) estimated multiple regression equation.
D) multiple regression equation.

Question 10

The adjusted multiple coefficient of determination is adjusted for the

A) number of dependent variables.
B) number of independent variables.
C) number of equations.
D) sample size.

Question 11

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) 1.
D) any value.

Question 12

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

A) adjusted correlation.
B) linearity.
C) multicollinearity.
D) adjusted coefficient of determination.

Question 13

In a multiple regression model, the error term ε is assumed to

A) have a mean of 1.
B) have a variance of zero.
C) have no distribution.
D) be normally distributed.

Question 14

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

A) a simple linear regression model.
B) a multiple regression model.
C) an independent model.
D) an adjusted prediction model.

Question 15

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

A) multiple coefficient of determination.
B) multicollinearity.
C) mean square due to regression.
D) studentized residual.

Question 16

The mathematical equation which has the form of E(y) = β₀ + β₁x₁ + β₂x₂ + ... + β_pxp relating the expected value of the dependent variable to the value of the independent variables is a(n)

A) estimated multiple nonlinear regression equation.
B) multiple nonlinear regression model.
C) estimated multiple regression equation.
D) multiple regression equation.

Question 17

The numerical value of the coefficient of determination.

A) is always larger than the coefficient of correlation.
B) is always smaller than the coefficient of correlation.
C) is negative if the coefficient of correlation is negative.
D) can be larger or smaller than the coefficient of correlation.

Question 18

In a multiple regression model, the values of the error term ε are assumed to be

A) zero.
B) dependent on each other.
C) independent of each other.
D) always negative.

Question 19

In multiple regression analysis,

A) there can be any number of dependent variables, but only one independent variable.
B) the adjusted coefficient of determination can never be negative.
C) the multiple coefficient of determination must be larger than 1.
D) there can be several independent variables, but only one dependent variable.

Question 20

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

A) Cook's D.
B) Leverage.
C) odd ratio.
D) unusual regression.

Question 21

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

A) we must use multiple regression.
B) there can only be two independent variables.
C) logistic regression should be applied.
D) all the independent variables must have values of either zero or one.

Question 22

For a multiple regression model, SST = 200 and SSE = 60. The multiple coefficient of determination is

A) .25.
B) .30.
C) .80.
D) .70.

Question 23

For a multiple regression model, SSR = 600 and SSE = 200. The multiple coefficient of determination is

A) .333.
B) .275.
C) .30.
D) .75.

Question 24

In order to test for the significance of a regression model involving 9 independent variables and 121 observations, the numerator and denominator degrees of freedom (respectively) for the critical value of F are

A) 9 and 121.
B) 7 and 120.
C) 9 and 111.
D) 7 and 111.

Question 25

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) 121 degrees of freedom.
B) 135 degrees of freedom.
C) 130 degrees of freedom.
D) 4 degrees of freedom.

Question 26

A regression model involved 20 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) 18 degrees of freedom.
B) 200 degrees of freedom.
C) 199 degrees of freedom.
D) 179 degrees of freedom.

Question 27

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

A) nonmeasurable random variable.
B) constant variable.
C) dependent variable.
D) categorical independent variable.

Question 28

In a multiple regression analysis involving 10 independent variables and 81 observations, SST = 100 and SSE = 40. The multiple coefficient of determination is

A) .241.
B) .11.
C) .40.
D) .60.

Question 29

A multiple regression model has the estimated form ​ = 7 + 3x₁ + 9x₂
​
As x₁ increases by 1 unit (holding x₂ constant), y is expected to

A) increase by 9 units.
B) decrease by 9 units.
C) increase by 3 units.
D) decrease by 3 units.

Question 30

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

A) SSR = SST + SSE.
B) SSR = SST - SSE.
C) SSE = SSR + SST.
D) n(SST) = p(SSR) + (n - p)(SSE).

Question 31

A multiple regression model has the estimated form ​ = 5 + 6x + 7w
​
As x increases by 1 unit (holding x constant), y is expected to

A) increase by 11 units.
B) decrease by 11 units.
C) increase by 7 units.
D) decrease by 7 units.

Question 32

The multiple coefficient of determination is

A) MSR/MST.
B) MSR/MSE.
C) SSR/SST.
D) SSE/SSR.

Question 33

In order to test for the significance of a regression model involving 14 independent variables and 260 observations, the numerator and denominator degrees of freedom (respectively) for the critical value of F are

A) 14 and 260.
B) 260 and 14.
C) 13 and 245.
D) 14 and 245.

Question 34

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) t test
B) F test
C) Either a t test or a chi-square test can be used.
D) chi-square test

Question 35

A regression analysis involved 8 independent variables and 100 observations. The critical value of t for testing the significance of each of the independent variable's coefficients will have

A) 9 degrees of freedom.
B) 97 degrees of freedom.
C) 91 degrees of freedom.
D) 7 degrees of freedom.

Question 36

In a multiple regression analysis involving 10 independent variables and 165 observations, SSR = 878 and SSE = 122. The multiple coefficient of determination is

A) .1389.
B) .122.
C) .878.
D) .7317.

Question 37

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

A) .300.
B) .192.
C) .500.
D) .700.

Question 38

In logistic regression,

A) there can only be two independent variables.
B) there are two dependent variables.
C) the dependent variable only assumes two discrete values.
D) the dependent variable only assumes two continuous values.

Question 39

The ratio of MSR to MSE yields

A) SST.
B) the F statistic.
C) SSR.
D) the chi-square statistic.

Question 40

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

A) 5.
B) 1200.
C) 800.
D) Not enough information is provided to answer this question.

Question 41

In a multiple regression model involving 50 observations, the following estimated regression equation was obtained: ​ = 20 + 5x₁ - 4x₂ + 8x₃ + 8x₄
​
For this model, SSR = 700 and SSE = 100. The computed F statistic for testing the significance of the above model is

A) 78.75.
B) 82.25.
C) 50.19.
D) 7.00.

Question 42

In a multiple regression model involving 44 observations, the following estimated regression equation was obtained. ​ = 50+ 13x₁ + 40x₂ + 68x₃
​
For this model, SSR = 600 and SSE = 300. MSR for this model is

A) 200.
B) 10.
C) 1000.
D) 43.

Question 43

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) -2.9.
B) 2.9.
C) 3.6.
D) -5.0.

Question 44

In a multiple regression model involving 50 observations, the following estimated regression equation was obtained: ​ = 20 + 5x₁ - 4x₂ + 8x₃ + 8x₄
​
For this model, SSR = 700 and SSE = 100. At the 5% level,

A) there is no evidence that the model is significant.
B) it can be concluded 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.

Question 45

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 rejected.
B) not be rejected.
C) be revised to test using F statistic.
D) be tested for β_₃ instead.

Question 46

A regression model between sales (y in $1000), unit price (x₁ in dollars), and television advertisement (x₂ in dollars) resulted in the following function: ​ = 8 - 4x₁ + 5x₂
​
For this model, SSR = 3500, SSE = 1500, and the sample size is 20. To test for the significance of the model, the test statistic F is

A) 19.83.
B) 88.23.
C) 17.
D) 2.33.

Question 47

Below you are given a partial computer output from a multiple regression analysis based on a sample of 16 observations. ​ The degrees of freedom for the sum of squares explained by the regression (SSR) are

A) 2.
B) 3.
C) 13.
D) 15.

Question 48

In a multiple regression analysis involving 5 independent variables and 30 observations, SSR = 380 and SSE = 45. The multiple coefficient of determination is

A) .80.
B) .89.
C) .25.
D) .11.

Question 49

Below you are given a partial computer output from a multiple regression analysis based on a sample of 16 observations. ​ The t value obtained from the table which is used to test an individual parameter at the 1% level is

A) 2.650.
B) 2.921.
C) 2.977.
D) 3.012.

Question 50

In a multiple regression model involving 44 observations, the following estimated regression equation was obtained. ​ = 50 + 13x₁ + 40x₂ + 68x₃
​
For this model, SSR = 600 and SSE = 400. The computed F statistic for testing the significance of the above model is

A) 28.00.
B) 20.00.
C) .600.
D) .667.

Question 51

A regression model between sales (y in $1000), unit price (x₁ in dollars), and television advertisement (x₂ in dollars) resulted in the following function: ​ = 8 - 4x₁ + 5x₂
​
For this model, SSR = 3500, SSE = 1500, and the sample size is 20. To test for the significance of the model, the p-value is

A) less than .01.
B) between .01 and .025.
C) between .025 and .05.
D) greater than .10.

Question 52

A regression analysis involved 10independent 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) 26 degrees of freedom.
C) 21 degrees of freedom.
D) 16 degrees of freedom.

Question 53

In a multiple regression model involving 44 observations, the following estimated regression equation was obtained. ​ = 45+ 19x₁ + 63x₂ + 80x₃
​
For this model, SSR = 800 and SSE = 200. The multiple coefficient of determination for the above model is

A) .667.
B) .800.
C) .336.
D) .200.

Question 54

A regression model between sales (y in $1000), unit price (x₁ in dollars), and television advertisement (x₂ in dollars) resulted in the following function: ​ = 7 - 4x₁ + 5x₂
For this model, SSR = 3500, SSE = 1500, and the sample size is 20. The adjusted multiple coefficient of determination for this problem is

A) .70.
B) .8367.
C) .6647.
D) .3353.

Question 55

In a multiple regression model involving 50 observations, the following estimated regression equation was obtained: ​ = 20 + 5x₁ - 4x₂ + 8x₃ + 8x₄
​
For this model, SSR = 700 and SSE = 100. The multiple coefficient of determination for the above model is

A) .934.
B) .875.
C) .125.
D) .144.

Question 56

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 7.682 unit decrease in y.
B) a one unit increase in x₁ will lead to a 7.682 unit decrease in y when all other variables are held constant.
C) a one unit increase in x₁ will lead to a 7.682 unit decrease in x₂ when all other variables are held constant.
D) The unit of measurement for y is required to interpret the coefficient.

Question 57

A regression model between sales (y in $1000), unit price (x₁ in dollars), and television advertisement (x₂ in dollars) resulted in the following function: ​ = 8 - 4x₁ + 5x₂
​
For this model, SSR = 3500, SSE = 1500, and the sample size is 20. The coefficient of the unit price indicates that if the unit price is

A) increased by $1 (holding advertisement constant), sales are expected to increase by $4.
B) decreased by $1 (holding advertisement constant), sales are expected to decrease by $4.
C) increased by $1 (holding advertisement constant), sales are expected to increase by $4000.
D) increased by $1 (holding advertisement constant), sales are expected to decrease by $4000.

Question 58

In order to test for the significance of a regression model involving 5 independent variables and 36 observations, the numerator and denominator degrees of freedom (respectively) for the critical value of F are

A) 4 and 36.
B) 3 and 35.
C) 5 and 30.
D) 5 and 31.

Question 59

In a multiple regression model involving 50 observations, the following estimated regression equation was obtained: ​ = 20 + 5x₁ - 4x₂ + 8x₃ + 8x₄
​
For this model, SSR = 700 and SSE = 100. The critical F value at α = .05 is (using the conservative value from the table)

A) 2.53.
B) 2.69.
C) 2.61.
D) 2.99.

Question 60

A regression model between sales (y in $1000), unit price (x₁ in dollars), and television advertisement (x₂ in dollars) resulted in the following function: ​ = 8 - 4x₁ + 5x₂
​
For this model, SSR = 3500, SSE = 1500, and the sample size is 20. 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 $5.
B) increase by $20,000.
C) increase by $5000.
D) decrease by $4000.

Question 61

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 1% level equals

A) 3.41.
B) 3.63.
C) 5.74.
D) 3.81.

Question 62

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

A) ​becomes larger or smaller depending on the statistical significance of the variable.
B) ​becomes larger even if the variable added is not statistically significant.
C) ​might or might not become larger even if the variable added is statistically significant.
D) is not affected by the variable added even if it is statistically significant.

Question 63

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). ​ = 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) 3.33.
B) 3.35.
C) 3.34.
D) 2.96.

Question 64

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) 3.06.
B) 3.48.
C) 3.34.
D) 3.11.

Question 65

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) ​16 degrees of freedom.
C) 679 degrees of freedom.
D) ​714 degrees of freedom.

Question 66

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). ​ = 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) $90,000.
D) $51.

Question 67

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). ​
​ = 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) would be significant if the sample size was larger than 30.
D) has significant individual parameters.

Question 68

Even though a residual may be unusually large, the standardized residual rule might fail to identify the observation as being an outlier. This difficulty can be circumvented by using​

A) categorical independent variables.
B) ​residual transformation.
C) ​studentized deleted residuals.
D) ​logistic regression.

Question 69

Below you are given a partial computer output from a multiple regression analysis based on a sample of 16 observations. ​ The test statistic used to determine if there is a relationship among the variables equals

A) 1.40.
B) .2.
C) .77.
D) 5.

Question 70

Below you are given a partial computer output from a multiple regression analysis based on a sample of 16 observations. ​ The sum of squares due to error (SSE) equals

A) 373.31.
B) 485.3.
C) 4853.
D) 6308.9.

Question 71

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

A) ​odds ratio
B) ​residual
C) ​collinearity
D) ​leverage

Question 72

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). ​ = 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) $19,800.
C) $49.80.
D) $49,800.

Question 73

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 1% level. The null hypothesis should

A) be rejected.
B) not be rejected.
C) be revised to test for multicollinearity.
D) test for individual significance instead.

Question 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). ​ = 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) 28.69.
D) 5.22.

Question 75

As the value of the multiple coefficient of determination increases, ​

A) ​the value of the adjusted multiple coefficient of determination decreases.
B) ​the value of the regression equation's constant b₀ decreases.
C) ​the goodness of fit for the estimated multiple regression equation increases.
D) ​the value of the correlation coefficient decreases.

Question 76

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). ​ = 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) $16,800.
B) $13,800.
C) $46,800.
D) $49,800.

Question 77

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). ​ = 30 + .7x₁ + 3x₂​
​
Also provided are SST = 1200 and SSE = 384. The multiple coefficient of determination is

A) .32.
B) .42.
C) .68.
D) .50.

Question 78

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) 3.480.
C) 5.455.
D) 6.875.

Question 79

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). ​ = 30 + .7x₁ + 3x₂
​
Also provided are SST = 1200 and SSE = 384. From the above linear function for multiple regression, it can be said that the expected yearly income of

A) males is $3 more than females.
B) females is $3 more than males.
C) males is $3000 more than females.
D) females is $3000 more than males.

Question 80

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) .3636.
B) .7333.
C) .275.
D) .5.