Exam 15: Multiple Regression Analysis and Model Building

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.

A multiple regression model of the form = B₀ + B₁x + B₂x² + B₃x³ + ε is called an expanded second-order polynomial since it contains all the terms up to x³ in the model at one time.

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

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 this information,the standard error of the estimate for the regression model is approximately 6.46 miles per gallon.

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

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.Included in these were two variables described as follows: If these two variables are to be included in a regression model,how many additional variables will be needed?

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 value for the standard error of the estimate?

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

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

To determine the aptness of the model,which of the following would most likely be performed?

Residuals are calculated by e = y - .

If given a choice in collecting data on age for use as an independent variable in a regression model,a decision maker would generally prefer to record the actual age rather than an age category so as to avoid using dummy variables.

Assume that a time series plot takes the form of that shown in the following graph: Given this plot,which of the following models would likely give the best fit?

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 is the result of using a forward selection stepwise regression approach. Based on the regression output,which of the following statements is true?

The variance inflation factor (VIF)provides a measure for each independent variable of how much multicollinearity is associated with that particular independent variable.

A multiple regression was conducted to predict the price of yachts in thousands of dollars.A dummy variable was included to indicate whether or not the yacht has a flying bridge,where 0 means "no" and 1 means "yes." Which of the following statements is correct using the 0.10 level of significance?

Which of the following is an advantage of using stepwise regression compared to just entering all the independent variables at one time?

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?

In a multiple regression model where three independent variables are included in the model,the percentage of explained variation will be equal to the square of the sum of the correlations between the independent variables and the dependent variable.

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,using an alpha = .05 level,you can conclude that the overall regression model is statistically significant.