Question 1

The interaction between two variables x1 and x2 can be modeled by including the predictor variable β1β2 into the multiple regression model.

Accepted Answer

A) True 
 B)False

Question 2

Multicollinearity is a model selection procedure that can be used to compare different models.

Accepted Answer

A) True 
 B)False

Question 3

The Carolina Reaper pepper is considered one of the hottest peppers in the world. However, manufacturers of sauces made from Carolina Reaper often overstate the pungency given on the package to separate their product and ensure sales. An independent laboratory provided a multiple regression model for determining the pungency of the sauce based on a sample of n = 20 sauces. ​ y = Pungency of a sauce (Scoville heat units) ​ x1 = Carolina Reaper content (%) ​ x2 = Sugar content (%) ​ x3 = Vinegar content (%) ​ The estimated regression function was   and R2 = 0.979. Does the result of a model utility test at α = 0.01 indicate that this multiple regression model is useful? Assume that the random deviation distribution is normal. ​

Accepted Answer

A)  P-value  0.01, there is no useful linear relationship between y and any of the predictors. 
C)  P-value  0.01, there is no useful linear relationship between y and at least one of the predictors. 
A)  P-value  0.01, there is no useful linear relationship between y and any of the predictors. 
C)  P-value  0.01, there is no useful linear relationship between y and at least one of the predictors.

Question 4

The predicted values, the residuals and SSResid for a multiple regression model are interpreted as they were for the simple linear regression model.

Accepted Answer

A) True 
 B)False

Question 5

In a multiple regression model, the utility of the model can be tested with a t test.

Accepted Answer

A) True 
 B)False

Question 6

Briefly explain how to interpret the value of β1 in the model y = α + β1x1 + β2x2 + e, when the variables x1 and x2 are independent.

Accepted Answer

Assuming the value of x₂ remain

Question 7

The polynomial regression model used to fit a parabolic pattern in the observed data is y = α + β1x + β2x2 +
e.

Accepted Answer

A) True 
 B)False

Question 8

A normal probability plot of the standardized residuals can be used to investigate whether it is plausible that the distribution of e is approximately normal.

Accepted Answer

A) True 
 B)False

Question 9

Consider a regression analysis with four independent variables x1, x2, x3, and x4. Select the equation for the regression model that includes all independent variables as predictors, two interaction terms, and one quadratic term. ​

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 10

Estimate the P-value for the model utility F test given that k = 4, n = 27, calculated F = 2.81. ​

Accepted Answer

A)  P-value  0.1 
A)  P-value  0.1

Question 11

In the general additive regression model, the mean value of y for fixed x1, x2, ... xk values is α + β1 + β2 + ... + βk.

Accepted Answer

A) True 
 B)False

Question 12

A producer of stainless steel products presented data on y = Workshop expenses (thousands of dollars) as a function of x1 = Amount of raw material (tons), x2 = Number of hours worked (hundreds), and x3 = Quantity of production (thousands of units). Suppose that there is an interaction between the amount of raw material and the quantity of production. What additional predictor variable should be added to the model? ​

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 13

Two variables x1 and x2 are said to interact when the change in the mean value of y associated with a one unit increase in one variable depends on the value of the other variable.

Accepted Answer

A) True 
 B)False

Question 14

Briefly explain what it means when two variables are said to interact.

Accepted Answer

There is interaction between t

Question 15

The largest R2 for any two-predictor model is always less than or equal to the largest R2 for any three-predictor model.

Accepted Answer

A) True 
 B)False

Question 16

The value of adjusted R2 is always smaller than the value of R2.

Accepted Answer

A) True 
 B)False

Question 17

The cost of renting premises consists of a plurality of parameters. A real estate company attempts to identify the most significant factors and proposes a multiple regression model based on a sample of n = 18 observations. ​ y = Monthly rent ($) ​ x1 = Surface area (m2) ​ x2 = Historic building (1 = yes, 0 = no) ​ x3 = Prestige of a district (1 to 5 scale) ​ x4 = Parking facilities (1 = yes, 0 = no) ​ x5 = Availability of infrastructure (1 to 5 scale) Suppose that SSRegr = 846,325 and SSTo = 3,900,000. Calculate the values of R2 and adjusted R2. Explain the difference between them. ​

Accepted Answer

A)  Adjusted R2 is significantly smaller than R2, because R2 itself is rather small. 
B)  Adjusted R2 is significantly smaller than R2, because the number of predictors is large as compared to the number of observations. 
C)  Adjusted R2 is significantly larger than R2, because R2 itself is rather small. 
D)  Adjusted R2 is significantly greater than R2, because the number of predictors is large as compared to the number of observations. 
E)  The difference between adjusted R2 and R2 is not significant, because R2 is substantial and there are only a few predictors. 
A)  Adjusted R2 is significantly smaller than R2, because R2 itself is rather small. 
B)  Adjusted R2 is significantly smaller than R2, because the number of predictors is large as compared to the number of observations. 
C)  Adjusted R2 is significantly larger than R2, because R2 itself is rather small. 
D)  Adjusted R2 is significantly greater than R2, because the number of predictors is large as compared to the number of observations. 
E)  The difference between adjusted R2 and R2 is not significant, because R2 is substantial and there are only a few predictors.

Question 18

A variable taking on only the values 0 and 1 is called a dummy or indicator variable.

Accepted Answer

A) True 
 B)False

The interaction between two variables x₁ and x₂ can be modeled by including the predictor variable β₁β₂ into the multiple regression model.

Multicollinearity is a model selection procedure that can be used to compare different models.

The predicted values, the residuals and SSResid for a multiple regression model are interpreted as they were for the simple linear regression model.

In a multiple regression model, the utility of the model can be tested with a t test.

Briefly explain how to interpret the value of β₁ in the model y = α + β₁x₁ + β₂x₂ + e, when the variables x₁ and x₂ are independent.

The polynomial regression model used to fit a parabolic pattern in the observed data is y = α + β₁x + β₂x² + e.

A normal probability plot of the standardized residuals can be used to investigate whether it is plausible that the distribution of e is approximately normal.

Consider a regression analysis with four independent variables x₁, x₂, x₃, and x₄. Select the equation for the regression model that includes all independent variables as predictors, two interaction terms, and one quadratic term.

Estimate the P-value for the model utility F test given that k = 4, n = 27, calculated F = 2.81.

In the general additive regression model, the mean value of y for fixed x₁, x₂, ... xk values is α + β₁ + β₂ + ... + βk.

Two variables x₁ and x₂ are said to interact when the change in the mean value of y associated with a one unit increase in one variable depends on the value of the other variable.

Briefly explain what it means when two variables are said to interact.

The largest R² for any two-predictor model is always less than or equal to the largest R² for any three-predictor model.

The value of adjusted R² is always smaller than the value of R².

A variable taking on only the values 0 and 1 is called a dummy or indicator variable.

The Role of Statistics and the Data Analysis Process

Collecting Data Sensibly

Graphical Methods for Describing Data

Numerical Methods for Describing Data

Summarizing Bivariate Data

Probability

Random Variables and Probability Distributions

Sampling Variability and Sampling Distributions

Estimation Using a Single Sample

Hypothesis Testing Using a Single Sample

Comparing Two Populations or Treatments

The Analysis of Categorical Data and Goodness-Of-Fit Tests

Simple Linear Regression and Correlation: Inferential Methods

Analysis of Variance

Nonparametric Distribution-Free Statistical Methods

Filters

Exam 14: Multiple Regression Analysis

The interaction between two variables x1 and x2 can be modeled by including the predictor variable β1β2 into the multiple regression model.

Multicollinearity is a model selection procedure that can be used to compare different models.

The predicted values, the residuals and SSResid for a multiple regression model are interpreted as they were for the simple linear regression model.

In a multiple regression model, the utility of the model can be tested with a t test.

Briefly explain how to interpret the value of β1 in the model y = α + β1x1 + β2x2 + e, when the variables x1 and x2 are independent.

The polynomial regression model used to fit a parabolic pattern in the observed data is y = α + β1x + β2x2 + e.

A normal probability plot of the standardized residuals can be used to investigate whether it is plausible that the distribution of e is approximately normal.

Consider a regression analysis with four independent variables x1, x2, x3, and x4. Select the equation for the regression model that includes all independent variables as predictors, two interaction terms, and one quadratic term. ​

Estimate the P-value for the model utility F test given that k = 4, n = 27, calculated F = 2.81. ​

In the general additive regression model, the mean value of y for fixed x1, x2, ... xk values is α + β1 + β2 + ... + βk.

Two variables x1 and x2 are said to interact when the change in the mean value of y associated with a one unit increase in one variable depends on the value of the other variable.

Briefly explain what it means when two variables are said to interact.

The largest R2 for any two-predictor model is always less than or equal to the largest R2 for any three-predictor model.

The value of adjusted R2 is always smaller than the value of R2.

A variable taking on only the values 0 and 1 is called a dummy or indicator variable.

The Role of Statistics and the Data Analysis Process

Collecting Data Sensibly

Graphical Methods for Describing Data

Numerical Methods for Describing Data

Summarizing Bivariate Data

Probability

Random Variables and Probability Distributions

Sampling Variability and Sampling Distributions

Estimation Using a Single Sample

Hypothesis Testing Using a Single Sample

Comparing Two Populations or Treatments

The Analysis of Categorical Data and Goodness-Of-Fit Tests

Simple Linear Regression and Correlation: Inferential Methods

Analysis of Variance

Nonparametric Distribution-Free Statistical Methods

Filters

The interaction between two variables x₁ and x₂ can be modeled by including the predictor variable β₁β₂ into the multiple regression model.

Briefly explain how to interpret the value of β₁ in the model y = α + β₁x₁ + β₂x₂ + e, when the variables x₁ and x₂ are independent.

The polynomial regression model used to fit a parabolic pattern in the observed data is y = α + β₁x + β₂x² + e.

Consider a regression analysis with four independent variables x₁, x₂, x₃, and x₄. Select the equation for the regression model that includes all independent variables as predictors, two interaction terms, and one quadratic term.

Estimate the P-value for the model utility F test given that k = 4, n = 27, calculated F = 2.81.

In the general additive regression model, the mean value of y for fixed x₁, x₂, ... xk values is α + β₁ + β₂ + ... + βk.

Two variables x₁ and x₂ are said to interact when the change in the mean value of y associated with a one unit increase in one variable depends on the value of the other variable.

The largest R² for any two-predictor model is always less than or equal to the largest R² for any three-predictor model.

The value of adjusted R² is always smaller than the value of R².