Exam 15: Multiple Regression Analysis and Model Building

In a multiple regression,the dependent variable is house value (in '000$)and one of the independent variables is a dummy variable,which is defined as 1 if a house has a garage and 0 if not.The coefficient of the dummy variable is found to be 5.4 but the t-test reveals that it is not significant at the 0.05 level.Which of the following is true?

On a survey there is a question that asks whether someone lives in a house,apartment,or condominium.These three responses could be coded in a dummy variable using value 0,1,and 2.

Which of the following is not an indication of potential multicollinearity problems?

The following output is for a second-order polynomial regression model where the independent variables are x and x² (x^2 in output).Some of the output has been omitted. Considering the above information,it is clear that the second-order polynomial model will be a more effective regression model for explaining the variation in the y variable than would a linear regression model involving only one independent variable,x.

In a forward stepwise regression process,it is actually possible for the R-square value to decline if variables are added to the regression model that do not help to explain the variation in the dependent variable.

To check out whether the regression assumption involving normality of the error terms is valid,it is appropriate to construct a normal probability plot.If this plot forms a straight line from the lower left-hand corner diagonally up to the upper right-hand corner,the error terms may be assumed to be normally distributed.

If one or more of the regression assumptions has been violated this means that the current regression model is not the best one for this data set,and another model should be sought.

A major car magazine has recently collected data on 30 leading cars in the U.S.market.It is interested in building a multiple regression model to explain the variation in highway miles.The following correlation matrix has been computed from the data collected: Based on this information,if we test using a 0.05 level of significance,the critical value for testing whether any of the independent variables are significantly correlated with the dependent variable is t = 2.0484.

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,which of the following statements is true?

A decision maker has five potential independent variables with which to build a regression model to explain the variation in the dependent variable.At step 1,variable x₃ enters the regression model.Which of the following indicates which of the four remaining independent variables will be next to enter the model?

A study has recently been conducted by a major computer magazine publisher in which the objective was to develop a multiple regression model to explain the variation in price of personal computers.Three independent variables were used.The following computer printout shows the final output.However,several values are omitted from the printout. Given this information,the calculated test statistic for the regression slope coefficient on the variable RAM,is approximately 1.54.

The three components of the regression model-building process are model specification,model fitting,and model diagnosis.

A study has recently been conducted by a major computer magazine publisher in which the objective was to develop a multiple regression model to explain the variation in price of personal computers.Three quantitative independent variables were used along with one qualitative variable.The qualitative variable was coded 1 if the computer included a monitor,0 otherwise.The following computer printout shows the final output. Based on this information,and with a 0.05 level of significance,which of the following conclusions can be justified?

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.To incorporate the type of club used,which of the following methods could be used?

A major car magazine has recently collected data on 30 leading cars in the U.S.market.It is interested in building a multiple regression model to explain the variation in highway miles.The following correltion matrix has been computed from the data collected: The analysts also produced the following multiple regression output using curb weight,cylinders,and horsepower as the three independent variables.Note,a number of the output fields are missing,but can be determined from the information provided. Based on the information provided,holding the other variables constant,increasing horsepower by one unit results in an average decrease in highway mileage by 0.016 miles per gallon.

The adjusted R² value can be larger or smaller that the R² values depending on the data set.

A correlation matrix shows the correlation between each independent variable and the dependent variable but gives no information about the potential for multicollinearity problems.

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,conduct the appropriate test to determine whether the overall regression model is statistically significant at the 0.05 level of significance using the critical value method.

The following regression output is the result of a multiple regression application in which we are interested in explaining the variation in retail price of personal computers based on three independent variables,CPU speed,RAM,and hard drive capacity.However,some of the regression output has been omitted. Given this information and your knowledge of multiple regression,what is the adjusted R-square value?

In a study of employees at a local company,the human resource manager wants to develop a multiple regression model to explain the difference in employee wage rates.She is thinking of including a variable,degree status,in which the following categories exist: no degree,H.S.degree,junior college degree,bachelor degree,graduate degree.Two other variables are being considered;Age and Years With the Company.Given this,the appropriate number of variables in the model will be six.