Exam 13: Linear Regression and Correlation

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?

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

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?

In a regression analysis, three independent variables are used in the equation based on a sample of Forty observations. What are the degrees of freedom associated with the F-statistic?

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?

i. The multiple standard error of estimate for two independent variables measures the variation About a regression plane. ii. A multiple coefficient of determination equalling -0.76 is definitely possible. iii. Multiple R2 measures the proportion of explained variation relative to total variation.

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:

The following correlations were computed as part of a multiple regression analysis that used Education, job, and age to predict income. Which independent variable has the weakest association with the dependent variable?

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 + 0.09X5 + 26.8X6. Explain the meaning of b3.

i. The multiple coefficient of determination, R2, reports the proportion of the variation in Y that is Explained by the variation in the set of independent variables. ii. The coefficient of multiple determination reports the strength of the association between the Dependent variable and the set of independent variables. iii. A coefficient of multiple determination equalling -0.76 is definitely possible.

i. The multiple standard error of estimate measures the variation about the regression plane when Two independent variables are considered. ii. 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. iii. The coefficient of multiple determination reports the strength of the association between the Dependent variable and the set of independent variables.

The following graph is used to evaluate an assumption of a multiple regression analysis. What is the Assumption?

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?

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?

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.

i. 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. ii. The coefficient of multiple determination reports the strength of the association between the Dependent variable and the set of independent variables. iii. The multiple standard error of estimate for two independent variables measures the variation About a regression plane.

The following correlations were computed as part of a multiple regression analysis that used Education, job, and age to predict income. Which independent variable has the strongest association with the dependent variable?

i. A coefficient of multiple determination equalling -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.

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 + 0.09X5 + 26.8X6. Explain the meaning of b4.

What is the difference in selling prices of a house with 1,650 square feet and one with 1,750 square Feet?