Question 1

What is it called when the independent variables are highly correlated?

Accepted Answer

A)  Autocorrelation 
B)  Multicollinearity 
C)  Homoscedasticity 
D)  Zero correlation

Question 2

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.

Accepted Answer

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.

Question 3

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.

Accepted Answer

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.

Question 4

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 standard error of estimate is:

Accepted Answer

A)  4.467 
B)  5.698 
C)  5.864 
D)  19.977 
E)  15.917

Question 5

A multiple regression analysis showed the following ANOVA table result.  Based on the information in the ANOVA, what is the decision regarding the global null hypothesis?

Accepted Answer

A)  The p-value 0.001742 is quite small, so we reject the null hypothesis and conclude that there is a relationship between the dependent variable and at least one of the independent variables. 
B)  The p-value 0.001742 is quite large, so we fail to reject the null hypothesis and conclude that there is a relationship between the dependent variable and the independent variables. 
C)  The p-value, 0.001742 is larger than the F value, so we reject the null hypothesis and conclude that there is no relationship between the dependent variable and the independent variables.

Question 6

The production of automobile tires in any given year is related to the number of automobiles produced this year and in prior years. Suppose our econometric model resulted in the following data.  What is the equation for our model?

Accepted Answer

A)  Y'= -50000 + 5.00X1 + 0.25X2 + 0.67X3 + 2.12X4 + 3.44X5 
B)  Y'= 0.25X2 + 0.67X3 + 2.12X4 - 3.44X5 
C)  Y'= 5.00X1 - 0.25X2 - 0.67X3 + 2.12X4 + 3.44X5 
D)  Y'= 10.4X1 + 0.6X2 + 1.4X3 + 2.7X4 + 6.5X5

Question 7

It has been hypothesized that overall academic success for freshmen at college as measured by grade point average (GPA) is a function of IQ scores (X1), hours spent studying each week (X2), and one's high school average (X3). Suppose the regression equation is: Y' = -6.9 + 0.055X1 + 0.107X2 + 0.0083X3.
The multiple standard error is 6.313 and R2 = 0.826.
What is the predicted GPA for a student with an IQ of 108, 32 hours spent studying per week and a high school average of 82?

Accepted Answer

A)  3.1446 
B)  2.9306 
C)  0.428 
D)  10.0446 
E)  13.1892

Question 8

i. The values of b1, b2 and b3in a multiple regression equation are called the net regression coefficients. They indicate the change in the predicted value for a unit change in one X when the other X variables are held constant. ii. A multiple regression equation defines the relationship between the dependent variable and the independent variables in the form of an equation.
iii. If an inverse relationship exists between the dependent variable and independent variables, the regression coefficients for the independent variables are positive.

Accepted Answer

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.

Exam 13: Multiple Regression and Correlation Analysis

What is it called when the independent variables are highly correlated?

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 standard error of estimate is:

A multiple regression analysis showed the following ANOVA table result. Based on the information in the ANOVA, what is the decision regarding the global null hypothesis?

The production of automobile tires in any given year is related to the number of automobiles produced this year and in prior years. Suppose our econometric model resulted in the following data. What is the equation for our model?