Exam 13: Multiple Regression and Correlation Analysis

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. Given the regression equation Poor (%) = -3.81 + 0.798 Single-Families (%) + 0.624 Unemployment Rate (%) - 0.170 Bachelor's Degree (%) - 0.003 High School (%) Interpret the numbers 3.81 and 0.798.

i. Autocorrelation often happens when data has been collected over periods of time. ii. Homoscedasticity occurs when the variance of the residuals (Y - Y') is different for different values of Y'. iii. Violating the need for successive observations of the dependent variable to be uncorrelated is called autocorrelation.

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. Given the regression equation Poor (%) = -3.81 + 0.798 Single-Families (%) + 0.624 Unemployment Rate (%) - 0.170 Bachelor's Degree (%) - 0.003 High School (%) Which single event would have the strongest effect in reducing the % poor in Ontario?

A multiple regression analysis showed the following ANOVA table result. Based on the information in the ANOVA, how many independent variables were included in the multiple regression analysis?

i. A coefficient of multiple determination equaling -0.76 is definitely possible. ii. Multiple R² measures the proportion of explained variation relative to total variation. iii. The number of degrees of freedom associated with the regression sum of squares in the regression equation model equals the number of independent variables.

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. Assuming other independent variables are held constant, what effect on the GPA will there be if the numbers of hours spent studying per week increases from 32 to 36?

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

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

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. Determine the regression equation.

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

i. 90% of total variation in the dependent variable is explained by the independent variable for a multiple R² = 0.90. ii. The multiple standard error of estimate measures the variation about the regression plane when two independent variables are considered. iii. The multiple coefficient of determination, R², reports the proportion of the variation in Y that is not explained by the variation in the set of independent variables.

A multiple regression analysis showed the following results of the individual independent variables. In stepwise regression, which independent variable would most likely be added first?

Twenty-one executives in a large corporation were randomly selected for a study in which several factors were examined to determine their effect on annual salary (expressed in $000's). The factors selected were age, seniority, years of college, number of company divisions they had been exposed to and the level of their responsibility. A regression analysis was performed using a popular spreadsheet program with the following regression output: What is the value of the denominator in the calculation of the multiple standard error of estimate?

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 sample of General Mills employees was studied to determine their degree of satisfaction with their present life. A special index, called the index of satisfaction, was used to measure satisfaction. Six factors were studied: age at the time of first marriage (X₁), annual income (X₂), number of children living (X₃), value of all assets (X₄), status of health in the form of an index (X₅), and the average number of social activities per week (X₆). Suppose the multiple regression equation is: Y' = 16.24 + 0.017X₁ + 0.00028X₂ +42X₃ + 0.0012X₄ + 0.19X₅ + 26.8X₆. What is the estimated index of satisfaction for a person who first married at 25, has an annual income of $60,000, has two children, has assets of $350,000, has in index of health status of 141, and has 2 social activities per week?

If the correlation between the two independent variables of a regression analysis is 0.11 and each independent variable is highly correlated to the dependent variable, what does this indicate?

For a unit change in the first independent variable with other things being held constant, what change can be expected in the dependent variable in the multiple regression equation Y' = 5.2 + 6.3X₁- 7.1X₂?

Hypotheses concerning individual regression coefficients are tested using which statistic?

It is thought that there are a variety of factors that affect a teacher's salary. Using the following printout and sample data, determine whether the holding of a PhD degree is a significant variable when tested at the 5% level of significance.

Twenty-one executives in a large corporation were randomly selected to study the effect of several factors on annual salary (expressed in $000s). The factors selected were age, seniority, years of college, number of company divisions they had been exposed to, and the level of their responsibility. The results of the regression analysis follow: Test the hypothesis that the regression coefficient for education is equal to 0 at the 0.05 significance level. Report the critical value, the calculated test-statistic, and your decision.