Exam 14: Multiple Regression Analysis

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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 It has been hypothesized that overall academic success for college freshmen as measured by grade point average (GPA) is a function of IQ scores, X<sub>1</sub>, hours spent studying each week, X<sub>2</sub>, and one's high school average, X<sub>3</sub>. Suppose the regression equation is   . The multiple standard error is 6.313 and R<sup>2</sup> = 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? . 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?

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In a multiple regression analysis with five independent variables, the null hypothesis, H0: β4 = 0, is not rejected. When predicting the dependent variable, the independent variable, X4, has ______ relationship to the dependent variable.

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In a multiple regression analysis, if the regression coefficient of a dummy variable is significant and has a sample value of 100, then the dummy variable's effect on the dependent variable is an increase of 100.

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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: 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 ______________. The results for the variable gender show that ______________.

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

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

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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: 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:   Which independent variable has the most significant effect on annual salary? Which independent variable has the most significant effect on annual salary?

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What-statistic is used to assess multicollinearity in multiple regression analysis?

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What can we conclude if the global test of regression rejects the null hypothesis?

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Which statistic is used to test a global hypothesis about a multiple regression equation?

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In an ANOVA table for a multiple regression analysis, the global test of significance is based on the _________.

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

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The best example of a null hypothesis for testing an individual regression coefficient is __________.

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When applying the stepwise regression technique, _________ independent is included in the first multiple regression model.

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How are scatter diagrams used to evaluate the assumptions of linear multiple regression?

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The adjusted R2 accounts for the number of independent variables by ____________.

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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?

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

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Consider a regression model involving more than one independent variable. The test used to determine if the relationship between the dependent variable and the set of independent variables is significant is the _______.

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A multiple regression model includes the term (X1)(X2). The term implies that:

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