Exam 15: Multiple Regression Analysis and Model Building

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

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?

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.

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

A standardized residual is:

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.

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?

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?

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.

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

A model is a representation of an actual system.

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

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 is not an assumption of the multiple regression model?

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

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

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.

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.

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

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