Question 1

The general form of the quadratic multiple regression models is A) y = β₁x₁ + β₂x₂ + ε B) y = β₀ + β₁x₁ + β₂x₂ + ε C) y = β₀ + β₁x + β₂x² + ε D) y = β₀ + β₁x² + ε E) y = β₀ + β₁x₁ +β₂x₂²+ ε

Accepted Answer

y = β₀+ β₁x + β₂x²+ ε is the general form of a quadratic multiple regression model.

Question 2

In using a regression model, if a new independent variable is added, the value of R² (the coefficient of multiple determination) will ________ decrease. A) always B) sometimes C) never

Accepted Answer

Adding independent variables will always increase R².

Question 3

As we increase the number of independent variables in a multiple regression model, the F-statistic will ________ increase.
A) always
B) sometimes
C) never

Accepted Answer

The F-statistic can change with an increase in the number of independent variables, but it does not necessarily increase nor decrease.

Question 4

In the quadratic regression model y = β₀ + β₁X₁ + β₂X₁² + ε, if the term β₂ is ________ zero, then the parabola opens ________. A) less than, upward B) greater than, upward C) greater than, either upward or downward D) less than, either upward or downward E) equal to, downward

Accepted Answer

If the leading coefficient is positive, the parabola opens upward.

Question 5

In a multiple regression analysis, the current model has three independent variables. The analyst decides to add another (fourth) independent variable while retaining the other three independent variables. As a result of this addition, the value of MSE will ________ decrease.
A) always
B) sometimes
C) never

Accepted Answer

Adding independent variables does not predict whether MSE increases or decreases.

Question 6

In the quadratic regression model y = β₀ + β₁X₁ + β₂X₁² + ε, the β₂ term represents the A) rate of curvature of the parabola. B) value of Y when X is zero. C) shift parameter of the parabola. D) y-intercept of the parabola.

Accepted Answer

The coefficient of the squared-term indicates the rate at which the parabola will curve.

Question 7

Assumptions of a regression model can be evaluated by plotting and analyzing the ________.
A) independent variables
B) dependent variables
C) error terms
D) beta values

Accepted Answer

Plot and analyze the error terms to evaluate assumptions of a regression model.

Question 8

The graph of the prediction equation obtained from the model y = β₀ + β₁X₁ + β₂X₁² + ε is a(n) ________. A) line B) plane C) parabola D) exponential curve

Accepted Answer

The graph of any quadratic equation is in the shape of a parabola.

Question 9

If a regression model with k independent variables has a C statistic less than ________, then the model is considered to be desirable.
A) k + 1
B) k
C) k − 1
D) 1/k
E) k − 2

Accepted Answer

If a regression model with k independent variables has a C statistic less than k + 1, then the model is considered to be desirable.

Question 10

The primary use of stepwise regression is to identify the most important ________ that should be included in the multiple regression model.
A) independent variables
B) dependent variables
C) dummy variables
D) quadratic variables

Accepted Answer

Stepwise regression will identify the most important independent variables to be included in the multiple regression model.

Question 11

In a multiple regression model, the residuals were plotted against the values of one of the independent variables. The plot exhibited a funneling out pattern of residuals. This means that as the value of the independent variable increases, the error terms tend to ________ and the model assumption of ________ is violated.
A) increase, constant variance
B) increase, independence
C) decrease, constant variance
D) decrease, normality

Accepted Answer

In a funneling out pattern, the error terms increase, thus violating the assumption of constant variance.

Question 12

Dummy variables take on the values of ________ and are used to model the effects of different levels of qualitative variables.
A) 1 or −1
B) 1 or 2
C) 0 or 2
D) 0 or 1

Accepted Answer

Dummy variables can only take on values of 0 and 1.

Question 13

Given the regression model y = β₀ + β₁x₁ + β₂x₂ + β₃x₁² + β₄x₂² + ε, if we wish to test the significance of higher-order terms (x₁² and x₂²), which test would we use? A) overall F test B) Durbin-Watson test C) partial F test D) t test E) Cook's distance measure

Accepted Answer

A partial F test is used to test the significance of the higher-order terms.

Question 14

A very insignificant independent variable (an independent variable that has a very weak relationship with the dependent variable) is added to a multiple regression equation. As a result of this change, the value of the explained variation (SSR) will ________, the value of the multiple coefficient of determination (R²) will ________, and the calculated value of the F statistic will most likely ________. A) decrease, increase, decrease B) increase, decrease, decrease C) increase, increase, increase D) increase, increase, decrease E) decrease, decrease, decrease

Accepted Answer

Adding an insignificant independent variable increases SSR and R², but will make the F statistic most likely decrease.

Question 15

If the simple correlation coefficient between two independent variables is greater than .90, then ________ is considered to be severe.
A) autocorrelation
B) interaction
C) multicollinearity
D) coefficient of determination

Accepted Answer

A correlation coefficient of .90, which is close to 1, indicates severe multicollinearity.

Question 16

In a multiple regression model, we can conclude that multicollinearity exists if the average variance inflation factor (VIF) is substantially greater than ________.
A) 100
B) 5
C) 10
D) 1

Accepted Answer

If VIF is much greater than 1, multicollinearity exists.

Question 17

In the quadratic regression model y = β₀ + β₁X₁ + β₂X₁² + ε, the β₁ term represents the A) rate of curvature of the parabola. B) value of Y when X is zero. C) shift parameter of the parabola. D) y-intercept of the parabola.

Accepted Answer

The coefficient of the linear term indicates how the parabola will shift.

Question 18

Adding any independent variable to a regression model will increase ________. A) adjusted R² or R⁻² B) s C) MSE D) R² E) the length of all prediction intervals

Accepted Answer

The coefficient of determination always increases with the addition of independent variables.

Question 19

Multicollinearity is severe if the largest variance inflation factor (VIF) is greater than ________.
A) 100
B) 5
C) 10
D) 1

Accepted Answer

10 is the standard for severe multicollinearity.

Question 20

Plotting the residuals in a time-ordered sequence will reveal possible violations of the ________ of error terms assumption.
A) normality
B) independence
C) constant variation
D) residual sum

Accepted Answer

Plotting the residuals in a time-ordered sequence will reveal possible violations of the independence of error terms assumption.

Quiz 15: Multiple Regression and Model Building

The general form of the quadratic multiple regression models is

In using a regression model, if a new independent variable is added, the value of R² (the coefficient of multiple determination) will ________ decrease.

As we increase the number of independent variables in a multiple regression model, the F-statistic will ________ increase.

In the quadratic regression model y = β₀ + β₁X₁ + β₂X₁² + ε, if the term β₂ is zero, then the parabola opens .

In a multiple regression analysis, the current model has three independent variables. The analyst decides to add another (fourth) independent variable while retaining the other three independent variables. As a result of this addition, the value of MSE will ________ decrease.

In the quadratic regression model y = β₀ + β₁X₁ + β₂X₁² + ε, the β₂ term represents the

Assumptions of a regression model can be evaluated by plotting and analyzing the ________.

The graph of the prediction equation obtained from the model y = β₀ + β₁X₁ + β₂X₁² + ε is a(n) ________.

If a regression model with k independent variables has a C statistic less than ________, then the model is considered to be desirable.

The primary use of stepwise regression is to identify the most important ________ that should be included in the multiple regression model.

Dummy variables take on the values of ________ and are used to model the effects of different levels of qualitative variables.

Given the regression model y = β₀ + β₁x₁ + β₂x₂ + β₃x₁² + β₄x₂² + ε, if we wish to test the significance of higher-order terms (x₁² and x₂²) , which test would we use?

If the simple correlation coefficient between two independent variables is greater than .90, then ________ is considered to be severe.

In a multiple regression model, we can conclude that multicollinearity exists if the average variance inflation factor (VIF) is substantially greater than ________.

In the quadratic regression model y = β₀ + β₁X₁ + β₂X₁² + ε, the β₁ term represents the

Adding any independent variable to a regression model will increase ________.

Multicollinearity is severe if the largest variance inflation factor (VIF) is greater than ________.

Plotting the residuals in a time-ordered sequence will reveal possible violations of the ________ of error terms assumption.