Exam 13: Linear Regression and Correlation

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.

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?

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?

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.

i. The coefficient of multiple determination reports the strength of the association between the Dependent variable and the set of independent variables. ii. The multiple standard error of estimate for two independent variables measures the variation About a regression plane. iii. A multiple coefficient of determination equalling -0.76 is definitely possible.

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

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:

i. If the null hypothesis β4 = 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 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?

The best example of a null hypothesis for a global test of a multiple regression model 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 + 0.09X5 + 26.8X6. Explain the meaning of b6.

The following summary is from home heating costs, using mean outside temperature as X1 the Number of centimetres of insulation as X2, and the presence of a garage as X3. Is the presence of the independent variable garage significant in predicting heating costs, when Tested at the 0.05 level of significance?

What does the correlation matrix for a multiple regression analysis contain?

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.

A multiple regression analysis showed the following results of the individual independent variables. Which independent variables are significantly related to the dependent variable?

i. The multiple standard error of estimate measures the variation about the regression plane when Two independent variables are considered. ii. A coefficient of multiple determination equalling -0.76 is definitely possible. 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 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: In the regression model, which of the following are dummy variables?

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 multiple correlation coefficient is:

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 + 0.09X5 + 26.8X6. Explain the meaning of b5.