Exam 15: Multiple Regression Analysis and Model Building

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, hard drive capacity, and-monitor included (1=Yes, 0=No). Given this output, what is the variable, Monitor, called? Also, given the other variables in the model, is Monitor significant in explaining the variation in the dependent variable? Test using a .05 level of alpha.

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 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, given the other variables in the model, whether or not a monitor is included has a significant impact on the price of the personal computer.

If a decision maker has several potential independent variables to select from in building a regression model, the variable that, by itself, will always be the most effective in explaining the variation in the dependent variable will be the variable that has a correlation closest to positive 1.00.

Which of the following is not considered to be a stepwise regression technique?

In a multiple regression model, the adjusted R-square value measures the explained variation in the dependent variable after taking into account the relationship between the sample size and the number of independent variables in the model.

In the best subsets approach to regression analysis, if we start with 4 independent variables, a total of 33 different regression models will actually be computed for possible selection as the best model to use.

If the R-square for a multiple regression model with two independent variables is .64, the correlation between the two independent variables will be .80

If a polynomial model has a larger R-square than a linear model for the same set of data, this is one indication that the polynomial model fits the data better than the linear 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. To incorporate the type of club used, which of the following methods could be used?

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, both independent variables in the model are considered statistically significant at the alpha = 0.05 level.

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 multiple regression model of the form = B0 + B1x + B2x2 + ε is called a second-degree polynomial model.

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.

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, which of the following is true regarding the slope coefficient for Age, where Age represents how many years old the yacht is?

If a decision maker wishes to develop a regression model in which the University Class Standing is a categorical variable with 5 possible levels of response, then he will need to include how many dummy variables?

If one independent variable affects the relationship between a second independent variable and the dependent variable, it is said that there is interaction between the two independent variables.

Second-order polynomial models:

A dummy variable is a dependent variable whose value is set at either zero or one.

One of the variables that are being considered for inclusion in a multiple regression model is marital status of the customer. There are four possible responses listed for this variable. Based on this, three dummy variables will need to be created and incorporated into the regression model.