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 the correct null hypothesis to test whether age has any effect on the number of weeks a worker is unemployed due to a layoff, while holding constant the effect of all the other independent variables?

TABLE 13-11 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: Y = Weight loss (in pounds) X1 = Length of time in weight-loss program (in months) X2 = 1 if morning session, 0 if not X3 = 1 if afternoon session, 0 if not (Base level = evening session) Data for 12 clients on a weight-loss program at the clinic were collected and used to fit the interaction model: Y = β0 + β1X1 + β2X2 + β3X3 + β4X1X2 + β5X1X3 + ε Partial output from Microsoft Excel follows: -In a multiple regression model, the adjusted

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, for these data, what is the value for the regression constant, b₀?

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, what is the p-value of the test statistic to determine whether there is a significant relationship between the number of weeks a worker is unemployed due to a layoff and the entire set of 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, to test whether aggregate price index has a positive impact on consumption, the p-value is ________.

TABLE 13-16 What are the factors that determine the acceleration time (in sec.) from 0 to 60 miles per hour of a car? Data on the following variables for 171 different vehicle models were collected: Accel Time: Acceleration time in sec. Cargo Vol: Cargo volume in cu. ft. HP: Horsepower MPG: Miles per gallon SUV: 1 if the vehicle model is an SUV with Coupe as the base when SUV and Sedan are both 0 Sedan: 1 if the vehicle model is a sedan with Coupe as the base when SUV and Sedan are both 0 The regression results using acceleration time as the dependent variable and the remaining variables as the independent variables are presented below. The various residual plots are as shown below. The coefficient of multiple determination for the regression model using each of the 5 variables Xj as the dependent variable and all other X variables as independent variables (Rj2) are, respectively, 0.7461, 0.5676, 0.6764, 0.8582, 0.6632. -Referring to Table 13-16, what is the p-value of the test statistic to determine whether MPG makes a significant contribution to the regression model in the presence of the other independent variables at a 5% level of significance?

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, what are the residual degrees of freedom that are missing from the output?

TABLE 13-16 What are the factors that determine the acceleration time (in sec.) from 0 to 60 miles per hour of a car? Data on the following variables for 171 different vehicle models were collected: Accel Time: Acceleration time in sec. Cargo Vol: Cargo volume in cu. ft. HP: Horsepower MPG: Miles per gallon SUV: 1 if the vehicle model is an SUV with Coupe as the base when SUV and Sedan are both 0 Sedan: 1 if the vehicle model is a sedan with Coupe as the base when SUV and Sedan are both 0 The regression results using acceleration time as the dependent variable and the remaining variables as the independent variables are presented below. The various residual plots are as shown below. The coefficient of multiple determination for the regression model using each of the 5 variables Xj as the dependent variable and all other X variables as independent variables (Rj2) are, respectively, 0.7461, 0.5676, 0.6764, 0.8582, 0.6632. -Referring to Table 13-16, ________ of the variation in Accel Time can be explained by the five independent variables after taking into consideration the number of independent variables and the number of observations.

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 fitted model for predicting mileages for 6-cylinder cars 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 Wages?

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 test whether being married or not makes a difference in the mean number of weeks a worker is unemployed due to a layoff, while holding constant the effect of all the other independent variables?

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, suppose the builder wants to test whether the coefficient on School is significantly different from 0. What is the value of the relevant t-statistic?

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, which of the independent variables in the model are significant at the 5% level?

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 $2 billion and an aggregate price index of 90?

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 fitted model for predicting mileages for 4-cylinder cars is ________.

TABLE 13-10 You worked as an intern at We Always Win Car Insurance Company last summer. You noticed 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 Microsoft Excel and obtained the following information: -Referring to Table 13-10, the 99% confidence interval for the change in mean insurance premiums of a person who has become one year older (i.e., the slope coefficient for AGE)is -0.82 ± ________.

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. -If you have taken into account all relevant explanatory factors, the residuals from a multiple regression model should be random.

TABLE 13-16 What are the factors that determine the acceleration time (in sec.) from 0 to 60 miles per hour of a car? Data on the following variables for 171 different vehicle models were collected: Accel Time: Acceleration time in sec. Cargo Vol: Cargo volume in cu. ft. HP: Horsepower MPG: Miles per gallon SUV: 1 if the vehicle model is an SUV with Coupe as the base when SUV and Sedan are both 0 Sedan: 1 if the vehicle model is a sedan with Coupe as the base when SUV and Sedan are both 0 The regression results using acceleration time as the dependent variable and the remaining variables as the independent variables are presented below. The various residual plots are as shown below. The coefficient of multiple determination for the regression model using each of the 5 variables Xj as the dependent variable and all other X variables as independent variables (Rj2) are, respectively, 0.7461, 0.5676, 0.6764, 0.8582, 0.6632. -Referring to Table 13-16, the error appears to be right-skewed.

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

TABLE 13-16 What are the factors that determine the acceleration time (in sec.) from 0 to 60 miles per hour of a car? Data on the following variables for 171 different vehicle models were collected: Accel Time: Acceleration time in sec. Cargo Vol: Cargo volume in cu. ft. HP: Horsepower MPG: Miles per gallon SUV: 1 if the vehicle model is an SUV with Coupe as the base when SUV and Sedan are both 0 Sedan: 1 if the vehicle model is a sedan with Coupe as the base when SUV and Sedan are both 0 The regression results using acceleration time as the dependent variable and the remaining variables as the independent variables are presented below. The various residual plots are as shown below. The coefficient of multiple determination for the regression model using each of the 5 variables Xj as the dependent variable and all other X variables as independent variables (Rj2) are, respectively, 0.7461, 0.5676, 0.6764, 0.8582, 0.6632. -Referring to Table 13-16, there is enough evidence to conclude that MPG makes a significant contribution to the regression model in the presence of the other independent variables at a 5% level of significance.