Exam 17: A Roadmap for Analyzing Data

TABLE 17-5 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 17-5,the proportion of the total variability in insurance premiums that can be explained by AGE,TICKETS,and DENSITY is ________.

TABLE 17-3 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 17-3,the analyst wants to use a t test to test for the significance of the coefficient of X₃.The value of the test statistic is ________.

TABLE 17-10 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.The coefficient of partial determination ( )of each of the 6 predictors are,respectively,0.2807,0.0386,0.0317,0.0141,0.0958,and 0.1201. 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 17-10,Model 1,which of the following is the correct null 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 17-1 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 17-1,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?

An investor wanted to forecast the price of a certain stock.He collected the mean daily price for the stock over the past 10 years.Which of the following would be the most appropriate analysis to perform?

TABLE 17-8 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 17-8,which of the following is the correct alternative hypothesis to test whether the daily mean of the percentage of students attending class has any effect on the percentage of students passing the proficiency test,taking into account the effect of all the other independent variables?

TABLE 17-3 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 17-3,the net regression coefficient of X₂ is ________.

TABLE 17-9 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 partial determination ( )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 X_j as the dependent variable and all other X variables as independent variables ( )are,respectively,0.7461,0.5676,0.6764,0.8582,0.6632. -True or False: Referring to Table 17-9,there is enough evidence to conclude that SUV makes a significant contribution to the regression model in the presence of the other independent variables at a 5% level of significance.

TABLE 17-3 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 17-3,the analyst wants to use an F-test to test H₀ : β₁ = β₂ = β₃ = β₄ = 0.The appropriate alternative hypothesis is ________.

TABLE 17-11 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). -Referring to Table 17-11,what is the estimated probability that a school with a mean SAT score of 1100,a TOEFL criterion that is not at least 550,and the room and board expense of 7 thousand dollars will be a private school?

TABLE 17-3 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 -True or False: Referring to Table 17-3,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 17-8 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 17-8,predict the percentage of students passing the proficiency test for a school which has a daily mean of 95% of students attending class,a mean teacher salary of 40,000 dollars,and an instructional spending per pupil of 2,000 dollars.

An airline wants to select a computer software package for its reservation system.Four software packages (1,2,3,and 4)are commercially available.An experiment is set up in which each package is used to make reservations for 5 randomly selected weeks and data on the number of passengers that are bumped over a month are collected.(A total of 20 weeks was included in the experiment.)The variability of the number of passengers that are bumped is found to be roughly the same for the 4 packages.The distribution on the number of passengers that are bumped has been found out to be right-skewed for package 1 and 4,left-skewed for package 2 and normal for package 3.Which of the following tests will be the most appropriate to find out if the mean number of passengers being bumped over a month is the same across the 4 packages?

A realtor wants to compare the variability of sales-to-appraisal ratios of residential properties sold in four neighborhoods (A,B,C,and D).Four properties are randomly selected from each neighborhood and the ratios recorded for each were collected.Which of the following tests will be the most appropriate?

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.She believed that holding everything else constant,instructional spending per pupil had a positive but decreasing impact on percentage.Which of the following would be the most appropriate analysis to perform?

TABLE 17-10 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.The coefficient of partial determination ( )of each of the 6 predictors are,respectively,0.2807,0.0386,0.0317,0.0141,0.0958,and 0.1201. 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 17-10,Model 1,which of the following is a correct statement?

TABLE 17-11 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). -Referring to Table 17-11,what are the degrees of freedom for the chi-square distribution when testing whether the model is a good-fitting model?

TABLE 17-12 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 (Attitude 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 17-12,which of the following is the correct expression for the estimated model?

A contractor wants to forecast the number of contracts in future quarters,using quarterly data on a number of contracts over the last 10 years.Which of the following would be the most appropriate analysis to perform?

TABLE 17-12 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 (Attitude 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 17-12,what should be the decision ('reject' or 'do not reject')on the null hypothesis when testing whether Teenager makes a significant contribution to the model in the presence of the other independent variables at a 0.05 level of significance?