Exam 13: Multiple Regression and Correlation Analysis

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 age is equal to 0 at the 0.05 significance level. Report the critical value, the calculated test-statistic, and your decision.

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. How much does tire production change for every thousand cars produced three years ago?

If the correlation between two variables X and Y, is +0.67, what is the regression coefficient for these two variables?

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 $100,000, has two children, has assets of $500,000, has in index of health status of 141, and has 3.5 social activities per week?

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 proportion of the variation in salary accounted for by the set of independent variables?

What is the range of values for multiple R?

The following correlations were computed as part of a multiple regression analysis that used education, job, and age to predict income. What is this table called?

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.

If there are four independent variables in a multiple regression equation, there are also four

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. For which independent variable does a unit change have the least effect on GPA?

How is the Y intercept in the multiple regression equation represented?

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 $100,000, has two children, has assets of $500,000, has in index of health status of 141, and has 3 social activities per week?

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: Which of the following has the most influence on salary--20years of seniority, 5 years of college or attaining 55 years of age?

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.

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

In a multiple regression analysis, the following correlation matrix was computed. What does the correlation matrix suggest about the independent variables?

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, and percent of population in the community holding a bachelor's degree as their highest level of education attained. Determine the regression equation.

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 $46,000, has two children, has assets of $350,000, has in index of health status of 141, and has 2.5 social activities per week?

Which test statistic do we apply to test the null hypothesis that the multiple regression coefficients are all zero?

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 $46,000, has two children, has assets of $200,000, has in index of health status of 141, and has 2.5 social activities per week?