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Exam 17: Multiple Regression

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Question 21

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When the independent variables are correlated with one another in a multiple regression analysis, this condition is called:

A) heteroscedasticity.
B) homoscedasticity.
C) multicollinearity.
D) None of these choices.

E) A) and D)
F) C) and D)

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Question 22

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In order to test the validity of a multiple regression model involving 5 independent variables and 30 observations, the numerator and denominator degrees of freedom for the critical value of F are, respectively,

A) 5 and 30
B) 6 and 29
C) 5 and 24
D) 6 and 25

E) A) and D)
F) B) and C)

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Question 23

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If multicollinearity exists among the independent variables included in a multiple regression model, then:

In a multiple regression model, the following statistics are given: SSE = 100, R² = 0.995, k = 5, and n = 15. Then, the coefficient of determination adjusted for degrees of freedom is:

Real Estate Builder: A real estate builder wishes to determine how house size is influenced by family income, family size, and education of the head of household. House size is measured in hundreds of square feet, income is measured in thousands of dollars, and education is measured in years. A partial computer output is shown below. SUMMARY OUTPUT ANOVA -Interpret the value of the Adjusted R-Square.

In multiple regression analysis, the ratio MSR/MSE yields the:

In regression analysis, the total variation in the dependent variable y, measured by , can be decomposed into two parts: the explained variation, measured by SSR, and the unexplained variation, measured by SSE.

Multicollinearity affects the t-tests of the individual coefficients as well as the F-test in the analysis of variance for regression because the F-test combines the t-tests into a single test.

Does it appear that the errors are normally distributed? Explain.

In a multiple regression analysis involving 4 independent variables and 30 data points, the number of degrees of freedom associated with the sum of squares for error, SSE, is 25.

One method of diagnosing heteroscedasticity is to plot the residuals against the predicted values of y, then look for a change in the spread of the plotted values.

A(n) ____________________ value of the F-test statistic indicates that the multiple regression model is valid.

A multiple regression analysis involving three independent variables and 25 data points results in a value of 0.769 for the unadjusted coefficient of determination. Then, the adjusted coefficient of determination is:

____________________ is a condition that exists when independent variables are correlated with one another.

The problem of multicollinearity arises when the:

The least squares method requires that the variance of the error variable $\varepsilon$ is a constant no matter what the value of x is. When this requirement is violated, the condition is called:

In multiple regression analysis, when the response surface (the graphical depiction of the regression equation) hits every single point, the sum of squares for error SSE = 0, the standard error of estimate s _{$\varepsilon$} = 0, and the coefficient of determination R² = 1.

In multiple regression analysis, the adjusted coefficient of determination is adjusted for the number of independent variables and the sample size.

A multiple regression model is assessed to be poor if the error sum of squares SSE and the standard error of estimate s _{$\varepsilon$} are both large, the coefficient of determination R² is close to 0, and the value of the test statistic F is large.

Student's Final Grade: A statistics professor investigated some of the factors that affect an individual student's final grade in her course. She proposed the multiple regression model , where y is the final grade (out of 100 points), x₁ is the number of lectures skipped, x₂ is the number of late assignments, and x₃ is the midterm exam score (out of 100). The professor recorded the data for 50 randomly selected students. The computer output is shown below. THE REGRESSION EQUATION IS ANALYSIS OF VARIANCE -Does this data provide enough evidence at the 1% significance level to conclude that the final grade and the midterm exam score are positively linearly related?