Exam 18: A Roadmap for Analyzing Data

SCENARIO 18-8 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, X ₂ = Salaries and X₃ = Spending: -Referring to Scenario 18-8,you can conclude that instructional spending per pupil has no impact on the mean percentage of students passing the proficiency test,considering the effect of all the other independent variables,at a 5% level of significance using the 95% confidence interval estimate for $\beta$ ₃ .

A wheel spinning game is played with a special wheel with 24 equal segments that determine the dollar values of a single spin.Which of the following distributions can best be used to compute the probability of winning a specific dollar value in a single spin?

SCENARIO 18-12 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 Scenario 18-10 Model 1,the null hypothesis H₀ : $\beta$ ₁ = $\beta$ ₂ = $\beta$ ₃ = $\beta$ ₄ = $\beta$ ₅ = $\beta$ ₆ = 0 implies that the number of weeks a worker is unemployed due to a layoff is not related to one of the explanatory variables.

When examining the effects of a two-level categorical independent variable in a multiple regression equation,two variables are needed to define the two states.

SCENARIO 18-9 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 ( R² _{yj.(All variables except j )} )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 ( R² _j )are,respectively, 0.7461,0.5676,0.6764,0.8582,0.6632. -Referring to Scenario 18-9,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.

SCENARIO 18-9 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 ( R² _{yj.(All variables except j )} )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 ( R² _j )are,respectively, 0.7461,0.5676,0.6764,0.8582,0.6632. -Referring to Scenario 18-9,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.

SCENARIO 18-12 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 Scenario 18-12, what is the p-value of the test statistic when testing whether Age makes a significant contribution to the model in the presence of the other independent variables?

SCENARIO 18-12 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 Scenario 18-12,what should be the decision ('reject' or 'do not reject')on the null hypothesis when testing whether LawnSize makes a significant contribution to the model in the presence of the other independent variables at a 0.05 level of significance?

SCENARIO 18-9 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 ( R² _{yj.(All variables except j )} )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 ( R² _j )are,respectively, 0.7461,0.5676,0.6764,0.8582,0.6632. -Referring to Scenario 18-9,_____of the variation in Accel Time can be explained by HP while controlling for the other independent variables.

SCENARIO 18-2 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 ( X ₂ ), the number of windows in the house ( X₃ ), and the age of the furnace in years ( X ₄ ). Given below are the EXCEL outputs of two regression models. -Referring to Scenario 18-2,what are the degrees of freedom of the partial F test for H₀ : $\beta$ ₃ = $\beta$ ₄ = 0 vs.H₁ : At least one $\beta$ j $\neq$ 0,j = 3,4 ?

SCENARIO 18-12 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 Scenario 18-10 Model 1,what is the 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?

SCENARIO 18-8 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, X ₂ = Salaries and X₃ = Spending: -Referring to Scenario 18-8,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.

A sample of 200 students at a Big-Ten university was taken after the midterm to ask whether they went bar hopping the weekend before the midterm or spent the weekend studying,and whether they did well or poorly on the midterm.You can use a contingency table to present this information.

SCENARIO 18-5 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 Scenario 18-5,to test the significance of the multiple regression model,what are the degrees of freedom?

SCENARIO 18-9 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 ( R² _{yj.(All variables except j )} )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 ( R² _j )are,respectively, 0.7461,0.5676,0.6764,0.8582,0.6632. -Referring to Scenario 18-9,what is the value of the test statistic to determine whether Cargo Vol makes a significant contribution to the regression model in the presence of the other independent variables at a 5% level of significance?

SCENARIO 18-12 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 Scenario 18-10 Model 1,what are the lower and upper limits of the 95% confidence interval estimate for the 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 after taking into consideration the effect of all the other independent variables?

SCENARIO 18-12 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 Scenario 18-10 Model 1,there is sufficient evidence that the number of weeks a worker is unemployed due to a layoff depends on at least one of the explanatory variables at a 10% level of significance.

SCENARIO 18-12 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 Scenario 18-10 Model 1,_____of the variation in the number of weeks a worker is unemployed due to a layoff can be explained by the number of years at the previous job while controlling for the other independent variables.

SCENARIO 18-9 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 ( R² _{yj.(All variables except j )} )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 ( R² _j )are,respectively, 0.7461,0.5676,0.6764,0.8582,0.6632. -Referring to Scenario 18-9,_____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.

SCENARIO 18-12 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 Scenario 18-10 Model 1,which of the following is a correct statement?