Question 1

The forward selection method and the backward elimination method will always lead to choosing the same final regression model.

Accepted Answer

Forward selection and backward elimination are different approaches to feature selection and can lead to different final models because they start from different points (an empty model for forward selection and a full model for backward elimination) and follow different paths to arrive at a final model.

Question 2

The best subsets method will involve trying fewer different regression models than stepwise regression.

Accepted Answer

The best subsets method involves trying all possible combinations of predictors, which can be a much larger number of models compared to stepwise regression, which adds or removes predictors one at a time based on certain criteria.

Question 3

The following residual plot was constructed based on a simple linear regression model.  Based on this plot, there appears to be no basis for concluding that a curvilinear model may be more appropriate than a linear model to explain the variation in the y variable.

Accepted Answer

The answer of The following residual plot was constructed based...

Question 4

The editors of a national automotive magazine recently studied 30 different automobiles sold in the United States with the intent of seeing whether they could develop a multiple regression model to explain the variation in highway miles per gallon. A number of different independent variables were collected. The following regression output (with some values missing) was recently presented to the editors by the magazine's analysts:  Based on this output and your understanding of multiple regression analysis, what percentage of variation in the dependent variable is explained by the regression model?

Accepted Answer

The answer of The editors of a national automotive magazine...

Question 5

In the best subsets approach to regression analysis, if we start with 4 independent variables, a total of 33 different regression models will actually be computed for possible selection as the best model to use.

Accepted Answer

In the best subsets approach, for $n$ independent variables, $2^n$ different regression models are computed. For 4 independent variables, $2^4 = 16$ different models are computed, not 33.

Question 6

Which of the following is not an assumption of the multiple regression model?

Accepted Answer

The correct statement that is not an assumption of the multiple regression model is A) The mean of the residuals is equal to the variance at all combinations of levels of the independent variables. This is incorrect because the assumption related to residuals in multiple regression is that they have a constant variance (homoscedasticity), not that their mean is equal to their variance.

Question 7

If a stepwise regression approach is used to enter, one at a time, four variables into a regression model, the resulting regression equation may differ from the regression equation that occurs when all four of the variables are entered at one step.

Accepted Answer

The answer of If a stepwise regression approach is used...

Question 8

To check out whether the regression assumption involving normality of the error terms is valid, it is appropriate to construct a normal probability plot. If this plot forms a straight line from the lower left- hand corner diagonally up to the upper right-hand corner, the error terms may be assumed to be normally distributed.

Accepted Answer

A normal probability plot, also known as a Q-Q (quantile-quantile) plot, is used to determine if a set of data approximates a normal distribution. If the points in the plot lie approximately along a straight line, it suggests that the data are normally distributed. In the context of regression analysis, checking the normality of the error terms (residuals) is important for fulfilling one of the key assumptions of linear regression.

Question 9

The editors of a national automotive magazine recently studied 30 different automobiles sold in the United States with the intent of seeing whether they could develop a multiple regression model to explain the variation in highway miles per gallon. A number of different independent variables were collected. The following regression output (with some values missing) was recently presented to the editors by the magazine's analysts:  Based on this output and your understanding of multiple regression analysis, what is the value of the standard error of the estimate for this model?

Accepted Answer

The answer of The editors of a national automotive magazine...

Question 10

If one or more of the regression assumptions has been violated this means that the current regression model is not the best one for this data set, and another model should be sought.

Accepted Answer

Violating regression assumptions can lead to biased or inefficient estimates, making the current model inappropriate for the data. Exploring alternative models or transformations that meet these assumptions is advisable for accurate analysis.

Question 11

The editors of a national automotive magazine recently studied 30 different automobiles sold in the United States with the intent of seeing whether they could develop a multiple regression model to explain the variation in highway mileage per gallon. A number of different independent variables were collected. The following correlation matrix was developed:  If only one variable were to be brought into the model, which variable should it be if the goal is to explain the highest possible percentage of variation in the dependent variable?

Accepted Answer

The answer of The editors of a national automotive magazine...

Question 12

A useful method for determining whether a linear function is the appropriate function to describe the relationship between the x and y variable is a residual plot in which the residuals are plotted on the vertical axis and the independent variable is on the horizontal axis.

Accepted Answer

A residual plot is a graph that shows the residuals on the vertical axis and the independent variable on the horizontal axis. If the points in a residual plot are randomly dispersed around the horizontal axis, a linear model is appropriate for the data.

Question 13

When we say that we wish to determine the aptness of a regression model, we are actually saying that we wish to check to see whether the resulting model meets the basic assumptions of regression analysis.

Accepted Answer

Determining the aptness of a regression model involves checking if the model meets the basic assumptions of regression analysis, such as linearity, independence of errors, homoscedasticity, and normal distribution of residuals.

Question 14

Standard stepwise regression is a good way of identifying potential multicollinearity problems since we are able to see the impact on the model at each step that occurs when a new variable is added to the model. For instance, if bringing in a new variable causes the sign to change on a previously entered variable, we have evidence of multicollinearity.

Accepted Answer

Standard stepwise regression allows us to observe the changes in the model as each new variable is added, including any changes in the signs of previously entered variables, which can indicate multicollinearity.

Question 15

The following residual plot is an output of a regression model.  Based on this residual plot, there is evidence to suggest that the underlying relationship between the y variable and the x variable is nonlinear.

Accepted Answer

The answer of The following residual plot is an output...

Question 16

The editors of a national automotive magazine recently studied 30 different automobiles sold in the United States with the intent of seeing whether they could develop a multiple regression model to explain the variation in highway miles per gallon. A number of different independent variables were collected. The following regression output (with some values missing) was recently presented to the editors by the magazine's analysts:  Based on this output and your understanding of multiple regression analysis, what is the adjusted R- square value for this model?

Accepted Answer

The answer of The editors of a national automotive magazine...

Question 17

One reason for examining the adjusted R-square value in a multiple regression analysis is that the R- square value will increase just by adding additional independent variables to the model, whereas the adjusted R-square accounts for the relationship between the number of independent variables and the sample size and may actually decline if inappropriate independent variables are included in the model.

Accepted Answer

The adjusted R-square compensates for the addition of variables not relevant to the model, providing a more accurate measure of the model's explanatory power, unlike the R-square which can increase with the mere addition of more variables, regardless of their relevance.

Question 18

The editors of a national automotive magazine recently studied 30 different automobiles sold in the United States with the intent of seeing whether they could develop a multiple regression model to explain the variation in highway miles per gallon. A number of different independent variables were collected. The following regression output (with some values missing) was recently presented to the editors by the magazine's analysts:  Based on this output and your understanding of multiple regression analysis, how many degrees of freedom are associated with the Residual in the ANOVA table?

Accepted Answer

The answer of The editors of a national automotive magazine...

Question 19

In a multiple regression model, which of the following is true?

Accepted Answer

In a least squares regression, the sum of the residuals is always zero.

Question 20

When the best subsets approach is used in a regression application, one method for determining which of the many possible models to select for potential use is called the Cp statistic.

Accepted Answer

The Cp statistic is indeed used in the context of the best subsets approach in regression analysis to help determine the most appropriate model among many possible ones by comparing the models' predictive power and complexity.

Quiz 15: Multiple Regression Analysis and Model Building

The forward selection method and the backward elimination method will always lead to choosing the same final regression model.

The best subsets method will involve trying fewer different regression models than stepwise regression.

The following residual plot was constructed based on a simple linear regression model. Based on this plot, there appears to be no basis for concluding that a curvilinear model may be more appropriate than a linear model to explain the variation in the y variable.

In the best subsets approach to regression analysis, if we start with 4 independent variables, a total of 33 different regression models will actually be computed for possible selection as the best model to use.

Which of the following is not an assumption of the multiple regression model?

If a stepwise regression approach is used to enter, one at a time, four variables into a regression model, the resulting regression equation may differ from the regression equation that occurs when all four of the variables are entered at one step.

If one or more of the regression assumptions has been violated this means that the current regression model is not the best one for this data set, and another model should be sought.

A useful method for determining whether a linear function is the appropriate function to describe the relationship between the x and y variable is a residual plot in which the residuals are plotted on the vertical axis and the independent variable is on the horizontal axis.

When we say that we wish to determine the aptness of a regression model, we are actually saying that we wish to check to see whether the resulting model meets the basic assumptions of regression analysis.

The following residual plot is an output of a regression model. Based on this residual plot, there is evidence to suggest that the underlying relationship between the y variable and the x variable is nonlinear.

In a multiple regression model, which of the following is true?

When the best subsets approach is used in a regression application, one method for determining which of the many possible models to select for potential use is called the Cp statistic.