Exam 14: Multiple Regression Analysis

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: The results for the variable gender show that ______________.

All other things being held constant, what is the change in the dependent variable for a unit change in X₁ for the multiple regression equation: Ŷ = 5.2 + 6.3X₁ - 7.1 X₂?

If the coefficient of multiple determination is 0.81, what percent of variation is not explained?

It has been hypothesized that overall academic success for college freshmen 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 . 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?

In multiple regression analysis, before testing the significance of the individual regression coefficients, _______________.

When expressed as a percentage, what is the range of values for multiple R²?

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?

In multiple regression, the form of the global hypothesis test is ____________.

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

In the ANOVA table for a multiple regression analysis, the regression degrees of freedom is equal to ___________________.

In multiple regression analysis, an F-statistic is used to test the global hypothesis, H₀: .

If a multiple regression analysis is based on 10 independent variables collected from a sample of 125 observations, what is the value of the denominator in the calculation of the multiple standard error of estimate?

A multiple regression analysis showed the following ANOVA table result. Based on the information in the ANOVA, what is the multiple coefficient of determination?

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?

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, the multiple coefficient of determination is _________.

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 degrees of freedom, the critical value, the test statistic, and your decision.

What can we conclude if the global test of regression does not reject the null hypothesis?

A correlation matrix shows individual correlation coefficients for all pairs of variables.

A researcher is studying the effect of 10 different variables on a critical measure of business performance. A multiple regression analysis including all 10 variables is performed. What criterion could be used to eliminate 1 of the 10 variables?

In multiple regression analysis, residuals (Y - Ŷ) should be ____________.