Exam 17: A Roadmap for Analyzing Data

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,the errors (residuals)appear to be normally distributed.

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,what is the value of the calculated F test statistic that is missing from the output for testing whether the whole regression model is significant?

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 and using both Model 1 and Model 2,what is the p-value of the test statistic for testing whether the independent variables that are not significant individually are also not significant as a group in explaining the variation in the dependent variable at a 5% level of significance?

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,the 0 to 60 miles per hour acceleration time of an SUV is predicted to be 0.1252 seconds higher than that of a sedan.

A Paso Robles wine producer wanted to forecast the cases of Merlot wine sold.The number of cases of merlot wine sold in a 28-year period was collected.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: -True or False: Referring to Table 17-8,the null hypothesis should be rejected at a 5% level of significance when testing 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 17-9 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. -Referring to Table 17-9,________ of the variation in Accel Time can be explained by Cargo Vol while controlling for the other independent variables.

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: -True or False: Referring to Table 17-12,there is not enough evidence to conclude that Attitude makes a significant contribution to the model in the presence of the other independent variables at a 0.05 level of significance.

TABLE 17-7 As a project for his business statistics class,a student examined the factors that determined parking meter rates throughout the campus area.Data were collected for the price per hour of parking,blocks to the quadrangle,and one of the three jurisdictions: on campus,in downtown and off campus,or outside of downtown and off campus.The population regression model hypothesized is Y_i = α + β₁X_1i + β₂X_2i + β₃X_3i + ε where Y is the meter price X₁ is the number of blocks to the quad X₂ is a dummy variable that takes the value 1 if the meter is located in downtown and off campus and the value 0 otherwise X₃ is a dummy variable that takes the value 1 if the meter is located outside of downtown and off campus,and the value 0 otherwise The following Excel results are obtained. -Referring to Table 17-7,if one is already outside of downtown and off campus but decides to park 3 more blocks from the quad,the estimated mean parking meter rate will

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: -True or False: Referring to Table 17-8,there is sufficient evidence that the percentage of students passing the proficiency test depends on all of the explanatory variables at a 5% level of significance.

TABLE 17-2 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 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. -Referring to Table 17-2,what is your decision and conclusion for the test H₀ : β₂ = 0 vs.H₁ : β₂ < 0 at the α = 0.01 level of significance using Model 1?

A physician and president of a Tampa Health Maintenance Organization (HMO)are attempting to show the benefits of managed health care to an insurance company.The physician believes that certain types of doctors are more cost-effective than others.To investigate this,the president obtained independent random samples of 20 HMO physicians from each of 4 primary specialties - General Practice (GP),Internal Medicine (IM),Pediatrics (PED),and Family Physicians (FP)- and recorded the total charges per member per month for each.A second variable which the president believes influences total charges per member per month is whether the doctor is a foreign or USA medical school graduate.To investigate this,the president also collected data on 20 foreign medical school graduates in each of the 4 primary specialty types described above.Altogether,information on charges for 40 doctors (20 foreign and 20 USA medical school graduates)was obtained for each of the 4 specialties.Which of the following tests will be the most appropriate to find out if the primary specialty and the origin of medical school degree interact to affect the charges?

TABLE 17-2 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 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. -Referring to Table 17-2,what can we say about Model 1?

TABLE 17-7 As a project for his business statistics class,a student examined the factors that determined parking meter rates throughout the campus area.Data were collected for the price per hour of parking,blocks to the quadrangle,and one of the three jurisdictions: on campus,in downtown and off campus,or outside of downtown and off campus.The population regression model hypothesized is Y_i = α + β₁X_1i + β₂X_2i + β₃X_3i + ε where Y is the meter price X₁ is the number of blocks to the quad X₂ is a dummy variable that takes the value 1 if the meter is located in downtown and off campus and the value 0 otherwise X₃ is a dummy variable that takes the value 1 if the meter is located outside of downtown and off campus,and the value 0 otherwise The following Excel results are obtained. -Referring to Table 17-7,what is the correct interpretation for the estimated coefficient for X₂?

Data on the amount of time spent studying for a particular exam at a high school were collected for 150 students.You want to know if half of the students spent at least how much time studying for that exam.Which of the following would you compute?

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: -True or False: Referring to Table 17-10,Model 1,we can conclude that,holding constant the effect of the other independent variables,there is a difference in the mean number of weeks a worker is unemployed due to a layoff between a worker who is married and one who is not at a 1% level of significance if all we have is the information of the 95% confidence interval estimate for β₄.

TABLE 17-6 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: Regression Statistics ANOVA F = 5.41118 Significance F = 0.040201 -Referring to Table 17-6,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 morning session.

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 Cargo Vol makes a significant contribution to the regression model in the presence of the other independent variables at a 5% level of significance.

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,________ of the variation in the number of weeks a worker is unemployed due to a layoff can be explained by whether the worker is head of household while controlling for the other independent variables.

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. -Referring to Table 17-9,what is the correct interpretation for the estimated coefficient for SUV?