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Exam 13: Multiple Regression Analysis

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Question 31

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If stepwise procedure is used, a variable selected at an earlier step can be removed from the model if, in the presence of other variables, it no longer contributes significantly to explaining the variation in the dependent variable y.

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Question 32

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In a simple linear regression problem, the following pairs of are given: (6.75, 7.42) , (8.96, 8.06) , (10.30, 11.65) , and (13.24, 12.15) . Then, the sum of squares for error is:

A) 39.2500
B) -0.0300
C) 4.2695
D) 39.2800

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Question 33

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Multiple linear regression is an extension of simple linear regression to allow for more than one dependent variable.

A chemist was interested in examining the effects of four chemicals on a chemical process yield. Let , i = 1, 2, 3, 4, represent the effects of the four chemicals, respectively and y be the process yield. The chemist's first instinct was to include each of the chemicals in the equation in a linear fashion. After the initial analysis, the chemist decided to remove chemicals 2 and 3 from the model. Complete model: Reduced model: Use the statistical software output above to test whether the reduced model is adequate at the 0.05 level of significance. Test Statistic: F = ______________ Reject Region: Reject if F > ______________ Conclusion: ______________ There ______________ evidence to indicate that at least one of or is not 0. The reduced model ______________ adequate.

Which of the following methods is used to help assess whether the regression model meets the assumption of having normally distributed residuals?

In testing the significance of a multiple regression model in which there are three independent variables, the null hypothesis is .

If you wish to develop a multiple regression model that includes a qualitative variable; education status, in which the following categories exist: no degree, high school diploma, junior college degree, bachelor degree, and graduate degree, you need to code the categories as 1, 2, 3, 4, and 5.

Which of the following statements is false?

Assume you are considering including two additional qualitative variables into a regression model. The first variable has 4 categories, and the second variable has 4 categories as well. Given this information, how many indicator variables will be incorporated into the model?

Multicollinearity is present if the dependent variable is linearly related to one of the explanatory variables.

Given MSR = 345 and MSE = 431.25, the value of the F-statistic:

An estimated partial-regression coefficient gives the partial change in y for a unit change in that independent variable, while holding other independent variables constant.

In stepwise regression procedure, the independent variable with the largest F-statistic, or equally with the smallest p-value, is chosen as the first entering variable. The standard, also called the F-to-enter, is usually set at F equals:

A multiple regression model has the form . The coefficient is interpreted as the change in y per unit change in .

Typical symptoms of the presence of multicollinearity include:

An estimated partial-regression coefficient is the coefficient of a dependent variable in an estimated multiple-regression equation.

In a multiple regression model, the regression coefficients are calculated such that the quantity is minimized.

A dummy or indicator variable is a dependent variable whose values are either 0.0 or 1.0.

What is the effect of multicollinearity on the estimated regression coefficients?

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