Exam 13: Introduction to Multiple Regression

TABLE 13-17 Given below are results from the regression analysis where the dependent variable is the number of weeks a worker is unemployed due to a layoff (Unemploy) and the independent variables are the age of the worker (Age), the number of years of education received (Edu), the number of years at the previous job (Job Yr), a dummy variable for marital status (Married: 1 = married, 0 = otherwise), a dummy variable for head of household (Head: 1 = yes, 0 = no) and a dummy variable for management position (Manager: 1 = yes, 0 = no). We shall call this Model 1. Model 2 is the regression analysis where the dependent variable is Unemploy and the independent variables are Age and Manager. The results of the regression analysis are given below: -Referring to Table 13-17 Model 1, which of the following is a correct statement?

TABLE 13-13 An econometrician is interested in evaluating the relationship of demand for building materials to mortgage rates in Los Angeles and San Francisco. He believes that the appropriate model is Y = 10 + 5X1 + 8X2 where X1 = mortgage rate in % X2 = 1 if SF, 0 if LA Y = demand in $100 per capita -Referring to Table 13-13, holding constant the effect of city, each additional increase of 1% in the mortgage rate would lead to an estimated increase of ________ per capita in the mean demand.

TABLE 13-15 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 mean of the percentage of students attending class (% Attendance), mean 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, = : % Attendance, = Salaries and = Spending: -Referring to Table 13-15, which of the following is a correct statement?

TABLE 13-17 Given below are results from the regression analysis where the dependent variable is the number of weeks a worker is unemployed due to a layoff (Unemploy) and the independent variables are the age of the worker (Age), the number of years of education received (Edu), the number of years at the previous job (Job Yr), a dummy variable for marital status (Married: 1 = married, 0 = otherwise), a dummy variable for head of household (Head: 1 = yes, 0 = no) and a dummy variable for management position (Manager: 1 = yes, 0 = no). We shall call this Model 1. Model 2 is the regression analysis where the dependent variable is Unemploy and the independent variables are Age and Manager. The results of the regression analysis are given below: -Referring to Table 13-17 Model 1, which of the following is the correct alternative hypothesis to determine whether there is a significant relationship between percentage of students passing the proficiency test and the entire set of explanatory variables?

TABLE 13-8 A financial analyst wanted to examine the relationship between salary (in $1,000) and four 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: -Referring to Table 13-8, the analyst wants to use a t test to test for the significance of the coefficient of X₃. At a level of significance of 0.01, the department head would decide that β₃ ≠ 0.

TABLE 13-6 One of the most common questions of prospective house buyers pertains to the cost of heating in dollars (Y). To provide its customers with information on that matter, a large real estate firm used the following four 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 Microsoft Excel outputs of two regression models. -In a particular model, the sum of the squared residuals was 847. If the model had 5 independent variables, and the data set contained 40 points, the value of the standard error of the estimate is 24.911.

TABLE 13-17 Given below are results from the regression analysis where the dependent variable is the number of weeks a worker is unemployed due to a layoff (Unemploy) and the independent variables are the age of the worker (Age), the number of years of education received (Edu), the number of years at the previous job (Job Yr), a dummy variable for marital status (Married: 1 = married, 0 = otherwise), a dummy variable for head of household (Head: 1 = yes, 0 = no) and a dummy variable for management position (Manager: 1 = yes, 0 = no). We shall call this Model 1. Model 2 is the regression analysis where the dependent variable is Unemploy and the independent variables are Age and Manager. The results of the regression analysis are given below: -Referring to Table 13-17 Model 1, the null hypothesis H₀: β₁ = β₂ = β₃ = β₄ = β₅ = β₆ = 0 implies that the number of weeks a worker is unemployed due to a layoff is not affected by any of the explanatory variables.

TABLE 13-3 An economist is interested to see how consumption for an economy (in $billions) is influenced by gross domestic product ($billions) and aggregate price (consumer price index). The Microsoft Excel output of this regression is partially reproduced below. -Referring to Table 13-3, what is the estimated mean consumption level for an economy with GDP equal to $4 billion and an aggregate price index of 150?

TABLE 13-8 A financial analyst wanted to examine the relationship between salary (in $1,000) and four 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: -Referring to Table 13-8, the analyst wants to use a t test to test for the significance of the coefficient of X₃. For a level of significance of 0.01, the critical values of the test are ________.

TABLE 13-4 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: -Referring to Table 13-4, at the 0.01 level of significance, what conclusion should the builder reach regarding the inclusion of Income in the regression model?

TABLE 13-2 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 six workers and collects the following information: -Referring to Table 13-2, 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?

TABLE 13-6 One of the most common questions of prospective house buyers pertains to the cost of heating in dollars (Y). To provide its customers with information on that matter, a large real estate firm used the following four 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 Microsoft Excel outputs of two regression models. -Referring to Table 13-6 and allowing for a 1% probability of committing a Type I error, what is the decision and conclusion for the test H₀: β₁ = β₂ = β₃ = β₄ = 0 vs. H₁: At least one βⱼ ≠ 0, j = 1, 2, ..., 4 using Model 1?

TABLE 13-7 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: -Referring to Table 13-7, the estimate of the unit change in the mean of Y per unit change in X₁, holding X₂ constant, is ________.

TABLE 13-14 An automotive engineer would like to be able to predict automobile mileages. She believes that the two most important characteristics that affect mileage are horsepower and the number of cylinders (4 or 6) of a car. She believes that the appropriate model is Y = 40 - 0.05X1 + 20X2 - 0.1X1X2 where X1 = horsepower X2 = 1 if 4 cylinders, 0 if 6 cylinders Y = mileage. -Referring to Table 13-14, the predicted mileage for a 200 horsepower, 4-cylinder car is ________.

TABLE 13-5 A microeconomist wants to determine how corporate sales are influenced by capital and wage spending by companies. She proceeds to randomly select 26 large corporations and record information in millions of dollars. The Microsoft Excel output below shows results of this multiple regression. -Referring to Table 13-5, what is the p-value for testing whether Wages have a negative impact on corporate sales?

TABLE 13-6 One of the most common questions of prospective house buyers pertains to the cost of heating in dollars (Y). To provide its customers with information on that matter, a large real estate firm used the following four 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 Microsoft Excel outputs of two regression models. -Referring to Table 13-6, what can we say about Model 1?

TABLE 13-15 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 mean of the percentage of students attending class (% Attendance), mean 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, = : % Attendance, = Salaries and = Spending: -Referring to Table 13-15, there is sufficient evidence that at least one of the explanatory variables is related to the percentage of students passing the proficiency test at a 5% level of significance.

TABLE 13-5 A microeconomist wants to determine how corporate sales are influenced by capital and wage spending by companies. She proceeds to randomly select 26 large corporations and record information in millions of dollars. The Microsoft Excel output below shows results of this multiple regression. -Referring to Table 13-5, when the microeconomist used a simple linear regression model with sales as the dependent variable and wages as the independent variable, she obtained an r² value of 0.601. What additional percentage of the total variation of sales has been explained by including capital spending in the multiple regression?

TABLE 13-6 One of the most common questions of prospective house buyers pertains to the cost of heating in dollars (Y). To provide its customers with information on that matter, a large real estate firm used the following four 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 Microsoft Excel outputs of two regression models. -Consider a regression in which b₂ = -1.5 and the standard error of this coefficient equals 0.3. To determine whether X₂ is a significant explanatory variable, you would compute an observed t-value of -5.0.

TABLE 13-5 A microeconomist wants to determine how corporate sales are influenced by capital and wage spending by companies. She proceeds to randomly select 26 large corporations and record information in millions of dollars. The Microsoft Excel output below shows results of this multiple regression. -Referring to Table 13-5, at the 0.01 level of significance, what conclusion should the microeconomist reach regarding the inclusion of Capital in the regression model?