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Exam 15: Multiple Regression Analysis and Model Building

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Question 71

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The editors of a national automotive magazine recently studied 30 different automobiles sold in the United States with the intent of seeing whether they could develop a multiple regression model to explain the variation in highway miles per gallon.A number of different independent variables were collected.The following regression output is the result of using a forward selection stepwise regression approach. Based on the regression output,which of the following statements is true?

A) There is a multicollinearity problem since the standard error of the estimate actually increased when the second variable,"Price as Tested," entered the model.
B) The R-square value increased when the second variable entered the model.
C) Neither variable in the model is statistically significant at the alpha = 0.05 level.
D) The reason that only two variables entered the model is due to the small sample size used in this study.

E) None of the above
F) A) and B)

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Question 72

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A standardized residual is:

A) equal to the sum of the residuals divided by n-1.
B) the ratio of each residual divided by an estimate for the standard deviation of the residuals.
C) a value that is normally distributed with a mean equal to zero and a standard deviation equal to one.
D) None of the above

E) None of the above
F) B) and D)

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Question 73

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A model is a representation of an actual system.

The standard error of the estimate is a term that is used for the standard deviation of the residuals in a multiple regression model.

In a multiple regression analysis involving 15 independent variables and 200 observations,SST = 800 and SSE = 240.The adjusted coefficient of determination is

A complete polynomial model contains terms of all orders less than or equal to the p^th order.

The editors of a national automotive magazine recently studied 30 different automobiles sold in the United States with the intent of seeing whether they could develop a multiple regression model to explain the variation in highway miles per gallon.A number of different independent variables were collected.The following regression output (with some values missing) was recently presented to the editors by the magazine's analysts: Based on this output and your understanding of multiple regression analysis,what percentage of variation in the dependent variable is explained by the regression model?

When a regression equation includes a term such as x₁x₂ where two independent variables are multiplied,this is an interaction term.

The following multiple regression was conducted to attempt to predict the price of yachts based on the independent variables shown. Given this information and your knowledge of multiple regression,determine which,if any,of the four independent variables are statistically significant in explaining the variation in the dependent variable.Use a 0.05 level of significance and use the p-value method.

Stepwise regression is the approach that is always taken when developing a regression model to fit a curvilinear relationship between the dependent and potential independent variables.

When we say that we wish to determine the aptness of a regression model,we are actually saying that we wish to check to see whether the resulting model meets the basic assumptions of regression analysis.

In the model diagnosis step in regression modeling,we are interested in the sign and size of the regression slope coefficients.

One reason for examining the adjusted R-square value in a multiple regression analysis is that the R-square value will increase just by adding additional independent variables to the model,whereas the adjusted R-square accounts for the relationship between the number of independent variables and the sample size and may actually decline if inappropriate independent variables are included in the model.

If the residuals have a constant variance,which of the following should be evident?

It is generally suggested that the sample size in developing a multiple regression model should be at least four times the number of independent variables.

Explain the difference between forward stepwise regression (standard stepwise),forward selection,and all possible subsets regression approaches.

Which of the following is not an assumption of the multiple regression model?

A multiple regression is shown for a data set of yachts where the dependent variable is the price in thousands of dollars. Given this information,what is the null hypothesis for testing the overall model?

Which of the following would best describe the situation that a second-degree polynomial regression equation would be used to model?

Golf handicaps are used to allow players of differing abilities to play against one another in a fair match.Recently a sample of golfers was selected in an effort to develop a model for explaining the difference in handicaps.One independent variable of interest is the number of rounds played per year.Another is whether or not the player is using an "original" name brand club or a copy.In recent years,a number of smaller golf club manufacturers have attempted to copy major golf club designs and sell "copies" of original clubs such as the Big Bertha by Calloway.The resulting regression analysis containing both Rounds Played and a Dummy variable for Club Used is shown as follows: Given this information,which of the following statements is not correct?