Exam 17: Multiple Regression

When an explanatory variable is dropped from a multiple regression model, the coefficient of determination can increase.

The computer output for the multiple regression model is shown below. However, because of a printer malfunction some of the results are not shown. These are indicated by the boldface letters a to i. Fill in the missing results (up to three decimal places). ANALYSIS OF VARIANCE

Life Expectancy An actuary wanted to develop a model to predict how long individuals will live. After consulting a number of physicians, she collected the age at death (y), the average number of hours of exercise per week (x₁), the cholesterol level (x₂), and the number of points that the individual's blood pressure exceeded the recommended value (x₃). A random sample of 40 individuals was selected. The computer output of the multiple regression model is shown below. THE REGRESSION EQUATION IS y = 55.8 + 1.79x₁ -0.021x₂ - 0.061x₃ ANALYSIS OF VARIANCE -{Life Expectancy Narrative} Interpret the coefficient b₂.

Real Estate Builder: A real estate builder wishes to determine how house size is influenced by family income, family size, and education of the head of household. House size is measured in hundreds of square feet, income is measured in thousands of dollars, and education is measured in years. A partial computer output is shown below. SUMMARY OUTPUT ANOVA -One individual in the sample had an annual income of $10,000, a family size of 1, and an education of 8 years. This individual owned a home with an area of 1,000 square fee (House = 10.00). What is the residual (in hundreds of square feet) for this data point?

There are several clues to the presence of multicollinearity. One clue is when a regression coefficient exhibits the wrong ____________________.

When an additional explanatory variable is introduced into a multiple regression model, the coefficient of determination will never decrease.

Which of the following statements regarding multicollinearity is not true?

Discuss two indicators that can be found in an analysis that suggest multicollinearity is present.

For a multiple regression model, the total variation in y can be expressed as:

Life Expectancy An actuary wanted to develop a model to predict how long individuals will live. After consulting a number of physicians, she collected the age at death (y), the average number of hours of exercise per week (x₁), the cholesterol level (x₂), and the number of points that the individual's blood pressure exceeded the recommended value (x₃). A random sample of 40 individuals was selected. The computer output of the multiple regression model is shown below. THE REGRESSION EQUATION IS y = 55.8 + 1.79x₁ -0.021x₂ - 0.061x₃ ANALYSIS OF VARIANCE -{Life Expectancy Narrative} What is the adjusted coefficient of determination in this situation? What does this statistic tell you?

Some of the requirements for the error variable in a multiple regression model are that the standard deviation is a(n) ____________________ and the errors are ____________________.

Real Estate Builder: A real estate builder wishes to determine how house size is influenced by family income, family size, and education of the head of household. House size is measured in hundreds of square feet, income is measured in thousands of dollars, and education is measured in years. A partial computer output is shown below. SUMMARY OUTPUT ANOVA -Which of the following values for the level of significance is the smallest for which all explanatory variables are significant individually: $\alpha$ = .01, .05, .10, or .15?

The parameter estimates are biased when multicollinearity is present in a multiple regression equation.

A multiple regression model has the form . The coefficient b₁ is interpreted as the change in the average value of y per unit change in ________ holding ________ constant.

From the coefficient of determination, we cannot detect the strength of the relationship between the dependent variable y and any individual independent variable.

Student's Final Grade: A statistics professor investigated some of the factors that affect an individual student's final grade in her course. She proposed the multiple regression model , where y is the final grade (out of 100 points), x₁ is the number of lectures skipped, x₂ is the number of late assignments, and x₃ is the midterm exam score (out of 100). The professor recorded the data for 50 randomly selected students. The computer output is shown below. THE REGRESSION EQUATION IS ANALYSIS OF VARIANCE -Interpret the coefficient b₂.

In reference to the equation , the value 0.60 is the average change in y per unit change in x₂, regardless of the value of x₁.

Three predictor variables are being considered for use in a linear regression model. Given the correlation matrix below, does it appear that multicollinearity could be a problem?

Real Estate Builder: A real estate builder wishes to determine how house size is influenced by family income, family size, and education of the head of household. House size is measured in hundreds of square feet, income is measured in thousands of dollars, and education is measured in years. A partial computer output is shown below. SUMMARY OUTPUT ANOVA -Suppose the builder wants to test whether the coefficient on education is significantly different from 0. What is the value of the relevant t-statistic?

In a multiple regression analysis, there are 20 data points and 4 independent variables, and the sum of the squared differences between observed and predicted values of y is 180. The standard error of estimate will be: