Question 1

The information below is from the multiple regression analysis computer output for 28 teams in Major League Baseball. The model is designed to predict wins using attendance, payroll, batting average, home runs, stolen bases, errors, and team ERA.    The critical value of F to be used in the global test of the model is: (5% level of significance)
A) 2.51
B) 2.58
C) 3.70
D) 5.57
E) 3.39

Accepted Answer

The answer of The information below is from the multiple...

Question 2

What test investigates whether all the independent variables have zero net regression coefficients?
A) Multicollinearity
B) Autocorrelation
C) Global
D) Pearson

Accepted Answer

The correct test for investigating whether all the independent variables have zero net regression coefficients in a regression model is the Global test, often referred to as the overall F-test in the context of ANOVA or regression analysis. This test evaluates the null hypothesis that all coefficients (except the intercept) are equal to zero simultaneously, essentially testing the model's explanatory power as a whole.

Question 3

Angela Chou has been asked to investigate the determinants of poverty in Ontario communities. She collected data on 60 communities from Statistics Canada. She selected the percentage of poor persons living under the poverty line [Poor (%)], measured by Low Income Cut-Off, and designed by Statistics Canada as a measure of poverty for a community, as the dependent variable. The independent variables selected are percent of single families in each community, the unemployment rate in each community, percent of population in the community holding a bachelor's degree as their highest level of education attained, and percent of population holding a High School Diploma as their highest level of education attained. Using the output below, determine which variable Angela should consider deleting.  
A) It doesn't matter which she uses, the results are virtually the same in any case.
B) Angela should delete the high school information, because the P-value is over 0.05.
C) Angela should delete the bachelor'sdegree information, because the P-value is close to 0.05.
D) Angela should delete the unemployment rate information because the P-value is 0.00.
E) Angela should exclude the single-family and unemployment information because the P-value values are 0.

Accepted Answer

The answer of Angela Chou has been asked to investigate...

Question 4

Angela Chou has been asked to investigate the determinants of poverty in Ontario communities. She collected data on 60 communities from Statistics Canada. She selected the percentage of poor persons living under the poverty line [Poor (%)], measured by Low Income Cut-Off, designed by Statistics Canada as a measure of poverty for a community, as the dependent variable. The independent variables selected are percent of single families in each community, the unemployment rate in each community, percent of population in the community holding a bachelor's degree as their highest level of education attained, and percent of population holding a High School Diploma as their highest level of education attained. Using the outputs below for this data set, determine whether Angela should use the model with the high school data included, or the data without the high school data, and why.    
A) It doesn't matter which she uses, the results are virtually the same in either case.
B) Angela should use the data that includes the high school information, because more information is always better than less information.
C) Angela should use the data that includes the high school information, because the calculated F value is lower.
D) Angela should include the high school data because the P-value is 0.977, close to 1.
E) Angela should exclude the high school data because the adjusted R-squared value is a little higher than in the data that includes the high school information.

Accepted Answer

The adjusted R-squared value is a measure of how well the model fits the data while adjusting for the number of variables included. The fact that the adjusted R-squared value is higher when high school diploma data is excluded suggests that this variable is not contributing much to the model's ability to explain poverty rates in Ontario communities. Therefore, it is better to exclude the variable and simplify the model.

Question 5

The best example of a null hypothesis for a global test of a multiple regression model is: A) H₀: $\beta$₁= $\beta$₂= $\beta$₃= $\beta$₄. B) H₀: $\mu$₁= $\mu$₂= $\mu$₃= $\mu$₄. C) H₀: $\beta$₁= 0. D) if F is greater than 20.00 then reject.

Accepted Answer

The null hypothesis for a global test of a multiple regression model is that all the coefficients are equal to zero, indicating that none of the independent variables have a significant effect on the dependent variable.

Question 6

The best example of an alternate hypothesis for a global test of a multiple regression model is: A) H₁: $\beta$₁= $\beta$₂= $\beta$₃= $\beta$₄. B) H₁: $\beta$₁$\neq$$\beta$₂$\neq$$\beta$₃$\neq$$\beta$₄. C) H₁: Not all the $\beta$'s are 0. D) if F is less than 20.00 then fail to reject.

Accepted Answer

The alternate hypothesis for a global test of a multiple regression model should state that not all of the regression coefficients (betas) are equal to zero, which is what choice C states. Choices A and B appear to be nonsensical and possibly contain typographical errors. Choice D is not an alternate hypothesis, but rather a decision rule for conducting the global test.

Question 7

The information below is from the multiple regression analysis computer output for 28 teams in Major League Baseball. The model is designed to predict wins using attendance, payroll, batting average, home runs, stolen bases, errors, and team ERA.    The number of degrees of freedom to be used in determining the critical value of t to be used in a hypothesis test of the regression coefficients is:
A) 27
B) 26
C) 22
D) 21
E) 20

Accepted Answer

The answer of The information below is from the multiple...

Question 8

The best example of a null hypothesis for testing an individual regression coefficient is: A) H₀: $\beta$₁= $\beta$₂= $\beta$₃= $\beta$₄. B) H₀: $\mu$₁= $\mu$₂= $\mu$₃= $\mu$₄. C) H₀: $\beta$₁= 0. D) if F is greater than 20.00 then reject.

Accepted Answer

The null hypothesis for testing an individual regression coefficient is that the coefficient is equal to 0. Choice C presents the null hypothesis in the correct format. Choices A and B are not in the correct format and do not make sense. Choice D is not a null hypothesis, but rather a significance level for rejecting the null hypothesis.

Question 9

A manager at a local bank analyzed the relationship between monthly salary and three independent variables: length of service (measured in months), gender (0 = female, 1 = male) and job type (0 = clerical, 1 = technical). The following ANOVA summarizes the regression results:  Based on the ANOVA and a 0.05 significance level, the global null hypothesis test of the multiple regression model.
A) will be rejected and conclude that monthly salary is related to all of the independent variables.
B) will be rejected and conclude that monthly salary is related to at least one of the independent variables.
C) will not be rejected.
D) will show a high multiple coefficient of determination.

Accepted Answer

The ANOVA shows a significant F-test result with a p-value of 0.042, indicating that at least one of the independent variables is related to monthly salary. Therefore, the null hypothesis of no relationship between monthly salary and any of the independent variables can be rejected at a 0.05 significance level.

Question 10

The information below is from the multiple regression analysis computer output for 28 teams in Major League Baseball. The model is designed to predict wins using attendance, payroll, batting average, home runs, stolen bases, errors, and team ERA.    The computed F for the global test is:
A) 7.802
B) 25.695
C) 15.790
D) 26.981
E) 114.779

Accepted Answer

The answer of The information below is from the multiple...

Question 11

Hypotheses concerning individual regression coefficients are tested using which statistic? A) t-statistic B) z-statistic C) $\chi$²(chi-square statistic) D) H

Accepted Answer

Individual regression coefficients are typically tested using a t-statistic. The t-test determines whether the coefficient is significantly different from 0, indicating whether the corresponding predictor variable has a significant effect on the outcome variable.

Question 12

i. A variable whose possible outcomes are coded as a "1" or a "0" is called a dummy variable. ii. A dummy variable is added to the regression equation to control for error. iii. If the null hypothesis $\beta$₄ = 0 is not rejected, then the independent variable X₄ has no effect in predicting the dependent variable. A) (i), (ii), and (iii) are all correct statements. B) (i) and (ii) are correct statements but not (iii). C) (i) and (iii) are correct statements but not (ii). D) (ii) and (iii) are correct statements but not (i). E) (i), (ii), and (iii) are all false statements.

Accepted Answer

- A dummy variable is indeed a variable that takes the value of 0 or 1 to indicate the absence or presence of some categorical effect that may be expected to shift the outcome. It is used in regression analysis to represent categorical variables.- The purpose of adding a dummy variable to a regression equation is not to control for error but to control for the effect of categorical variables. It allows the model to differentiate between different groups or conditions represented by the categorical variable.- If the null hypothesis that the coefficient of an independent variable is equal to zero is not rejected, it suggests that the independent variable does not have a statistically significant effect on the dependent variable in the context of the model. This means the variable does not contribute to explaining the variation in the dependent variable, assuming the model is correctly specified and all relevant variables are included.

Question 13

i. If the null hypothesis $\beta$₄= 0 is not rejected, then the independent variable X₄ has a strong effect in predicting the dependent variable. ii. A dummy variable is added to the regression equation to control for error. iii. A variable whose possible outcomes are coded as a "1" or a "0" is called a strong independent variable. A) (i), (ii), and (iii) are all correct statements. B) (i) and (ii) are correct statements but not (iii). C) (i) and (iii) are correct statements but not (ii). D) (ii) and (iii) are correct statements but not (i). E) (i), (ii), and (iii) are all false statements.

Accepted Answer

i. If the null hypothesis that the coefficient equals 0 is not rejected, it means there is not enough evidence to say the independent variable has a significant effect on the dependent variable, not a strong effect.ii. A dummy variable is added to account for categorical variables in regression, not to control for error.iii. A variable coded as "1" or "0" is called a dummy variable, not a strong independent variable.

Question 14

A manager at a local bank analyzed the relationship between monthly salary and three independent variables: length of service (measured in months), gender (0 = female, 1 = male) and job type (0 = clerical, 1 = technical). The following ANOVA summarizes the regression results:  Based on the hypothesis tests for the individual regression coefficients,
A) all the regression coefficients are not equal to zero.
B) "job" is the only significant variable in the model.
C) only months of service and gender are significantly related to monthly salary.
D) "service" is the only significant variable in the model.

Accepted Answer

The ANOVA summary indicates that at least one of the regression coefficients is not zero, which supports choice A. However, the hypothesis tests for individual regression coefficients indicate that only the coefficients for months of service and gender are statistically significant at the 5% level. The coefficient for job type is not significant. Therefore, choice B and D are incorrect. The correct choice is C, which states that only months of service and gender are significantly related to monthly salary.

Question 15

The information below is from the multiple regression analysis computer output for 28 teams in Major League Baseball. The model is designed to predict wins using attendance, payroll, batting average, home runs, stolen bases, errors, and team ERA.    The t-value computed for testing the coefficient "Batg. Avg." is:
A) 112.991.
B) 2.086.
C) 7.438.
D) 2.832.
E) -1.593.

Accepted Answer

The answer of The information below is from the multiple...

Question 16

i. A variable whose possible outcomes are coded as a "1" or a "0" is called a dummy variable. ii. If the null hypothesis $\beta$₄= 0 is not rejected, then the independent variable X₄ has no effect in predicting the dependent variable. iii. A dummy variable is added to the regression equation to control for error. A) (i), (ii), and (iii) are all correct statements. B) (i) and (ii) are correct statements but not (iii). C) (i) and (iii) are correct statements but not (ii). D) (ii) and (iii) are correct statements but not (i). E) (i), (ii), and (iii) are all false statements.

Accepted Answer

Statement (i) is correct as a variable with two possible outcomes coded as "1" or "0" is known as a dummy variable. Statement (ii) is also correct as if the null hypothesis is not rejected, it indicates that the independent variable has no significant effect on the dependent variable. However, statement (iii) is incorrect as the main purpose of adding a dummy variable is not to control error, but to capture the effect of a categorical variable in the regression equation.

Question 17

Which of the following is a characteristic of the F-distribution?
A) Normally distributed
B) Positively skewed
C) Negatively skewed
D) Equal to the t-distribution

Accepted Answer

The F-distribution is positively skewed, meaning that it has a long tail to the right of the mean. This is because it is the ratio of two independent chi-squared distributions, which are themselves positively skewed.

Question 18

A manager at a local bank analyzed the relationship between monthly salary and three independent variables: length of service (measured in months), gender (0 = female, 1 = male) and job type (0 = clerical, 1 = technical). The following ANOVA summarizes the regression results:  The results for the variable gender show that,
A) males average $222.78 more than females in monthly salary.
B) females average $222.78 more than males in monthly salary.
C) gender is not related to monthly salary.
D) gender and months of service are correlated.

Accepted Answer

The coefficient for the gender variable is -222.78, which means that males, coded as 1, have a higher average salary than females, coded as 0, by $222.78.

Question 19

In multiple regression, a dummy variable can be included in a multiple regression model as
A) an additional quantitative variable.
B) a nominal variable with three or more values.
C) a nominal variable with only two values.
D) a new regression coefficient.

Accepted Answer

A dummy variable is a nominal variable with two values, usually coded as 0 and 1. In multiple regression, a dummy variable can be included to represent a categorical variable with two groups. The variable takes the value of 0 for one group and 1 for the other group. Therefore, the correct choice is C, a nominal variable with only two values. A is incorrect because a dummy variable is not a quantitative variable. B is incorrect because a categorical variable with three or more groups would require multiple dummy variables (one for each group). D is incorrect because a dummy variable does not add a new regression coefficient, but it changes the interpretation of the existing coefficients in the model.

Question 20

What can we conclude if the net regression coefficients in the population are not significantly different from zero?
A) Strong relationship exists among the variables.
B) No relationship exists between the dependent variable and the independent variables.
C) Independent variables are good predictors.
D) Good forecasts are possible.

Accepted Answer

If the net regression coefficients in the population are not significantly different from zero, it means that there is no relationship between the dependent variable and the independent variables. Therefore, the best choice is B.

Quiz 13: Multiple Regression and Correlation Analysis

What test investigates whether all the independent variables have zero net regression coefficients?

The best example of a null hypothesis for a global test of a multiple regression model is:

The best example of an alternate hypothesis for a global test of a multiple regression model is:

The best example of a null hypothesis for testing an individual regression coefficient is:

The information below is from the multiple regression analysis computer output for 28 teams in Major League Baseball. The model is designed to predict wins using attendance, payroll, batting average, home runs, stolen bases, errors, and team ERA. The computed F for the global test is:

Hypotheses concerning individual regression coefficients are tested using which statistic?

Which of the following is a characteristic of the F-distribution?

In multiple regression, a dummy variable can be included in a multiple regression model as

What can we conclude if the net regression coefficients in the population are not significantly different from zero?