Question 1

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?
A)0 to 60 mph
B)Horsepower
C)Curb weight
D)Displacement

Accepted Answer

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

Question 2

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 3

It is possible for the standard error of the estimate to actually increase if variables are added to the model that do not aid in explaining the variation in the dependent variable.

Accepted Answer

This can happen if the added variables are not significant and add noise to the model. This can cause the standard error of the estimate to increase, meaning that the model's predictions are less precise.

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 is the adjusted R-square value for this model?
A)About 0.82
B)Approximately 0.90
C)Just under 0.48
D)None of the above

Accepted Answer

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

Question 5

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

This is a correct statement. A normal probability plot can be used to check the normality assumption of the error terms in regression, and if the plot forms a straight line, it suggests that the error terms are normally distributed.

Question 6

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 C_p statistic.

Accepted Answer

The C_p statistic is a criterion used in model selection to assess the fit of a regression model, helping to identify models that have a good balance between complexity and goodness of fit.

Question 7

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?
A)19
B)22
C)7
D)29

Accepted Answer

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

Question 8

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 can help identify potential multicollinearity problems by observing the impact on the model at each step when a new variable is added. If adding a new variable causes a sign change on a previously entered variable, it is evidence of multicollinearity.

Question 9

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

Accepted Answer

The forward selection method adds variables one at a time to the model, while the backward elimination method removes variables one at a time. Therefore, these two methods may start with different initial models and can converge to different final regression models.

Question 10

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?
A)Approximately 82 percent
B)Over 90 percent
C)About 37 percent
D)None of the above

Accepted Answer

The R-squared value of 0.815 indicates that approximately 82 percent of the variation in the dependent variable (highway miles per gallon) is explained by the independent variables in the regression model. Therefore, option A is the correct choice.

Question 11

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 statement is true. Adjusted R-square is a modification of the R-square that adjusts for the number of independent variables and the sample size. Since adding more independent variables to a model will always increase the R-square value, the adjusted R-square value may give a better indication of the goodness of fit of the model. Additionally, including irrelevant or inappropriate independent variables in the model can also reduce the adjusted R-square value, indicating a weaker relationship between the dependent and independent variables.

Question 12

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

If one or more of the regression assumptions has been violated, this can result in biased or inefficient estimates, and the model may not accurately represent the relationship between the variables. Therefore, it is important to examine alternative models that may better fit the data and address the potential violations.

Question 13

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 residual plot shows a curved shape, indicating that the errors are not randomly scattered around zero and that the relationship between the dependent and independent variables is not linear. Therefore, there is evidence to suggest that the underlying relationship between the y variable and the x variable is nonlinear.

Question 14

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

This statement is true. Residual plots can be used to assess whether a linear function is a good fit for a given set of data. The residuals represent the difference between the observed y-values and the predicted y-values based on the linear function. If the residuals are randomly distributed around zero, then a linear function may be a good fit for the data. If there is a clear pattern in the residuals, then a linear function may not be appropriate and another type of function may be necessary.

Question 15

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 16

In a multiple regression model,which of the following is true?
A)The coefficient of determination will be equal to the square of the highest correlation in the correlation matrix.
B)Adding variables that have a low correlation with the dependent variable will cause the R-square value to decline.
C)The sum of the residuals computed for the least squares regression equation will be zero.
D)The adjusted R-square might be higher or lower than the value of the R-square.

Accepted Answer

The answer of In a multiple regression model,which of the...

Question 17

Which of the following is not an assumption of the multiple regression model?
A)The mean of the residuals is equal to the variance at all combinations of levels of the independent variables.
B)The regression error terms are normally distributed.
C)The model error terms are independent.
D)The residuals have a constant variance for all combinations of values for the independent variables.

Accepted Answer

The assumption that the mean of the residuals is equal to the variance at all combinations of levels of the independent variables is not an assumption of the multiple regression model. The correct assumption is that the variance of the residuals is constant for all combinations of values for the independent variables.

Question 18

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 19

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

This statement is true. Checking the aptness of a regression model involves assessing whether it has satisfied the underlying assumptions of regression analysis, such as linearity, normality, constant variance, and independence of errors.

Question 20

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.

Quiz 15: Multiple Regression Analysis and Model Building

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.

It is possible for the standard error of the estimate to actually increase if variables are added to the model that do not aid in explaining the variation in the dependent variable.

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.

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

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.

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.

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.

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

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

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

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.

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.

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 C_p statistic.