Exam 17: Multiple Regression

When the independent variables are correlated with one another in a multiple regression analysis, this condition is called:

There are several clues to the presence of multicollinearity. One clue is when an independent variable is added or deleted, the regression coefficients for the other variables ____________________.

In reference to the equation , the value - 0.80 is the y -intercept.

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 ( x ₁), the cholesterol level ( x ₂), and the number of points that the individual's blood pressure exceeded the recommended value ( x ₃). 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 + 1.79 x ₁ - 0.021 x ₂ - 0.061 x ₃ S = 9.47 R - Sq = 22.5% {Life Expectancy Narrative} Interpret the coefficient b ₃.

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), x ₁ is the number of lectures skipped, x ₂ is the number of late assignments, and x ₃ 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 S = 13.74 R - Sq = 30.0%     {Student's Final Grade Narrative} Does this data provide enough evidence at the 5% significance level to conclude that the final grade and the number of late assignments are negatively linearly related?

One method of diagnosing heteroscedasticity is to plot the residuals against the predicted values of y , then look for a change in the spread of the plotted values.

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 {Real Estate Builder Narrative} Which of the following values for the level of significance is the smallest for which all explanatory variables are significant individually: a = .01, .05, .10, or .15?

A multiple regression model involves 10 independent variables and 30 observations. If we want to test at the 5% significance level whether one of the coefficients is = 0 (vs. ¹ 0)the critical value will be:

An adverse effect of multicollinearity is that the estimated regression coefficients of the independent variables that are correlated tend to have large sampling ____________________.

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), x ₁ is the number of lectures skipped, x ₂ is the number of late assignments, and x ₃ 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 S = 13.74 R - Sq = 30.0% {Student's Final Grade Narrative} Interpret the coefficient b ₁.

The coefficient of determination ranges from:

One clue to the presence of multicollinearity is an independent variable known to be an important predictor that ends up having a regression coefficient that is not ____________________.

In reference to the equation , the value 0.12 is the average change in y per unit change in x ₁, when x ₂ is held constant.

In multiple regression, the standard error of estimate is defined by , where n is the sample size and k is the number of independent variables.

____________________ is a condition that exists when independent variables are correlated with one another.

A multiple regression model has the form . As x ₃ increases by one unit, with x ₁ and x ₂ held constant, the y on average is expected to:

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       {Real Estate Builder Narrative} 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?

For a multiple regression model, the following statistics are given: Total variation in y = 500, SSE = 80, and n = 25. Then, the coefficient of determination is:

In multiple regression analysis, the adjusted coefficient of determination is adjusted for the number of independent variables and the sample size.

Marc Anthony Concert At a recent Marc Anthony concert, a survey was conducted that asked a random sample of 20 people their age and how many concerts they have attended since the first of the year. The following data were collected: An Excel output follows: {Marc Anthony Concert Narrative} Use the regression equation to determine the predicted values of y .