Deck 16: Regression Analysis: Model Building

Question 1

The joint effect of two variables acting together is called _____.

A) autocorrelation
B) interaction
C) serial correlation
D) joint regression

Answer 1

interaction

Question 2

In multiple regression analysis, the word "linear" in the term "general linear model" refers to the fact that_____.

A) β₀, β₁, . . . β_p, all have exponents of 0
B) β₀, β₁, . . . β_p, all have exponents of 1
C) β₀, β₁, . . . β_p, all have exponents of at least 1
D) β₀, β₁, . . . β_p, all have exponents of less than 1

Answer 2

β₀, β₁, . . . β_p, all have exponents of 1

Question 3

The following regression model y = β₀ + β₁x₁ + β₂x² + ε is known as _____.

A) first-order model with one predictor variable
B) second-order model with two predictor variables
C) second-order model with one predictor variable
D) None of the answers is correct.

Answer 3

second-order model with one predictor variable

Question 4

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 5

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) None of the answers is correct.

Question 6

Serial correlation is_____.

A) the correlation between serial numbers of products
B) the same as autocorrelation
C) the same as leverage
D) None of the answers is correct.

Question 7

All the 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 be positive
D) None of the answers is correct.

Question 8

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

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

Question 9

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

A) expected value of the error term ε is zero
B) variance of the error term ε is the same for all values of x
C) values of the error term ε are independent
D) values of the error term ε are normally distributed for all values of x

Question 10

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

A) positive autocorrelation
B) negative autocorrelation
C) either positive or negative autocorrelation
D) no autocorrelation

Question 11

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

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

Question 12

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) parallel correlation

Question 13

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) called transformation effect

Question 14

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 15

Excel's Regression tool can be used to perform the ____ procedure.

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

Question 16

The parameters of nonlinear models have exponents _____.

A) larger than 0
B) other than 1
C) only equal to 2
D) larger than 3

Question 17

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

A) a t test
B) the Durbin-Watson test
C) an F test
D) a chi-square test

Question 18

The forward selection procedure starts with how many independent variable(s) in the multiple regression model?

A) 0
B) 1
C) 2
D) All of the answers are correct.

Question 19

The range of the Durbin-Watson statistic is _____.

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

Question 20

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

Question 21

Thirty-four observations of a dependent variable (y) 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. At a 5% level of significance, determine if the third independent variable contributes significantly to the model.

Question 22

A researcher is trying to decide whether or not to add another variable to his model. He has estimated the following model from a sample of 28 observations:
​ = 23.62 + 18.86x₁ + 24.72x₂
​
SSE = 1,425 SSR = 1,326
​
He has also estimated the model with an additional variable x₃. The results are
​ = 25.32 + 15.29x₁ + 7.63x₂ + 12.72x₃
​
SSE = 1,300 SSR = 1,451
​
What advice would you give this researcher? Use a .05 level of significance.

Question 23

A sample of six recent college graduates shows their current annual income (in $1000s), years of education, and current age (in years). The data follow: Use Excel's Regression tool to estimate a general linear model of the form that predicts annual income. ​

Question 24

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 price (x₂) resulted in an SSE of 396. At α = .05, determine if the competitor's product price contributed significantly to the model. The sample size for both models was 33.

Question 25

Consider the following data: ​
Use Excel's Regression tool to estimate a general linear model of the form

Question 26

A regression analysis (involving 45 observations) relating a dependent variable (y) and two independent variables resulted in the following information.
​ = 0.408 + 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 + 3.0x₁ + 12x₂ + 4.0x₃ + 8x₄
​
This latter model's SSE is 40.
At a 5% significance level, test to determine if the two added independent variables contribute significantly to the model.

Question 27

Consider the following data: Use Excel's Regression tool to estimate a general linear model that uses a reciprocal transformation on the dependent variable.
​

Question 28

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 and x2, 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 29

In a regression analysis involving 18 observations and four independent variables, the following information was obtained: Based on the above information, fill in all the blanks in the following ANOVA table.

Question 30

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 = 0.05, determine if x₂ contributes significantly to the model. The sample size for both models was 30.

Question 31

Consider the following data. Use Excel's Regression tool to estimate a second-order model of the form

Question 32

Monthly total production costs and the number of units produced at a local company over a period of 10 months are shown below. Use Excel's Regression tool to estimate a second-order model of the form ​

Question 33

Consider the following data: Use Excel's Regression tool to estimate a general linear model of the form ​

Question 34

In a regression analysis involving 20 observations and five independent variables, the following information was obtained: Fill in all the blanks in the above ANOVA table.

Question 35

Consider the following data. Use Excel's Regression tool to estimate a general linear model that uses a reciprocal transformation on the dependent variable.
​

Question 36

Forty-eight observations of a dependent variable (y) 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 if the two additional independent variables contribute significantly to the model.