Question 1

In using the multiple regression method,we can model the effects of the different levels of a qualitative independent variable by using a(n):

Accepted Answer

Dummy (indicator) variables are used to model the effects of qualitative independent variables in multiple regression analysis. They allow for the inclusion of categorical data in the regression model by coding each category as a separate variable. For example, if our independent variable is "Gender" with two categories of "Male" and "Female", we can use a dummy variable by coding "Male" as 0 and "Female" as 1.

Question 2

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

Accepted Answer

Adding an independent variable to a multiple regression model will always decrease the SSE, as it allows the model to better fit the data.

Question 3

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

Accepted Answer

Adding a new variable to a regression model can sometimes decrease the MSE if the new variable improves the model's explanatory power. However, this is not guaranteed, as the new variable might not be significantly related to the dependent variable, or it might introduce multicollinearity, which could potentially worsen the model's performance.

Question 4

Given the regression model y = β₀+ β₁X₁+ β₂X₁²+ ε,if we wish to test the significance of X₁²,the appropriate null hypothesis is:

Accepted Answer

To test the significance of a variable in a regression model, the null hypothesis typically posits that the coefficient of that variable is equal to zero. In this case, the variable in question is represented by the coefficient β₁₂, so the appropriate null hypothesis is that β₁₂ = 0, indicating that the variable has no effect.

Question 5

Given the regression model y = β₀ + β₁X₁ + β₂X₂ + ε,if we are testing the significance of the independent variable X₁ and we reject the null hypothesis H₀: β₁= 0,we conclude that:

Accepted Answer

Rejecting the null hypothesis means that the coefficient of X₁ (β₁) is not zero and is therefore significantly related to the dependent variable y in this model.

Question 6

Below is a partial multiple regression ANOVA table.
$$\begin{array} { l l l } 
\text { Source } & \text { SS } & \text { df } \
\text { Model } & 0.242 & 2 \
\text { Error } & 0.105 & 3
\end{array}$$
-What is the value of F?

Accepted Answer

The answer of Below is a partial multiple regression ANOVA...

Question 7

Below is a partial multiple regression ANOVA table. $$\begin{array} { l l l } \text { Source } & \text { SS } & \text { df } \ \text { Model } & 0.242 & 2 \ \text { Error } & 0.105 & 3 \end{array}$$ -What is the value of R²?

Accepted Answer

The value of $R^2$ is calculated as the ratio of the model sum of squares (SS) to the total sum of squares (Model SS + Error SS). Here, $R^2 = \frac{0.242}{0.242 + 0.105} = \frac{0.242}{0.347} \approx 0.697$.

Question 8

Below is a partial multiple regression ANOVA table.
$$\begin{array} { l l l } 
\text { Source } & \text { SS } & \text { df } \
\text { Model } & 0.242 & 2 \
\text { Error } & 0.105 & 3
\end{array}$$
-What is the mean square error?

Accepted Answer

The mean square error (MSE) is calculated by dividing the sum of squares for error (SS Error) by its degrees of freedom (df Error). Thus, MSE = 0.105 / 3 = 0.035.

Question 9

Below is a partial multiple regression ANOVA table.
$$\begin{array} { l l l } 
\text { Source } & \text { SS } & \text { df } \
\text { Model } & 0.242 & 2 \
\text { Error } & 0.105 & 3
\end{array}$$
-What is the explained variation?

Accepted Answer

The explained variation in a regression model is represented by the sum of squares for the model (SS Model), which in this case is 0.242.

Question 10

Below is a partial multiple regression ANOVA table.
$$\begin{array} { l l l } 
\text { Source } & \text { SS } & \text { df } \
\text { Model } & 0.242 & 2 \
\text { Error } & 0.105 & 3
\end{array}$$
-What is the number of observations in the sample?

Accepted Answer

The total degrees of freedom is the sum of the model and error degrees of freedom, which is 2 + 3 = 5. The total degrees of freedom is equal to the number of observations minus 1, so the number of observations is 5 + 1 = 6.

Question 11

In a multiple regression analysis,the current model has three independent variables.The analyst decides to add another (fourth)independent variable from the same data set while retaining the other three independent variables.As a result of this addition,the value of explained variation will ____________ decrease.

Accepted Answer

Adding an independent variable to a regression model can only increase or maintain the explained variation (R-squared value), as it provides the model with more information to explain the variability in the dependent variable. It cannot decrease because the model can simply assign a coefficient of zero to the new variable if it does not improve the model's explanatory power.

Question 12

In a multiple regression analysis,if the normal plot of the residuals approximately displays the shape of a ____________,then it can be concluded that the assumption of error term normality is not significantly violated.

Accepted Answer

The normal plot of residuals in a multiple regression analysis is expected to approximate the shape of a straight line if the assumption of error term normality is met. This indicates that the residuals are normally distributed.

Question 13

Below is a partial multiple regression ANOVA table.
$$\begin{array} { l l l } 
\text { Source } & \text { SS } & \text { df } \
\text { Model } & 0.242 & 2 \
\text { Error } & 0.105 & 3
\end{array}$$
-What is the total sum of squares (total variation)?

Accepted Answer

The total sum of squares (total variation) is obtained by adding the sum of squares for the model (SS Model) and the sum of squares for the error (SS Error). Thus, 0.242 (Model SS) + 0.105 (Error SS) = 0.347.

Question 14

Given the regression model y = β₀ + β₁ X₁ + β₂ X₂ + β₃ X₁² + β₄X₂² + ε,if we wish to test the significance of higher order terms, (X₁² and X₂²)we would use the following test:

Accepted Answer

To test the significance of higher order terms, we would use the Partial F test. This test provides information regarding the contribution of each independent variable to the model on top of the information provided by the lower order model.

Question 15

A multiple regress model is fit using five independent variables.A sixth independent variable is added from the data set and the model is refit.As a result,the value of explained variation (SSR)will _________,and the value of multiple coefficient of determination (R²)will _________.

Accepted Answer

Adding an independent variable to a multiple regression model will generally increase the explained variation (SSR) because the model can account for more variability in the dependent variable with more predictors. Consequently, the multiple coefficient of determination (R^2) will also increase, as it measures the proportion of the variance in the dependent variable that is predictable from the independent variables.

Question 16

In a multiple regression model,as a result of adding a new independent variable,as s ___________,the length of the prediction interval for y will _________.

Accepted Answer

The answer of In a multiple regression model,as a result...

Question 17

Dropping an independent variable from a multiple linear regression model will always result in:

Accepted Answer

Dropping an independent variable from a multiple linear regression model will result in a decrease in the R² value (also known as the R-squared value), as the model will explain less of the variation in the dependent variable. It is possible that the MSE value (mean squared error) might increase or decrease depending on the specific model and the variable being dropped. The F test statistic value might also increase or decrease depending on the specific model and the variable being dropped. Hence, options A, B, D, and E are not always true.

Question 18

A fitted multiple regression model yields an R² of 0.64.Interpret this value.

Accepted Answer

R² (or R-squared) measures the proportion of variance in the dependent variable that is explained by the independent variables in the model. Therefore, a value of 0.64 indicates that 64% of the variation in the observed values of the dependent variable is accounted for by the regression model. Choices A, C, D, and E are incorrect interpretations of R-squared.

Question 19

In a multiple regression analysis,the current model has three independent variables.The analyst decides to add another (fourth)independent variable from the same data set while retaining the other three independent variables.As a result of this addition,the value of the adjusted R²will ____________ decrease.

Accepted Answer

The adjusted R-squared compensates for the addition of variables and only increases if the new variable improves the model more than would be expected by chance. Adding a variable can sometimes lead to an increase or decrease in adjusted R-squared, depending on whether the new variable significantly contributes to the model's explanatory power.

Question 20

In multiple regression analysis an outlier observation is ____________ influential.

Accepted Answer

An outlier observation may be influential in multiple regression analysis, but it depends on the degree to which it differs from the other observations and its effect on the regression model. Therefore, it is not always influential, but sometimes it can be.

Quiz 12: Multiple Regression and Model Building

In using the multiple regression method,we can model the effects of the different levels of a qualitative independent variable by using a(n) :

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

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

Given the regression model y = β₀+ β₁X₁+ β₂X₁²+ ε,if we wish to test the significance of X₁²,the appropriate null hypothesis is:

Given the regression model y = β₀ + β₁X₁ + β₂X₂ + ε,if we are testing the significance of the independent variable X₁ and we reject the null hypothesis H₀: β₁= 0,we conclude that:

Below is a partial multiple regression ANOVA table. $\begin{array} { l l l } \text { Source } & \text { SS } & \text { df } \\\text { Model } & 0.242 & 2 \\\text { Error } & 0.105 & 3\end{array}$ -What is the value of F?

Below is a partial multiple regression ANOVA table. $\begin{array} { l l l } \text { Source } & \text { SS } & \text { df } \\\text { Model } & 0.242 & 2 \\\text { Error } & 0.105 & 3\end{array}$ -What is the value of R²?

Below is a partial multiple regression ANOVA table. $\begin{array} { l l l } \text { Source } & \text { SS } & \text { df } \\\text { Model } & 0.242 & 2 \\\text { Error } & 0.105 & 3\end{array}$ -What is the mean square error?

Below is a partial multiple regression ANOVA table. $\begin{array} { l l l } \text { Source } & \text { SS } & \text { df } \\\text { Model } & 0.242 & 2 \\\text { Error } & 0.105 & 3\end{array}$ -What is the explained variation?

Below is a partial multiple regression ANOVA table. $\begin{array} { l l l } \text { Source } & \text { SS } & \text { df } \\\text { Model } & 0.242 & 2 \\\text { Error } & 0.105 & 3\end{array}$ -What is the number of observations in the sample?

In a multiple regression analysis,if the normal plot of the residuals approximately displays the shape of a ____________,then it can be concluded that the assumption of error term normality is not significantly violated.

Below is a partial multiple regression ANOVA table. $\begin{array} { l l l } \text { Source } & \text { SS } & \text { df } \\\text { Model } & 0.242 & 2 \\\text { Error } & 0.105 & 3\end{array}$ -What is the total sum of squares (total variation) ?

Given the regression model y = β₀ + β₁ X₁ + β₂ X₂ + β₃ X₁² + β₄X₂² + ε,if we wish to test the significance of higher order terms, (X₁² and X₂²) we would use the following test:

A multiple regress model is fit using five independent variables.A sixth independent variable is added from the data set and the model is refit.As a result,the value of explained variation (SSR) will _,and the value of multiple coefficient of determination (R²) will _.

In a multiple regression model,as a result of adding a new independent variable,as s ___,the length of the prediction interval for y will _.

Dropping an independent variable from a multiple linear regression model will always result in:

A fitted multiple regression model yields an R² of 0.64.Interpret this value.

In multiple regression analysis an outlier observation is ____________ influential.

Quiz 12: Multiple Regression and Model Building

In using the multiple regression method,we can model the effects of the different levels of a qualitative independent variable by using a(n) :

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

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

Given the regression model y = β0+ β1X1+ β2X12+ ε,if we wish to test the significance of X12,the appropriate null hypothesis is:

Given the regression model y = β0 + β1X1 + β2X2 + ε,if we are testing the significance of the independent variable X1 and we reject the null hypothesis H0: β1= 0,we conclude that:

In a multiple regression analysis,if the normal plot of the residuals approximately displays the shape of a ____________,then it can be concluded that the assumption of error term normality is not significantly violated.

Given the regression model y = β0 + β1 X1 + β2 X2 + β3 X12 + β4X22 + ε,if we wish to test the significance of higher order terms, (X12 and X22) we would use the following test:

A multiple regress model is fit using five independent variables.A sixth independent variable is added from the data set and the model is refit.As a result,the value of explained variation (SSR) will _________,and the value of multiple coefficient of determination (R2) will _________.

In a multiple regression model,as a result of adding a new independent variable,as s ___________,the length of the prediction interval for y will _________.

Dropping an independent variable from a multiple linear regression model will always result in:

A fitted multiple regression model yields an R2 of 0.64.Interpret this value.

In multiple regression analysis an outlier observation is ____________ influential.

Given the regression model y = β₀+ β₁X₁+ β₂X₁²+ ε,if we wish to test the significance of X₁²,the appropriate null hypothesis is:

Given the regression model y = β₀ + β₁X₁ + β₂X₂ + ε,if we are testing the significance of the independent variable X₁ and we reject the null hypothesis H₀: β₁= 0,we conclude that:

Given the regression model y = β₀ + β₁ X₁ + β₂ X₂ + β₃ X₁² + β₄X₂² + ε,if we wish to test the significance of higher order terms, (X₁² and X₂²) we would use the following test:

A multiple regress model is fit using five independent variables.A sixth independent variable is added from the data set and the model is refit.As a result,the value of explained variation (SSR) will _,and the value of multiple coefficient of determination (R²) will _.

In a multiple regression model,as a result of adding a new independent variable,as s ___,the length of the prediction interval for y will _.

A fitted multiple regression model yields an R² of 0.64.Interpret this value.