Exam 18: A Roadmap for Analyzing Data

An Undergraduate Study Committee of 6 members at a major university is to be formed from a pool of faculty of 18 men and 6 women.Which of the following distributions would you use to determine the probability that half of the members will be women?

SCENARIO 18-11 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). The Minitab output is given below: -Referring to Scenario 18-11, 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?

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 as the dependent variable, -Referring to Scenario 18-8, which of the following is the correct null hypothesis to test whether instructional spending per pupil has any effect on percentage of students passing the proficiency test, considering the effect of all the other independent variables?

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

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: Regression Analysis -Referring to Scenario 18-5, to test the significance of the multiple regression model, the p- value of the test statistic in the sample is ______.

An economist is interested to see how consumption for an economy (in $ billions)is influenced by gross domestic product ($ billions)and aggregate price (consumer price index).Annual data from 30 years were collected.Which of the following would be the most appropriate analysis to perform?

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 Income makes a significant contribution to the model in the presence of 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. SCENARIO 18-9 cont. The various residual plots are as shown below. SCENARIO 18-9 cont. SCENARIO 18-9 cont. 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 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 Scenario 18-9, 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.

SCENARIO 18-10 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 Scenario 18-10 Model 1, what is the value of the test statistic when testing whether age has any effect on the number of weeks a worker is unemployed due to a layoff while holding constant the effect of all the other independent variables?

SCENARIO 18-11 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). The Minitab output is given below: -Referring to Scenario 18-11, which of the following is the correct interpretation for the Tofel500 slope coefficient?

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 ( ), the amount of insulation in inches ( ), the number of windows in the house ( ), and the age of the furnace in years ( ).Given below are the EXCEL outputs of two regression models. -Referring to Scenario 18-2, the estimated value of the partial regression parameter in Model 1 means that

SCENARIO 18-1 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: SUMMARY OUTPUT -Referring to Scenario 18-1, when the builder used a simple linear regression model with house size (House)as the dependent variable and education (School)as the independent variable, he obtained an value of 23.0%.What additional percentage of the total variation in house size has been explained by including family size and income in the multiple regression?

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?

SCENARIO 18-3 A financial analyst wanted to examine the relationship between salary (in $1,000)and 4 variables: age ( = Age), experience in the field ( = Exper), number of degrees ( = Degrees), and number of previous jobs in the field ( = Prevjobs).He took a sample of 20 employees and obtained the following Microsoft Excel output: SUMMARY OUTPUT -Referring to Scenario 18-3, the analyst wants to use a t test to test for the significance of the coefficient of X3.The p-value of the test is ________.

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

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 ( ), the amount of insulation in inches ( ), the number of windows in the house ( ), and the age of the furnace in years ( ).Given below are the EXCEL outputs of two regression models. -Referring to Scenario 18-2, what is your decision and conclusion for the test 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.So, information on charges for 40 doctors (20 foreign and 20 USA medical school graduates)was obtained for each of the 4 specialties.The president has already found out that specialty types and origin of the medical degree do not interact to affect the charges.He has also found out special types do have an impact on average charges.Which of the following tests will be the most appropriate to find out which primary specialty has the highest charges?

SCENARIO 18-1 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: SUMMARY OUTPUT -Referring to Scenario 18-1, which of the independent variables in the model are significant at the 5% level?

SCENARIO 18-4 You decide to predict gasoline prices in different cities and towns in the United States for your term project.Your dependent variable is price of gasoline per gallon and your explanatory variables are per capita income, the number of firms that manufacture automobile parts in and around the city, the number of new business starts in the last year, population density of the city, percentage of local taxes on gasoline, and the number of people using public transportation.You collected data of 32 cities and obtained a regression sum of squares SSR= 122.8821.Your computed value of standard error of the estimate is 1.9549. -Referring to Scenario 18-4, what is the value of the coefficient of multiple determination?

SCENARIO 18-10 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 Scenario 18-10 Model 1, the alternative hypothesis : At least one of for j = 1, 2, 3, 4, 5, 6 implies that the number of weeks a worker is unemployed due to a layoff is affected by at least one of the explanatory variables.