Question 1

Heteroscedasticity exists when all the errors (residuals)have the same variance.

Accepted Answer

Heteroscedasticity exists when the errors (residuals) have different variances, not the same variance.

Question 2

In a multiple regression with six predictors in a sample of 67 U.S.cities,what would be the critical value for an F-test of overall significance at α = .05?
A)2.29
B)2.25
C)2.37
D)2.18

Accepted Answer

The answer of In a multiple regression with six predictors...

Question 3

A squared predictor is used to test for nonlinearity in the predictor's relationship to Y.

Accepted Answer

A squared predictor is used to test for curvilinearity or nonlinearity in the predictor's relationship to Y.

Question 4

The t test shows the ratio of an estimated coefficient to its standard error.

Accepted Answer

This is true. The t test is used to determine if the estimated coefficient is significantly different from zero, by comparing it to its standard error.

Question 5

Which of the following is not true of the standard error of the regression?
A)It is a measure of the accuracy of the prediction.
B)It is based on squared vertical deviations between the actual and predicted values of Y.
C)It would be negative when there is an inverse relationship in the model.
D)It is used in constructing confidence and prediction intervals for Y.

Accepted Answer

The standard error of the regression can never be negative, regardless of the relationship between the independent and dependent variables in the model. It is always non-negative, reflecting the variability of the data around the regression line. The other options (A, B, and D) are all true of the standard error of the regression.

Question 6

If X2 is a binary predictor in Y = β0 + β1X1 + β2X2,then which statement is most nearly correct?
A)X2 = 1 should represent the most desirable condition.
B)X2 would be a significant predictor if β2 = 423.72.
C)X2 = 0,X2 = 1,X2 = 2 would be appropriate if three categories exist.
D)X2 will shift the estimated equation either by 0 units or by β2 units.

Accepted Answer

Since X2 is a binary predictor, it can only take on two values (0 and 1). Therefore, the addition of X2 to the model will result in two separate estimated equations, one when X2 = 0 and one when X2 = 1. These equations will differ only in the intercept term. As a result, X2 will shift the estimated equation either by 0 units (when X2 = 0) or by β2 units (when X2 = 1). Therefore, option D is the most correct statement.

Question 7

Unlike other predictors,a binary predictor has a t-value that is either 0 or 1.

Accepted Answer

A binary predictor is not evaluated based on t-values, but rather on whether it takes on only two possible values (usually 0 or 1).

Question 8

The unexplained sum of squares measures variation in the dependent variable Y about the
A)mean of the Y values.
B)estimated Y values.
C)mean of the X values.
D)Y-intercept.

Accepted Answer

The unexplained sum of squares, also known as the residual sum of squares, measures the variation in the dependent variable Y that is not explained by the regression model, hence it is about the estimated Y values.

Question 9

Given that the fitted regression is Y = 76.40 − 6.388X1 + 0.870X2,the standard error of b1 is 1.453,and n = 63,at α = .05,we can conclude that X1 is a significant predictor of Y.

Accepted Answer

To determine if X1 is a significant predictor of Y, we need to conduct a hypothesis test on the regression coefficient b1. Using the given standard error of b1 and n, we can calculate the t-statistic as:

t = ( b1 - 0 ) / SE(b1)
  = ( -6.388 - 0 ) / 1.453
  = -4.396

Assuming a two-tailed test at α = .05, the critical t-value for 61 degrees of freedom (n-2) is ±2.002. Since |-4.396| > 2.002, we reject the null hypothesis that b1 = 0, and conclude that X1 is a significant predictor of Y. Therefore, the answer is A.

Question 10

Nonnormal residuals lead to biased estimates of the coefficients in a regression model.

Accepted Answer

The normality of residuals is not a requirement for the unbiasedness of the coefficients in a regression model. The unbiasedness of the estimates is primarily ensured by the linear model assumptions, specifically the expectation of the error term being zero. Non-normal residuals can affect inference (e.g., hypothesis testing, confidence intervals) but not the unbiasedness of the coefficient estimates.

Question 11

A test is conducted in 22 cities to see if giving away free transit system maps will increase the number of bus riders.In a regression analysis,the dependent variable Y is the increase in bus riders (in thousands of persons)from the start of the test until its conclusion.The independent variables are X1 = the number (in thousands)of free maps distributed and a binary variable X2 = 1 if the city has free downtown parking,0 otherwise.The estimated regression equation is Y = 1.32 + 0.0345X1 − 1.45X2.In city 3,the observed Y value is 7.3,X1 = 140,and X2 = 0.The residual for city 3 (in thousands)is
A)6.15
B)1.15
C)4.83
D)1.57

Accepted Answer

The predicted Y value for city 3 is calculated as 1.32 + 0.0345(140) - 1.45(0) = 6.15. The residual is the observed Y value minus the predicted Y value: 7.3 - 6.15 = 1.15.

Question 12

When predictor variables are strongly related to each other,the ________ of the regression estimates is questionable.
A)logic
B)fit
C)parsimony
D)stability

Accepted Answer

When predictor variables are strongly related to each other, it is referred to as multicollinearity. This can lead to unstable or unpredictable regression estimates, making the stability of the regression estimates questionable. Therefore, option D is the correct answer.

Question 13

Nonnormality of residuals is not usually considered a major problem unless there are outliers.

Accepted Answer

The answer of Nonnormality of residuals is not usually considered...

Question 14

Multicollinearity refers to relationships among the independent variables.

Accepted Answer

Multicollinearity refers to the presence of correlation between independent variables in a regression model. It can cause issues with model interpretation and accuracy.

Question 15

A large VIF (e.g. ,10 or more)would indicate multicollinearity.

Accepted Answer

A VIF (Variance Inflation Factor) value of 10 or more is generally considered to indicate a high degree of multicollinearity among the independent variables in a regression model. Therefore, a large VIF value indicates a problem with multicollinearity.

Question 16

In a multiple regression with five predictors in a sample of 56 U.S.cities,what would be the critical value for an F-test of overall significance at α = .05?
A)2.45
B)2.37
C)2.40
D)2.56

Accepted Answer

The critical value for an F-test with five predictors and 56 degrees of freedom at α = .05 is 2.40. This can be found using a F-distribution table or calculator.

Question 17

In a multiple regression with five predictors in a sample of 56 U.S.cities,we would use F5,50 in a test of overall significance.

Accepted Answer

This is true because F5,50 represents the F-statistic with 5 predictors and 50 degrees of freedom for error in a multiple regression analysis. It is used to test the overall significance of the model, which tests whether the predictors as a group significantly predict the outcome variable.

Question 18

A multiple regression analysis with two independent variables yielded the following results in the ANOVA table: SS(Total)= 798,SS(Regression)= 738,SS(Error)= 60.The multiple correlation coefficient is
A)0.2742
B)0.0752
C)0.9248
D)0.9617

Accepted Answer

The multiple correlation coefficient (R) is the square root of the coefficient of determination (R^2). R^2 is calculated as SS(Regression) / SS(Total) = 738 / 798 = 0.9248. Therefore, R = sqrt(0.9248) = 0.9617.

Question 19

In the fitted regression Y = 12 + 3X1 − 5X2 + 27X3 + 2X4 the most significant predictor is X3.

Accepted Answer

The answer of In the fitted regression Y = 12...

Question 20

A fitted multiple regression equation is Y = 12 + 3X1 - 5X2 + 7X3 + 2X4.When X1 increases 2 units and X2 increases 2 units as well,while X3 and X4 remain unchanged,what change would you expect in your estimate of Y?
A)Decrease by 2
B)Decrease by 4
C)Increase by 2
D)No change in Y

Accepted Answer

When X1 increases 2 units, the estimate of Y will increase by 3(2) = 6. 
When X2 increases 2 units, the estimate of Y will decrease by 5(2) = 10. 
The net effect is a decrease of 4 in the estimate of Y.

Quiz 13: Multiple Regression

Heteroscedasticity exists when all the errors (residuals)have the same variance.

In a multiple regression with six predictors in a sample of 67 U.S.cities,what would be the critical value for an F-test of overall significance at α = .05?

A squared predictor is used to test for nonlinearity in the predictor's relationship to Y.

The t test shows the ratio of an estimated coefficient to its standard error.

Which of the following is not true of the standard error of the regression?

If X2 is a binary predictor in Y = β0 + β1X1 + β2X2,then which statement is most nearly correct?

Unlike other predictors,a binary predictor has a t-value that is either 0 or 1.

The unexplained sum of squares measures variation in the dependent variable Y about the

Given that the fitted regression is Y = 76.40 − 6.388X1 + 0.870X2,the standard error of b1 is 1.453,and n = 63,at α = .05,we can conclude that X1 is a significant predictor of Y.

Nonnormal residuals lead to biased estimates of the coefficients in a regression model.

When predictor variables are strongly related to each other,the ________ of the regression estimates is questionable.

Nonnormality of residuals is not usually considered a major problem unless there are outliers.

Multicollinearity refers to relationships among the independent variables.

A large VIF (e.g. ,10 or more)would indicate multicollinearity.

In a multiple regression with five predictors in a sample of 56 U.S.cities,what would be the critical value for an F-test of overall significance at α = .05?

In a multiple regression with five predictors in a sample of 56 U.S.cities,we would use F5,50 in a test of overall significance.

A multiple regression analysis with two independent variables yielded the following results in the ANOVA table: SS(Total) = 798,SS(Regression) = 738,SS(Error) = 60.The multiple correlation coefficient is

In the fitted regression Y = 12 + 3X1 − 5X2 + 27X3 + 2X4 the most significant predictor is X3.

A fitted multiple regression equation is Y = 12 + 3X1 - 5X2 + 7X3 + 2X4.When X1 increases 2 units and X2 increases 2 units as well,while X3 and X4 remain unchanged,what change would you expect in your estimate of Y?