Exam 14: Introduction to Multiple Regression

TABLE 14-18 A logistic regression model was estimated in order to predict the probability that a randomly chosen university or college would be a private university using information on mean total Scholastic Aptitude Test score (SAT)at the university or college,the room and board expense measured in thousands of dollars (Room/Brd),and whether the TOEFL criterion is at least 550 (Toefl550 = 1 if yes,0 otherwise.)The dependent variable,Y,is school type (Type = 1 if private and 0 otherwise). The Minitab output is given below: -Referring to Table 14-18,which of the following is the correct interpretation for the Tofel500 slope coefficient?

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

TABLE 14-5 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 14-5,the observed value of the F-statistic is given on the printout as 25.432.What are the degrees of freedom for this F-statistic?

In a multiple regression model,the value of the coefficient of multiple determination

TABLE 14-19 The marketing manager for a nationally franchised lawn service company would like to study the characteristics that differentiate home owners who do and do not have a lawn service.A random sample of 30 home owners located in a suburban area near a large city was selected; 15 did not have a lawn service (code 0)and 15 had a lawn service (code 1).Additional information available concerning these 30 home owners includes family income (Income,in thousands of dollars),lawn size (Lawn Size,in thousands of square feet),attitude toward outdoor recreational activities (Atitude 0 = unfavorable,1 = favorable),number of teenagers in the household (Teenager),and age of the head of the household (Age). The Minitab output is given below: -Referring to Table 14-19,there is not enough evidence to conclude that Age makes a significant contribution to the model in the presence of the other independent variables at a 0.05 level of significance.

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 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 14-18 A logistic regression model was estimated in order to predict the probability that a randomly chosen university or college would be a private university using information on mean total Scholastic Aptitude Test score (SAT)at the university or college,the room and board expense measured in thousands of dollars (Room/Brd),and whether the TOEFL criterion is at least 550 (Toefl550 = 1 if yes,0 otherwise.)The dependent variable,Y,is school type (Type = 1 if private and 0 otherwise). The Minitab output is given below: -Referring to Table 14-18,what is the estimated odds ratio for a school with an mean SAT score of 1250,a TOEFL criterion that is at least 550,and the room and board expense of 5 thousand dollars?

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,the total degrees of freedom that are missing in the ANOVA table should be ________.

TABLE 14-14 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 14-14,the fitted model for predicting mileages for 4-cylinder cars is ________.

TABLE 14-18 A logistic regression model was estimated in order to predict the probability that a randomly chosen university or college would be a private university using information on mean total Scholastic Aptitude Test score (SAT)at the university or college,the room and board expense measured in thousands of dollars (Room/Brd),and whether the TOEFL criterion is at least 550 (Toefl550 = 1 if yes,0 otherwise.)The dependent variable,Y,is school type (Type = 1 if private and 0 otherwise). The Minitab output is given below: -Referring to Table 14-18,what is the estimated probability that a school with an mean SAT score of 1250,a TOEFL criterion that is at least 550,and the room and board expense of 5 thousand dollars will be a private school?

TABLE 14-16 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 coefficients of partial determination (R )of each of the 5 predictors are,respectively,0.0380,0.4376,0.0248,0.0188,and 0.0312. 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 (R )are,respectively,0.7461,0.5676,0.6764,0.8582,0.6632. -Referring to 14-16,what is the p-value of the test statistic to determine whether SUV makes a significant contribution to the regression model in the presence of the other independent variables at a 5% level of significance?

TABLE 14-19 The marketing manager for a nationally franchised lawn service company would like to study the characteristics that differentiate home owners who do and do not have a lawn service.A random sample of 30 home owners located in a suburban area near a large city was selected; 15 did not have a lawn service (code 0)and 15 had a lawn service (code 1).Additional information available concerning these 30 home owners includes family income (Income,in thousands of dollars),lawn size (Lawn Size,in thousands of square feet),attitude toward outdoor recreational activities (Atitude 0 = unfavorable,1 = favorable),number of teenagers in the household (Teenager),and age of the head of the household (Age). The Minitab output is given below: -Referring to Table 14-19,what should be the decision ('reject' or 'do not reject')on the null hypothesis when testing whether Attitude makes a significant contribution to the model in the presence of the other independent variables at a 0.05 level of significance?

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,the standard error of the estimate is ________.

TABLE 14-16 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 coefficients of partial determination (R )of each of the 5 predictors are,respectively,0.0380,0.4376,0.0248,0.0188,and 0.0312. 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 (R )are,respectively,0.7461,0.5676,0.6764,0.8582,0.6632. -Referring to 14-16,________ 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 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: 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 + β₅X₁X₂ + ε Partial output from Microsoft Excel follows: -Referring to Table 14-11,in terms of the βs in the model,give the mean change in weight-loss (Y)for every 1 month increase in time in the program (X₁)when attending the evening session.

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 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,X₁ = % Attendance,X₂= Salaries and X₃= Spending: -Referring to Table 14-15,the null hypothesis should be rejected at a 5% level of significance when testing whether instructional spending per pupil has any effect on percentage of students passing the proficiency test,taking into account the effect of all the other independent variables.

TABLE 14-16 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 coefficients of partial determination (R )of each of the 5 predictors are,respectively,0.0380,0.4376,0.0248,0.0188,and 0.0312. 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 (R )are,respectively,0.7461,0.5676,0.6764,0.8582,0.6632. -Referring to 14-16,what is the value of the test statistic to determine whether HP makes a significant contribution to the regression model in the presence of the other independent variables at a 5% level of significance?

A regression had the following results: SST = 82.55,SSE = 29.85.It can be said that 73.4% of the variation in the dependent variable is explained by the independent variables in the regression.

TABLE 14-16 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 coefficients of partial determination (R )of each of the 5 predictors are,respectively,0.0380,0.4376,0.0248,0.0188,and 0.0312. 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 (R )are,respectively,0.7461,0.5676,0.6764,0.8582,0.6632. -Referring to 14-16,the 0 to 60 miles per hour acceleration time of a sedan is predicted to be 0.7679 seconds higher than that of an SUV.