Exam 14: Multiple Regression and Model Building

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A very insignificant independent variable (an independent variable that has a very weak relationship with the dependent variable)is added to a multiple regression equation.As a result of this change,the value of the explained variation (SSR)will _________,the value of the multiple coefficient of determination (R2)will _________,and the calculated value of the F statistic will most likely _________.

(Multiple Choice)
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In the quadratic regression model In the quadratic regression model   the β<sub>2</sub> term represents the: the β2 term represents the:

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Using squared and interaction variables in a multiple regression model results in extreme multicollinearity.

(True/False)
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Consider the following partial computer output for a multiple regression model. Consider the following partial computer output for a multiple regression model.   Test the overall usefulness of the model at α = .01.Calculate F and make your decision. Test the overall usefulness of the model at α = .01.Calculate F and make your decision.

(Short Answer)
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In multiple regression analysis,the explained sum of squares divided by the total sum of squares yields the __________.

(Multiple Choice)
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A multiple regression model with four independent variables consists of 29 observations.The multiple coefficient of determination R2 = .80,and the standard error s = 2.0.Complete the analysis of variance table for this model,and test the overall model for significance.

(Essay)
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If a regression model with k independent variables has a C statistic less than _______,then the model is considered to be desirable.

(Multiple Choice)
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In a multiple regression analysis,if the normal probability plot exhibits approximately a straight line,then it can be concluded that the assumption of normality is not violated.

(True/False)
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The multiple correlation coefficient can assume any value between zero and 1,inclusive.

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In general,a multiple regression model is considered to be desirable if the value of the C statistic is small and the value of C is less than _____.

(Multiple Choice)
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If the simple correlation coefficient between two independent variables is greater than .90,then ______________________ is considered to be severe.

(Multiple Choice)
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A multiple regression model with 3 independent variables and 16 observations produced the following analysis of variance table. A multiple regression model with 3 independent variables and 16 observations produced the following analysis of variance table.   After some consideration,the analyst decided to add two new independent variables to the multiple regression model.As a result of this change,the unexplained variation (SSE)decreased by 5.Complete the new analysis of variance table after the addition of the two new independent variables.Did the two newly added variables improve the model? After some consideration,the analyst decided to add two new independent variables to the multiple regression model.As a result of this change,the unexplained variation (SSE)decreased by 5.Complete the new analysis of variance table after the addition of the two new independent variables.Did the two newly added variables improve the model?

(Essay)
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A member of the state legislature has expressed concern about the differences in the mathematics test scores of high school freshmen across the state.She asks her research assistant to conduct a study to investigate what factors could account for the differences.The research assistant looks at a random sample of school districts across the state and uses the factors of percentage of mathematics teachers in each district with a degree in mathematics,the average age of mathematics teachers,and the average salary of mathematics teachers. A member of the state legislature has expressed concern about the differences in the mathematics test scores of high school freshmen across the state.She asks her research assistant to conduct a study to investigate what factors could account for the differences.The research assistant looks at a random sample of school districts across the state and uses the factors of percentage of mathematics teachers in each district with a degree in mathematics,the average age of mathematics teachers,and the average salary of mathematics teachers.   Test the overall usefulness of the model at α = .01.Calculate F and make your decision. Test the overall usefulness of the model at α = .01.Calculate F and make your decision.

(Short Answer)
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Which of the following residual plots is not used in regression analysis?

(Multiple Choice)
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Below is a partial multiple regression ANOVA table. Below is a partial multiple regression ANOVA table.   Calculate the proportion of the variation explained by the multiple regression model. Calculate the proportion of the variation explained by the multiple regression model.

(Short Answer)
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If a particular multiple regression model has a small value of the C statistic and C for this model is less than k + 1,where k is the number of independent variables in the model,then the model should be considered biased and therefore undesirable.

(True/False)
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Below is a partial multiple regression ANOVA table. Below is a partial multiple regression ANOVA table.   What is the total sum of squares and the degrees of freedom for the total sum of squares? What is the total sum of squares and the degrees of freedom for the total sum of squares?

(Short Answer)
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The ____________ term describes the effects on y of all factors other than the independent variables in a multiple regression model.

(Multiple Choice)
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Below is a partial multiple regression ANOVA table. Below is a partial multiple regression ANOVA table.   How many observations were in the sample? How many observations were in the sample?

(Short Answer)
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The range of feasible values for the multiple coefficient of determination is from ________.

(Multiple Choice)
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