Question 1

In multiple regression, the prediction equation  is the line that minimizes SSE, the sum of squares of the deviations of the observed values y from the predicted values  .

Accepted Answer

This statement is true. The prediction equation in multiple regression is the equation that minimizes the sum of squares of the deviations (SSE) between the observed values and the predicted values.

Question 2

Which of the following is an advantage of using stepwise regression compared to just entering all the independent variables at one time?
A) There are no advantages of using stepwise regression over entering all the variables at one time.
B) Stepwise regression allows us to observe the effects of multicollinearity more early than when all variables are entered at one time.
C) Stepwise regression will generally produce a model with larger value for the coefficient of determination.
D) All of these.
E) None of these.

Accepted Answer

Stepwise regression allows us to observe the effects of multicollinearity more early than when all variables are entered at one time. This is because stepwise regression considers each independent variable one at a time and only adds variables that significantly improve the model, thus reducing the chances of including highly correlated variables.

Question 3

If you wish to develop a regression model in which the High School Class standing is a qualitative variable with 4 possible levels of response, then you will need to include how many dummy variables?
A) 6
B) 5
C) 4
D) 3
E) none of these

Accepted Answer

When a qualitative variable has k possible levels of response, we need to include (k-1) dummy variables in the regression model. In this case, High School Class standing has 4 possible levels, so we need to include (4-1) = 3 dummy variables in the model. Therefore, the answer is D.

Question 4

Having a large number of predictors in a regression model guarantees that the model fit is good.

Accepted Answer

The answer of Having a large number of predictors in...

Question 5

Which of the following statements is true?
A) It is appropriate to compute a correlation coefficient for the relationship between a dummy variable and a dependent variable.
B) If a qualitative variable has m categories, you should use m - 1 dummy variables to incorporate the qualitative variable into a regression model.
C) Dummy variables are used to incorporate qualitative variables into a regression model.
D) All of these.
E) None of these.

Accepted Answer

A) It is appropriate to compute a correlation coefficient for the relationship between a dummy variable and a dependent variable. This statement is true as correlation coefficient measures the extent of the linear relationship between two variables.

B) If a qualitative variable has m categories, you should use m - 1 dummy variables to incorporate the qualitative variable into a regression model. This statement is also true as using m-1 dummy variables captures the complete information about the qualitative variable, and the additional dummy variable is captured in the constant term.

C) Dummy variables are used to incorporate qualitative variables into a regression model. This statement is also true as the qualitative variables are incorporated into regression models using dummy variables.

Therefore, the correct choice is D, i.e., all of these statements are true.

Question 6

Same statistical packages print a second  statistic, called the adjusted coefficient of determination, which has been adjusted for the degrees of freedom to take into account the sample size and the number of predictor variables.

Accepted Answer

This statement is true. The adjusted coefficient of determination is a modification of the coefficient of determination (R-squared) that adjusts for the number of independent variables in the model and the sample size. This adjustment helps to prevent overfitting and provides a more accurate measure of the model's goodness of fit.

Question 7

Assume that a company is tracking their advertising expenditures as they relate to television (  ) and radio advertising (  ). The owner of the company believes that it would improve the regression model to add a third variable that represents the sum of the advertising on radio and television (  =  +  ). This assessment is generally correct.

Accepted Answer

The answer of Assume that a company is tracking their...

Question 8

The coefficient of determination R² represents the proportion of the total variability in y that can be explained by the regression of y on x. When transformed to a percentage, it represents the percentage reduction in the sum of the squares of the error that can be accomplished by using the model to predict the dependent variable as opposed to just using the sample mean of the dependent variable.

Accepted Answer

This statement is true. The coefficient of determination (R squared) represents the proportion of the total variability in the dependent variable (y) that can be explained by the independent variable (x) in the regression model. When transformed to a percentage, it represents the percentage reduction in the sum of the squares of the error that can be accomplished by using the regression model to predict y instead of just using the sample mean of y.

Question 9

In testing the significance of a multiple regression model in which there are three independent variables, the null hypothesis is  .

Accepted Answer

The answer of In testing the significance of a multiple...

Question 10

Residuals are the deviations between the observed values of y and their predicted values  .

Accepted Answer

This is the definition of residuals.

Question 11

The more predictors that are added to a regression model, the larger the coefficient of determination R² value will be.

Accepted Answer

The answer of The more predictors that are added to...

Question 12

In order to test the usefulness of a multiple regression model involving 5 predictor variables and 25 observations, the numerator and denominator degrees of freedom for the critical value of F are 4 and 24, respectively.

Accepted Answer

In a multiple regression model, the numerator degrees of freedom for the F-test are determined by the number of predictor variables, which is 5 in this case. However, the denominator degrees of freedom are calculated as the total number of observations minus the number of predictor variables minus 1 (for the intercept), which would be 25 - 5 - 1 = 19, not 24.

Question 13

Which of the following statements is correct?
A) The number of dummy variables that must be added to a regression model is one less than the number of categories for a qualitative independent variable.
B) A dummy variable is incorporated into a regression model if the dependent variable is qualitative.
C) Including a dummy variable into a regression model will simplify the regression results and help people to interpret the meaning of the regression parameters.
D) The number of dummy variables that must be added to a regression model is one more than the number of categories for a qualitative independent variable.
E) All of these.

Accepted Answer

Dummy variables are used in regression analysis to represent qualitative data. The correct number of dummy variables needed is one less than the number of categories to avoid the dummy variable trap, which can cause multicollinearity problems in the analysis.

Question 14

Suppose that one equation has 3 explanatory variables and an F-ratio of 52. Another equation has 5 explanatory variables and an F-ratio of 40. The first equation will always be considered a better model.

Accepted Answer

The F-ratio alone cannot determine which model is better as it does not take into account the number of explanatory variables. In order to compare the two models, we need to use other measures such as adjusted R-squared or AIC/BIC.

Question 15

In reference to the equation  , the value 0.63 is the average change in y per unit change in  , regardless of the value of  .

Accepted Answer

The answer of In reference to the equation  ,...

Question 16

Let  be the least squares estimate of the population coefficient  . If the regression assumptions hold true, the test statistic given by  has an F distribution with k and n-k-1 degrees of freedom, where n is the number of observations and k is the number of predictor variables.

Accepted Answer

The answer of Let  be the least squares estimate...

Question 17

A multiple regression equation includes 5 predictor variables, and the coefficient of multiple determination is 0.7921. The percentage of the variation in y that is explained by the regression equation is 89%.

Accepted Answer

The percentage of the variation in y that is explained by the regression equation is actually 79.21%, not 89%. This is because the coefficient of multiple determination (R squared) represents the proportion of variability in the dependent variable explained by all the predictor variables together.

Question 18

Assume you are considering including two additional qualitative variables into a regression model. The first variable has 4 categories, and the second variable has 4 categories as well. Given this information, how many indicator variables will be incorporated into the model?
A) 8
B) 7
C) 6
D) 5
E) 4

Accepted Answer

To incorporate two qualitative variables with 4 categories each, we need to create 3 indicator variables for each variable. Therefore, a total of 6 (3 + 3) indicator variables will be incorporated into the model.

Question 19

A multiple regression model has the form  . The coefficient  is interpreted as the change in y per unit change in  .

Accepted Answer

The answer of A multiple regression model has the form...

Question 20

In multiple regression analysis, which procedure permits variables to enter and leave the model at different stages of its development?
A) forward selection
B) residual analysis
C) backward elimination
D) stepwise regression
E) chi-square test

Accepted Answer

Stepwise regression allows variables to enter and leave the model at different stages of its development based on their statistical significance. This is more flexible than forward selection or backward elimination which only allow variables to enter or leave at specific stages, and is a commonly used procedure in multiple regression analysis. Residual analysis and chi-square test are not relevant procedures for selecting variables in multiple regression analysis.

Quiz 13: Multiple Regression Analysis

In multiple regression, the prediction equation is the line that minimizes SSE, the sum of squares of the deviations of the observed values y from the predicted values .

Which of the following is an advantage of using stepwise regression compared to just entering all the independent variables at one time?

If you wish to develop a regression model in which the High School Class standing is a qualitative variable with 4 possible levels of response, then you will need to include how many dummy variables?

Having a large number of predictors in a regression model guarantees that the model fit is good.

Which of the following statements is true?

Same statistical packages print a second statistic, called the adjusted coefficient of determination, which has been adjusted for the degrees of freedom to take into account the sample size and the number of predictor variables.

In testing the significance of a multiple regression model in which there are three independent variables, the null hypothesis is .

Residuals are the deviations between the observed values of y and their predicted values .

The more predictors that are added to a regression model, the larger the coefficient of determination R2 value will be.

In order to test the usefulness of a multiple regression model involving 5 predictor variables and 25 observations, the numerator and denominator degrees of freedom for the critical value of F are 4 and 24, respectively.

Which of the following statements is correct?

Suppose that one equation has 3 explanatory variables and an F-ratio of 52. Another equation has 5 explanatory variables and an F-ratio of 40. The first equation will always be considered a better model.

In reference to the equation , the value 0.63 is the average change in y per unit change in , regardless of the value of .

Let be the least squares estimate of the population coefficient . If the regression assumptions hold true, the test statistic given by has an F distribution with k and n-k-1 degrees of freedom, where n is the number of observations and k is the number of predictor variables.

A multiple regression equation includes 5 predictor variables, and the coefficient of multiple determination is 0.7921. The percentage of the variation in y that is explained by the regression equation is 89%.

Assume you are considering including two additional qualitative variables into a regression model. The first variable has 4 categories, and the second variable has 4 categories as well. Given this information, how many indicator variables will be incorporated into the model?

A multiple regression model has the form . The coefficient is interpreted as the change in y per unit change in .

In multiple regression analysis, which procedure permits variables to enter and leave the model at different stages of its development?

The more predictors that are added to a regression model, the larger the coefficient of determination R² value will be.