Exam 15: Multiple Regression Analysis and Model Building

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 from a multiple regression model: The variables t, t2, and t3 represent the t, t-squared, and t-cubed respectively where t is the indicator of time from periods t = 1 to t = 20. Which of the following best describes the type of forecasting model that has been developed?

Backward elimination is the reverse of the forward stepwise selection procedure. The resulting model can be different than the forward model.

Interaction exists in a multiple regression model when:

Under what circumstances does the variance inflation factor signal that multicollinearity may be a problem?

A decision maker is considering constructing a multiple regression model with two independent variables. The correlation between x1 and y is 0.70, and the correlation between variable x2 and y is 0.50. Based on this, the regression model containing both independent variables will explain 74 percent of the variation in the dependent variable.

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: If the independent variables, curb weight, cylinders, and horsepower are used together in a multiple regression model, there may be a potential problem with multicollinearity since horsepower and cylinders are highly correlated.

Consider the following scatter plot: Given the apparent relationship between the x and y variable, a possible curvilinear regression model to consider would be a second-order polynomial model.

The forward selection method and the backward elimination method will always lead to choosing the same final regression model.

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

A useful method for determining whether a linear function is the appropriate function to describe the relationship between the x and y variable is a residual plot in which the residuals are plotted on the vertical axis and the independent variable is on the horizontal axis.

In a study of individuals' television viewing hours per week, the predictors are defined as income, job in terms of hours per week, number of people living in the household and stress level. The stress level is the only categorical variable with self-reported levels of stress as 1 = none to 5 = extreme. The stress level can be used as a number in the regression equation.

Interaction terms and polynomial terms should not be included in the same multiple regression model.

Multicollinearity occurs when one or more independent variables is highly correlated with the dependent variable.

The best subsets method will involve trying fewer different regression models than stepwise regression.

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: 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, the 95 percent confidence interval estimate for regression slope coefficient for horsepower is approximately - 0.041 to 0.009 and since this interval crosses zero, we are unable to conclude that the regression slope coefficient for this variable is different from zero.

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.

A forecasting model of the following form was developed: Which of the following best describes the form of this model?

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

Which of the following is the difference between forward selection and standard stepwise regression?