Exam 14: Introduction to Multiple Regression

TABLE 14-4 A real estate builder wishes to determine how house size (House) is influenced by family income (Income), family size (Size), and education of the head of household (School). House size is measured in hundreds of square feet, income is measured in thousands of dollars, and education is in years. The builder randomly selected 50 families and ran the multiple regression. Microsoft Excel output is provided below: SUMMARY OUTPUT Regression Statistics ANOVA -Referring to Table 14-4, at the 0.01 level of significance, what conclusion should the builder draw regarding the inclusion of Income in the regression model?

TABLE 14-6 One of the most common questions of prospective house buyers pertains to the average cost of heating in dollars (Y). To provide its customers with information on that matter, a large real estate firm used the following 4 variables to predict heating costs: the daily minimum outside temperature in degrees of Fahrenheit (X₁), the amount of insulation in inches (X₂), the number of windows in the house (X₃), and the age of the furnace in years (X₄). Given below are the EXCEL outputs of two regression models. Model 1 Note: 2.96869E-05 = 2.96869×10^-5 Model 2 Note: 2.9036E-06 = 2.9036×10^-6 -Referring to Table 14-6, the estimated value of the partial regression parameter β₁ in Model 1 means that

TABLE 14-9 You decide to predict gasoline prices in different cities and towns in the United States for your term project. Your dependent variable is price of gasoline per gallon and your explanatory variables are per capita income, the number of firms that manufacture automobile parts in and around the city, the number of new business starts in the last year, population density of the city, percentage of local taxes on gasoline, and the number of people using public transportation. You collected data of 32 cities and obtained a regression sum of squares SSR= 122.8821. Your computed value of standard error of the estimate is 1.9549. -Referring to Table 14-9, if variables that measure the number of new business starts in the last year and population density of the city were removed from the multiple regression model, which of the following would be true?

TABLE 14-10 You worked as an intern at We Always Win Car Insurance Company last summer. You notice that individual car insurance premiums depend very much on the age of the individual, the number of traffic tickets received by the individual, and the population density of the city in which the individual lives. You performed a regression analysis in EXCEL and obtained the following information: -Referring to Table 14-10, to test the significance of the multiple regression model, what are the degrees of freedom?

TABLE 14-7 The department head of the accounting department wanted to see if she could predict the GPA of students using the number of course units (credits) and total SAT scores of each. She takes a sample of students and generates the following Microsoft Excel output: SUMMARY OUTPUT Regression Statistics ANOVA -Referring to Table 14-7, the department head wants to use a t test to test for the significance of the coefficient of X₁. The value of the test statistic is ________.

TABLE 14-8 A financial analyst wanted to examine the relationship between salary (in $1,000) and 4 variables: age (X₁ = Age), experience in the field (X₂ = Exper), number of degrees (X₃ = Degrees), and number of previous jobs in the field (X₄ = Prevjobs). He took a sample of 20 employees and obtained the following Microsoft Excel output: SUMMARY OUTPUT Regression Statistics ANOVA -Referring to Table 14-8, the value of the coefficient of multiple determination, r²_Y.1234, is ________.

TABLE 14-4 A real estate builder wishes to determine how house size (House) is influenced by family income (Income), family size (Size), and education of the head of household (School). House size is measured in hundreds of square feet, income is measured in thousands of dollars, and education is in years. The builder randomly selected 50 families and ran the multiple regression. Microsoft Excel output is provided below: SUMMARY OUTPUT Regression Statistics ANOVA -Referring to Table 14-4, which of the following values for the level of significance is the smallest for which at least two explanatory variables are significant individually?

A multiple regression is called "multiple" because it has several data points.

TABLE 14-2 A professor of industrial relations believes that an individual's wage rate at a factory (Y) depends on his performance rating (X₁) and the number of economics courses the employee successfully completed in college (X₂). The professor randomly selects 6 workers and collects the following information: -The variation attributable to factors other than the relationship between the independent variables and the explained variable in a regression analysis is represented by

TABLE 14-7 The department head of the accounting department wanted to see if she could predict the GPA of students using the number of course units (credits) and total SAT scores of each. She takes a sample of students and generates the following Microsoft Excel output: SUMMARY OUTPUT Regression Statistics ANOVA -Referring to Table 14-7, the predicted GPA for a student carrying 15 course units and who has a total SAT of 1,100 is ________.

Multiple regression is the process of using several independent variables to predict a number of dependent variables.

TABLE 14-10 You worked as an intern at We Always Win Car Insurance Company last summer. You notice that individual car insurance premiums depend very much on the age of the individual, the number of traffic tickets received by the individual, and the population density of the city in which the individual lives. You performed a regression analysis in EXCEL and obtained the following information: -Referring to Table 14-10, to test the significance of the multiple regression model, what is the form of the null hypothesis?

TABLE 14-13 An econometrician is interested in evaluating the relation of demand for building materials to mortgage rates in Los Angeles and San Francisco. He believes that the appropriate model is -Referring to Table 14-13, the predicted demand in Los Angeles when the mortgage rate is 8% is ________.

TABLE 14-1 A manager of a product sales group believes the number of sales made by an employee (Y) depends on how many years that employee has been with the company (X₁) and how he/she scored on a business aptitude test (X₂). A random sample of 8 employees provides the following: -Referring to Table 14-1, for these data, what is the estimated coefficient for the variable representing scores on the aptitude test, b₂?

TABLE 14-11 A weight-loss clinic wants to use regression analysis to build a model for weight-loss of a client (measured in pounds). Two variables thought to affect weight loss are client's length of time on the weight loss program and time of session. These variables are described below: Data for 12 clients on a weight-loss program at the clinic were collected and used to fit the interaction model: Partial output from Microsoft Excel follows: Regression Statistics ANOVA -Referring to Table 14-11, what is the experimental unit for this analysis?

TABLE 14-4 A real estate builder wishes to determine how house size (House) is influenced by family income (Income), family size (Size), and education of the head of household (School). House size is measured in hundreds of square feet, income is measured in thousands of dollars, and education is in years. The builder randomly selected 50 families and ran the multiple regression. Microsoft Excel output is provided below: SUMMARY OUTPUT Regression Statistics ANOVA -Referring to Table 14-4, the observed value of the F-statistic is missing from the printout. What are the degrees of freedom for this F-statistic?

TABLE 14-2 A professor of industrial relations believes that an individual's wage rate at a factory (Y) depends on his performance rating (X₁) and the number of economics courses the employee successfully completed in college (X₂). The professor randomly selects 6 workers and collects the following information: -Referring to Table 14-2, suppose an employee had never taken an economics course and managed to score a 5 on his performance rating. What is his estimated expected wage rate?

A dummy variable is used as an independent variable in a regression model when

TABLE 14-15 The superintendent of a school district wanted to predict the percentage of students passing a sixth-grade proficiency test. She obtained the data on percentage of students passing the proficiency test (% Passing), daily average of the percentage of students attending class (% Attendance), average teacher salary in dollars (Salaries), and instructional spending per pupil in dollars (Spending) of 47 schools in the state. Following is the multiple regression output with Y = % Passing as the dependent variable, X₁= % Attendance, X₂= Salaries and X₃= Spending: Note: -Referring to Table 14-15, there is sufficient evidence that all of the explanatory variables is related to the percentage of students passing the proficiency test.

TABLE 14-4 A real estate builder wishes to determine how house size (House) is influenced by family income (Income), family size (Size), and education of the head of household (School). House size is measured in hundreds of square feet, income is measured in thousands of dollars, and education is in years. The builder randomly selected 50 families and ran the multiple regression. Microsoft Excel output is provided below: SUMMARY OUTPUT Regression Statistics ANOVA -Referring to Table 14-4, what are the regression degrees of freedom that are missing from the output?