Question 1

Real Estate Builder
 A real estate builder wishes to determine how house size is influenced by family income,family size,and education of the head of household.House size is measured in hundreds of square feet,income is measured in thousands of dollars,and education is measured in years.A partial computer output is shown below. SUMMARY OUTPUT Regression Statistics Multiple R 0.865 R Square 0.748 Adjusted R Square 0.726 Standard Error 5.195 Observations 50 ANOVA   ​ ​
-{Real Estate Builder Narrative} What are the residual degrees of freedom that are missing from the output?

Accepted Answer

The answer of  Real Estate Builder
 A real estate...

Question 2

Multicollinearity affects the t-tests of the individual coefficients as well as the F-test in the analysis of variance for regression because the F-test combines the t-tests into a single test.

Accepted Answer

Multicollinearity primarily affects the reliability and interpretation of the individual coefficients' t-tests by inflating their variances, making it harder to determine their individual significance. However, the F-test, which assesses the overall significance of the regression model, remains unaffected by multicollinearity because it evaluates the model as a whole, not the individual predictors.

Question 3

One of the consequences of multicollinearity in multiple regression is biased estimates on the slope coefficients.

Accepted Answer

Multicollinearity does not cause biased estimates of the slope coefficients; it causes high variances and covariances among the estimated coefficients, making them less precise and potentially more difficult to interpret.

Question 4

Multicollinearity is present when there is a high degree of correlation between the dependent variable and any of the independent variables.

Accepted Answer

Multicollinearity is present when there is a high degree of correlation between the independent variables themselves, not between the dependent variable and any of the independent variables.

Question 5

Multicollinearity is present when there is a high degree of correlation between the independent variables included in the regression model.

Accepted Answer

Multicollinearity is indeed present when there is a high degree of correlation between independent variables included in a regression model. This can cause issues with interpreting the coefficients and lead to unreliable results.

Question 6

Multicollinearity is present if the dependent variable is linearly related to one of the explanatory variables.

Accepted Answer

Multicollinearity is present if there is a high correlation between two or more explanatory variables, but it does not necessarily indicate a linear relationship between the dependent variable and one explanatory variable.

Question 7

Real Estate Builder
 A real estate builder wishes to determine how house size is influenced by family income,family size,and education of the head of household.House size is measured in hundreds of square feet,income is measured in thousands of dollars,and education is measured in years.A partial computer output is shown below. SUMMARY OUTPUT Regression Statistics Multiple R 0.865 R Square 0.748 Adjusted R Square 0.726 Standard Error 5.195 Observations 50 ANOVA   ​ ​
-{Real Estate Builder Narrative} Suppose the builder wants to test whether the coefficient on education is significantly different from 0.What is the value of the relevant t-statistic?

Accepted Answer

The answer of  Real Estate Builder
 A real estate...

Question 8

Real Estate Builder
 A real estate builder wishes to determine how house size is influenced by family income,family size,and education of the head of household.House size is measured in hundreds of square feet,income is measured in thousands of dollars,and education is measured in years.A partial computer output is shown below. SUMMARY OUTPUT Regression Statistics Multiple R 0.865 R Square 0.748 Adjusted R Square 0.726 Standard Error 5.195 Observations 50 ANOVA   ​ ​
-{Real Estate Builder Narrative} Suppose the builder wants to test whether the coefficient on income is significantly different from 0.What is the value of the relevant t-statistic?

Accepted Answer

The answer of  Real Estate Builder
 A real estate...

Question 9

Real Estate Builder
 A real estate builder wishes to determine how house size is influenced by family income,family size,and education of the head of household.House size is measured in hundreds of square feet,income is measured in thousands of dollars,and education is measured in years.A partial computer output is shown below. SUMMARY OUTPUT Regression Statistics Multiple R 0.865 R Square 0.748 Adjusted R Square 0.726 Standard Error 5.195 Observations 50 ANOVA   ​ ​
-{Real Estate Builder Narrative} What are the numerator and denominator degrees of freedom for the F-statistic?

Accepted Answer

The answer of  Real Estate Builder
 A real estate...

Question 10

The parameter estimates are biased when multicollinearity is present in a multiple regression equation.

Accepted Answer

Multicollinearity affects the precision of the parameter estimates (making their standard errors larger) but does not cause the estimates themselves to be biased.

Question 11

Multicollinearity will result in excessively low standard errors of the parameter estimates reported in the regression output.

Accepted Answer

Multicollinearity typically results in excessively high standard errors for the parameter estimates, making it difficult to determine the individual effect of each predictor variable on the outcome variable.

Question 12

Real Estate Builder
 A real estate builder wishes to determine how house size is influenced by family income,family size,and education of the head of household.House size is measured in hundreds of square feet,income is measured in thousands of dollars,and education is measured in years.A partial computer output is shown below. SUMMARY OUTPUT Regression Statistics Multiple R 0.865 R Square 0.748 Adjusted R Square 0.726 Standard Error 5.195 Observations 50 ANOVA   ​ ​
-{Real Estate Builder Narrative} At the 0.01 level of significance,what conclusion should the builder draw regarding the inclusion of income in the regression model?

Accepted Answer

The answer of  Real Estate Builder
 A real estate...

Question 13

One of the consequences of multicollinearity in multiple regression is inflated standard errors in some or all of the estimated slope coefficients.

Accepted Answer

Multicollinearity can cause instability in the estimation of coefficients and can lead to inflated standard errors, which in turn can make it difficult to identify significant predictors.

Question 14

Which of the following statements regarding multicollinearity is not true?
A)It exists in virtually all multiple regression models.
B)It is also called collinearity and intercorrelation.
C)It is a condition that exists when the independent variables are highly correlated with the dependent variable.
D)All of these choices are true.

Accepted Answer

Multicollinearity is a condition that exists when the independent variables in a multiple regression model are highly correlated with each other, rather than with the dependent variable. Statement C incorrectly suggests that multicollinearity occurs when the independent variables are highly correlated with the dependent variable.

Question 15

Real Estate Builder
 A real estate builder wishes to determine how house size is influenced by family income,family size,and education of the head of household.House size is measured in hundreds of square feet,income is measured in thousands of dollars,and education is measured in years.A partial computer output is shown below. SUMMARY OUTPUT Regression Statistics Multiple R 0.865 R Square 0.748 Adjusted R Square 0.726 Standard Error 5.195 Observations 50 ANOVA   ​ ​
-{Real Estate Builder Narrative} What is the value of the calculated F-test statistic that is missing from the output for testing whether the whole regression model is significant?

Accepted Answer

The answer of  Real Estate Builder
 A real estate...

Question 16

Real Estate Builder
 A real estate builder wishes to determine how house size is influenced by family income,family size,and education of the head of household.House size is measured in hundreds of square feet,income is measured in thousands of dollars,and education is measured in years.A partial computer output is shown below. SUMMARY OUTPUT Regression Statistics Multiple R 0.865 R Square 0.748 Adjusted R Square 0.726 Standard Error 5.195 Observations 50 ANOVA   ​ ​
-{Real Estate Builder Narrative} At the 0.01 level of significance,what conclusion should the builder draw regarding the inclusion of education in the regression model?

Accepted Answer

The answer of  Real Estate Builder
 A real estate...

Question 17

Real Estate Builder
 A real estate builder wishes to determine how house size is influenced by family income,family size,and education of the head of household.House size is measured in hundreds of square feet,income is measured in thousands of dollars,and education is measured in years.A partial computer output is shown below. SUMMARY OUTPUT Regression Statistics Multiple R 0.865 R Square 0.748 Adjusted R Square 0.726 Standard Error 5.195 Observations 50 ANOVA   ​ ​
-{Real Estate Builder Narrative} What are the regression degrees of freedom that are missing from the output?

Accepted Answer

The answer of  Real Estate Builder
 A real estate...

Question 18

When the independent variables are correlated with one another in a multiple regression analysis,this condition is called:
A)heteroscedasticity.
B)homoscedasticity.
C)multicollinearity.
D)None of these choices.

Accepted Answer

Multicollinearity refers to the situation when two or more independent variables in a multiple regression analysis are highly correlated with one another. This can cause problems in the regression analysis, as it becomes difficult to determine the independent effect of each variable on the dependent variable. Heteroscedasticity refers to the unequal variance of the residuals, while homoscedasticity refers to the equal variance of the residuals. Neither of these conditions directly relates to the correlation between independent variables in a multiple regression analysis.

Question 19

Multicollinearity is a situation in which two or more of the independent variables are highly correlated with each other.

Accepted Answer

Multicollinearity occurs when there is a high correlation between two or more independent variables, which can pose problems in statistical analysis and modeling.

Question 20

Because of multicollinearity,the t-tests of the individual coefficients may indicate that some independent variables are not linearly related to the dependent variable,when in fact they are.

Accepted Answer

Multicollinearity can cause the t-tests of individual coefficients to show that some independent variables are not significantly related to the dependent variable, even though they may have a linear relationship with the dependent variable when considered together with the other independent variables.

Quiz 17: Multiple Regression

Multicollinearity affects the t-tests of the individual coefficients as well as the F-test in the analysis of variance for regression because the F-test combines the t-tests into a single test.

One of the consequences of multicollinearity in multiple regression is biased estimates on the slope coefficients.

Multicollinearity is present when there is a high degree of correlation between the dependent variable and any of the independent variables.

Multicollinearity is present when there is a high degree of correlation between the independent variables included in the regression model.

Multicollinearity is present if the dependent variable is linearly related to one of the explanatory variables.

The parameter estimates are biased when multicollinearity is present in a multiple regression equation.

Multicollinearity will result in excessively low standard errors of the parameter estimates reported in the regression output.

One of the consequences of multicollinearity in multiple regression is inflated standard errors in some or all of the estimated slope coefficients.

Which of the following statements regarding multicollinearity is not true?

When the independent variables are correlated with one another in a multiple regression analysis,this condition is called:

Multicollinearity is a situation in which two or more of the independent variables are highly correlated with each other.

Because of multicollinearity,the t-tests of the individual coefficients may indicate that some independent variables are not linearly related to the dependent variable,when in fact they are.