Deck 16: Regression Analysis: Model Building

Question 1

A model in the form of y = β₀ + β₁z₁ + β₂z₂ + . . . + β_pz_p + ε, where each independent variable z_j (for j = 1, 2, . . ., p) is a function of x₁, x_2,..., x_k, is known as the _____ model.

A) general linear
B) general curvilinear
C) pth-order z
D) experimental

Answer 1

general linear

Question 2

The following model ​
Y = β₀ + β₁x₁ + ε
​
Is referred to as a

A) curvilinear model.
B) curvilinear model with one predictor variable.
C) simple second-order model with one predictor variable.
D) simple first-order model with one predictor variable.

Answer 2

simple first-order model with one predictor variable.

Question 3

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

A) independent models.
B) nonlinear models.
C) autocorrelated models.
D) linear models.

Answer 3

nonlinear models.

Question 4

In multiple regression analysis, the general linear model

A) cannot be used to accommodate curvilinear relationships between dependent variables and independent variables.
B) can be used to accommodate curvilinear relationships between the independent variables and dependent variable.
C) must contain more than two independent variables.
D) cannot use the standard multiple regression procedures for estimation and prediction.

Question 5

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

A) 1/x as the independent variable instead of x.
B) x² as the independent variable instead of x.
C) y² as the dependent variable instead of y.
D) 1/y as the dependent variable instead of y.

Question 6

All the independent variables in a multiple regression analysis

A) must be quantitative.
B) must be either quantitative or qualitative but not a mix of both.
C) must assume only positive values.
D) can be either quantitative or qualitative or both.

Question 7

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

A) serial-autocorrelation
B) t
C) chi-square
D) Durbin-Watson

Question 8

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) impossible to occur.
B) called interaction.
C) called multicollinearity effect.
D) one of the transformation effects.

Question 9

The following regression model ​
Y = β₀ + β₁x₁ + β₂

+ ε
​is known as a

A) simple first-order model with one predictor variable.
B) second-order model with two predictor variables.
C) second-order model with one predictor variable.
D) simple first-order model with two predictor variables.

Question 10

In a regression analysis of a first-order model involving 3 predictor variables and 25 observations, the following estimated regression equation was developed. = 12 - 18x₁ + 4x₂ + 15x₃ Also, the following standard errors and the sum of squares were obtained.
S_b1 = 3
S_b2 = 6
S_b3 = 7
SST = 4900
SSE = 1296
​
If you want to determine whether or not the coefficients of the independent variables are significant, the critical t value at α = .01 is

A) 2.080.
B) 2.831.
C) 2.518.
D) 2.807.

Question 11

In a regression analysis of a first-order model involving 3 predictor variables and 25 observations, the following estimated regression equation was developed. ​ = 12 - 18x₁ + 4x₂ + 15x₃
​
Also, the following standard errors and the sum of squares were obtained.
S_b1 = 3
S_b2 = 6
S_b3 = 7
SST = 4900
SSE = 1296
At the .01 level of significance, the coefficient of x₃

A) is significant.
B) is not found to be significant.
C) cannot be tested, because not enough information is provided.
D) should be estimated again, because it is incorrect in the above equation.

Question 12

What value of Durbin-Watson statistic indicates no autocorrelation is present?

A) 1
B) 2
C) 4
D) 0

Question 13

The joint effect of two independent variables acting together is called

A) autocorrelation.
B) interaction.
C) transformation.
D) joint regression.

Question 14

In a regression analysis of a first-order model involving 3 predictor variables and 25 observations, the following estimated regression equation was developed. = 12 - 18x₁ + 4x₂ + 15x₃ Also, the following standard errors and the sum of squares were obtained.
S_b1 = 3
S_b2 = 6
S_b3 = 7
SST = 4900
SSE = 1296
​
At the 5% level, the coefficient of x₁

A) is significant.
B) is not found to be significant.
C) cannot be tested, because not enough information is provided.
D) should be estimated again, because it is incorrect in the above equation.

Question 15

Serial correlation is

A) the correlation between serial numbers of the independent variables.
B) the same as autocorrelation.
C) the same as leverage.
D) used to identify the effects of multicollinearity.

Question 16

In a regression analysis of a first-order model involving 3 predictor variables and 25 observations, the following estimated regression equation was developed. ​ = 12 - 18x₁ + 4x₂ + 15x₃
​
Also, the following standard errors and the sum of squares were obtained.
S_b1 = 3
S_b2 = 6
S_b3= 7
SST = 4900
SSE = 1296
​
At the 1% level, the coefficient of x₂

A) is significant.
B) is not found to be significant.
C) cannot be tested, because not enough information is provided.
D) should be estimated again, because it is incorrect in the above equation.

Question 17

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

A) leverage.
B) multicorrelation.
C) autocorrelation.
D) interaction.

Question 18

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) 0.
B) 1.
C) at least 1.
D) less than 0.

Question 19

The range of the Durbin-Watson statistic is from

A) -1 to 1.
B) 0 to 1.
C) -∞ to +∞.
D) 0 to 4.

Question 20

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

A) a t test
B) a z test
C) an F test
D) a chi-square test

Question 21

A regression model with one independent variable, x₁, resulted in an SSE of 50. When a second independent variable, x₂, was added to the model, the SSE was reduced to 40. At α = .05, determine if x₂ contributes significantly to the model. The sample size for both models was 30.

Question 22

When a regression model was developed relating sales (y) of a company to its product's price (x₁), the SSE was determined to be 495. A second regression model relating sales (y) to product's price (x₁) and competitor's product's price (x₂) resulted in an SSE of 396. At α = .05, determine if the competitor's product's price contributed significantly to the model. The sample size for both models was 33.

Question 23

In a regression analysis of a first-order model involving 3 predictor variables and 25 observations, the following estimated regression equation was developed. ​ = 12 - 18x₁ + 4x₂ + 15x₃
​
Also, the following standard errors and the sum of squares were obtained. The multiple coefficient of determination is

A) .23.
B) .74.
C) .50.
D) .33.

Question 24

Which of the following variable selection procedures would be considered non-heuristic

A) forward selection.
B) backward elimination.
C) best-subsets regression.
D) stepwise regression.

Question 25

Thirty-four observations of a dependent variable and two independent variables resulted in an SSE of 300. When a third independent variable was added to the model, the SSE was reduced to 250. Using α = .05, determine whether or not the third independent variable contributes significantly to the model.

Question 26

In a regression analysis of a first-order model involving 3 predictor variables and 25 observations, the following estimated regression equation was developed. ​ = 12 - 18x₁ + 4x₂ + 15x₃
​
Also, the following standard errors and the sum of squares were obtained.
S_b1 = 3
S_b2 = 6
S_b3 = 7
SST = 4900
SSE = 1296
​
The test statistic for testing the significance of the model is

A) .73.
B) 18.93.
C) 19.47.
D) 1.37.

Question 27

In a regression analysis of a first-order model involving 3 predictor variables and 25 observations, the following estimated regression equation was developed. = 12 - 18x₁ + 4x₂ + 15x₃ Also, the following standard errors and the sum of squares were obtained. 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) 2.76.
B) 4.87.
C) 3.10.
D) 3.07.

Question 28

A researcher is trying to decide whether or not to add another variable to his regression model. He has estimated the following equation for the model from a sample of 28 observations. = 23.62 + 18.86x₁ + 24.72x₂
SSE = 1425
SSR = 1320
​
He has also estimated the model with an additional variable x₃. The results are: = 25.32 + 15.29x₁ + 7.63x₂ + 12.72x₃
SSE = 1350
SSR = 1465
​
What advice would you give this researcher? Use a .10 level of significance.

Question 29

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

A) ​d > 4 - d_L.
B) ​d < d_L.
C) ​d < d_U.
D) ​d < 4 - d_U.

Question 30

In a regression analysis of a first-order model involving 3 predictor variables and 25 observations, the following estimated regression equation was developed. ​ = 12 - 18x₁ + 4x₂ + 15x₃
​
Also, the following standard errors and the sum of squares were obtained.
​
S_b1 = 3
S_b2 = 6
S_b3 = 7
SST = 4900
SSE = 1296
​
The p-value for testing the significance of the regression model is

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

Question 31

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

A) ​It is a one-variable-at-a-time procedure.
B) ​It begins with the regression model found using the forward selection procedure.
C) ​It does not permit an independent variable to be reentered once it has been removed.
D) ​It does not guarantee that the best regression model will be found.

Question 32

A data set consisting of 7 observations of a dependent variable y and two independent variables x₁ and x₂ was used in a regression analysis. Using x₁ as the only independent variable, the following function is provided. = .408 + 1.338x₁
The SSE for the above model is 39.535.
Using both x₁ and x₂ as independent variables yields the following function. = .805 + .498x₁ - .477x₂
The SSE for this function is 1.015.
Use an F test and determine if x₂ contributes significantly to the model. Let α = .10.

Question 33

An example of a first-order model with three predictor variables is

A) y = $\beta$ ₀ + $\beta$ ₁x₁ + $\beta$ ₂x₂ + $\beta$ ₃x₃ + $\varepsilon$
B) y = $\beta$ ₀ + $\beta$ ₁x₁ + $\beta$ ₂x₂ + $\varepsilon$
C) y = $\beta$ ₀ + $\beta$ ₁x² + $\beta$ ₃x₃+ $\varepsilon$
D) y² = $\beta$ ₀ + $\beta$ ₁x₁ + $\beta$ ₂x₂+ $\beta$ ₃x₃ + $\varepsilon$ .

Question 34

A regression analysis involving 45 observations relating a dependent variable and two independent variables resulted in the following information.
​ = .408 + 1.3387x₁ + 2x₂
​
The SSE for the above model is 49. When two other independent variables were added to the model, the following information was provided.
​ = 1.2 + 3x₁ + 12x₂ + 4x₃ + 8x₄
​
This model's SSE is 40.
​
At a .05 level of significance, test to determine if the two added independent variables contribute significantly to the model.

Question 35

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

A) 1
B) 2
C) 3
D) 4

Question 36

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

A) ?the expected value of the error term $\Sigma$ is zero.
B) ?the variance of the error term $\Sigma$ is the same for all values of x.
C) ?the values of the error term $\Sigma$ are independent.
D) ?the values of the error term $\Sigma$ are normally distributed for all values of x.

Question 37

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

A) H₀: ρ > 0.
B) H₀: ρ < 0.
C) H₀: ρ ≠ 0.
D) H₀: ρ = 0.

Question 38

A regression model relating a dependent variable, y, with one independent variable, x₁, resulted in an SSE of 400. Another regression model with the same dependent variable, y, and two independent variables, x₁ (used in the first model) and x₂ (added in the second model), resulted in an SSE of 320. At α = .05, determine if x₂ contributed significantly to the model. The sample size for both models was 20.

Question 39

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

A) ​stepwise regression.
B) ​forward selection.
C) ​backward elimination.
D) ​best-subsets regression.

Question 40

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

A) ​no
B) ​one
C) ​two
D) ​all

Question 41

Forty-eight observations of a dependent variable and five independent variables resulted in an SSE of 438. When two additional independent variables were added to the model, the SSE was reduced to 375. At a 5% level of significance, determine whether or not the two added independent variables contribute significantly to the model.