Exam 15: Multiple Regression Analysis and Model Building

Based on the residual plot below, which of the following is correct? The above residual plot shows:

In a multiple regression analysis with three independent variables the alternative hypothesis for conducting the test of the overall model is: HA : More than one βi ≠ 0.

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, it is possible to determine that 4 of the PCs in the data set did not have a monitor included.

In a multiple regression model, each regression slope coefficient measures the average change in the dependent variable for a one-unit change in the independent variable, all other variables held constant.

The method used in regression analysis for incorporating a categorical variable into the model is by organizing the categorical variable into one or more dummy variables.

Consider the following regression model: then the parabola will open downward and if B2 < 0, then the parabola will open downward.

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 is the critical value for testing the significance of the overall regression model at a 0.05 level of statistical significance?

If a stepwise regression approach is used to enter, one at a time, four variables into a regression model, the resulting regression equation may differ from the regression equation that occurs when all four of the variables are entered at one step.

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.

A regression model of the form: is called a 3rd order polynomial model.

The adjusted R2 value is a particularly important measure when the number of independent variables is large relative to the sample size.

Consider the following residual plot. Given this plot, what conclusion should be reached?

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

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 mileage per gallon. A number of different independent variables were collected. The following correlation matrix was developed: If only one variable were to be brought into the model, which variable should it be if the goal is to explain the highest possible percentage of variation in the dependent variable?

The multiple coefficient of determination is the average of all the squared correlations of the independent variables.

In multiple regression analysis, the model will be developed with one dependent variable and two or more independent variables.

Which of the following statements is true?

Which of the following regression output values is used in computing the variance inflation factors?

Based on the correlations below: we could say that x1 accounts for 64 percent of the variation in y and x2 accounts for 49 percent of the variation in y. So if both xs are included in a multiple regression model, then the resulting R-square = 1.13.