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. -Referring to Table 17-9,what is the p-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?

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 critical 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 17-11 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). -True or False: Referring to Table 17-11,there is not enough evidence to conclude that SAT score makes a significant contribution to the model in the presence of the other independent variables at a 0.05 level of significance.

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,you can conclude that instructional spending per pupil individually has no impact on the mean percentage of students passing the proficiency test,taking into account the effect of all the other independent variables,at a 10% level of significance based solely on the 95% confidence interval estimate for β₃.

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,which of the following values for the level of significance is the smallest for which the regression model as a whole 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: -True or False: Referring to Table 17-10,Model 1,we can conclude that,holding constant the effect of the other independent variables,the number of years of education received has no impact on the mean number of weeks a worker is unemployed due to a layoff at a 1% level of significance if all we have is the information of the 95% confidence interval estimate for β₂.

An agronomist wants to compare the crop yield of 3 varieties of chickpea seeds.She plants all 3 varieties of the seeds on each of 5 different patches of fields.She then measures the crop yield in bushels per acre.Which of the following tests will be the most appropriate to find out if there is any difference in crop yield among the 3 varieties?

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 a sedan is predicted to be 0.7679 seconds higher than that of an SUV.

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,what is the value of the test statistic when testing whether instructional spending per pupil has any effect on the percentage of students passing the proficiency test,taking into account the effect of all the other independent variables?

TABLE 17-1 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,the observed value of the F-statistic is missing from the printout.What are the degrees of freedom for this F-statistic?

An agronomist wants to compare the crop yield of 3 varieties of chickpea seeds.She plants all 3 varieties of the seeds on each of 5 different patches of fields.She then measures the crop yield in bushels per acre.She has found out that the different varieties do have an impact on crop yield.Which of the following tests will be the most appropriate to find out which variety will produce the highest yield?

The use of preservatives by food processors has become a controversial issue.Suppose 2 preservatives are extensively tested and determined safe for use in meats.A processor wants to compare the preservatives for their effects on retarding spoilage.They will choose to use the preservative that can keep the meat fresh for the longest amount of time.Suppose 15 cuts of fresh meat are treated with preservative I and 15 are treated with preservative II,and the number of hours until spoilage begins is recorded for each of the 30 cuts of meat.Suppose the variability of the number of hours until spoilage is the same for meat treated by both preservatives but the normal probability plots reveal that the number of hours until spoilage is right-skewed for the 15 cuts treated by preservative I and left-skewed for the 15 cuts treated with preservative II.Which of the following tests will be the most appropriate?

An entrepreneur is considering the purchase of a coin-operated laundry.The current owner claims that over the past 5 years,the mean daily revenue was $675 with a standard deviation of $75.A sample of 30 days reveals a daily mean revenue of $625 and a standard deviation of $70.Which of the following tests will be the most appropriate?

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,you can conclude that the mean teacher salary individually has no impact on the mean percentage of students passing the proficiency test,taking into account the effect of all the other independent variables,at a 1% level of significance based solely on the 95% confidence interval estimate for β₂.

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,the alternative hypothesis H₁ : At least one of β_j ≠ 0 for j = 1,2,3,4,5,6 implies that the number of weeks a worker is unemployed due to a layoff is related to at least one of the explanatory variables.

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 10% level of significance if we use only the information of the 95% confidence interval estimate for β₄.

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,the null hypothesis should be rejected at a 10% level of significance when testing 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,what are the regression degrees of freedom that are missing from the output?

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,the null hypothesis should be rejected at a 10% level of significance when testing whether age has any effect on the number of weeks a worker is unemployed due to a layoff.

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 the six independent variables after taking into consideration the number of independent variables and the number of observations.