Exam 15: Multiple Regression Analysis and Model Building

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

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?

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.

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,which of the following conclusions can be justified?

In regression model: y = β₀ + β₁x₁ + + ε ,if β₂ < 0,then the value of y is expected to increase with x until x reaches a certain point after which the value of y is expected to decrease.

Interaction exists in a multiple regression model when:

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

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.

A decision maker is considering including two additional variables into a regression model that has as the dependent variable,Total Sales.The first additional variable is the region of the country (North,South,East,or West)in which the company is located.The second variable is the type of business (Manufacturing,Financial,Information Services,or Other).Given this,how many additional variables will be incorporated into the model?

Standard stepwise regression is a good way of identifying potential multicollinearity problems since we are able to see the impact on the model at each step that occurs when a new variable is added to the model.For instance,if bringing in a new variable causes the sign to change on a previously entered variable,we have evidence of multicollinearity.

A regression equation that predicts the price of homes in thousands of dollars is _t = 24.6 + 0.055x₁ - 3.6x₂,where x₂ is a dummy variable that represents whether the house in on a busy street or not.Here x₂ = 1 means the house is on a busy street and x₂ = 0 means it is not.Based on this information,which of the following statements is true?

The following output is for a second-order polynomial regression model where the independent variables are x and x² (x^2).Some of the output has been omitted. Considering the above information,the model explains approximately 56.7 percent of the variation in the y variable.