Exam 18: A Roadmap for Analyzing Data

The weight of a randomly selected cookie from a production line can most likely be modeled by which of the following distributions?

SCENARIO 18-7 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 where Y is the meter price is the number of blocks to the quad is a dummy variable that takes the value 1 if the meter is located in downtown and off campus and the value 0 otherwise 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 Scenario 18-7, 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

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, what minimum annual income would an individual with a family size of 4 and 16 years of education need to attain a predicted 10,000 square foot home (House = 100)?

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

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 following values for the level of significance is the smallest for which the regression model as a whole is significant?

Suppose the light bulbs in a factory burn out at a rate of 50 bulbs per month.Which of the following distributions would you use to determine the probability that the next two light bulbs will burn out 2 days apart?

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 p-value of the F test for the significance of the entire regression is ________.

Data on the amount of time spent studying for a particular exam at a high school was collected for 150 students.Which of the following would you compute if you wanted to know the time spent studying done by half of the students?

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 null hypothesis implies that the number of weeks a worker is unemployed due to a layoff is not related to any of the explanatory 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, ________ of the variation in the number of weeks a worker is unemployed due to a layoff can be explained by the six 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, the null hypothesis that the model is a good- fitting model cannot be rejected when allowing for a 5% probability of making a type I error.

A professor of economics at a small Texas university wanted to determine what year in school students were taking his tough economics course.Data were collected on the class status ("freshman", "sophomore", "junior" or "senior")of 50 students enrolled in one of his economics courses.A side-by-side bar chart can be used to present this information.

Data were collected on the amount of detergent used in gallons in a month by 25 drive- through car wash operations in Phoenix.You can use a time-series plot to process this information.

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 following values for the level of significance is the smallest for which every explanatory variable is significant individually?

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, the estimated mean change in insurance premiums for every 2 additional tickets received is _____.

A manager of a product sales group believes the number of sales made by an employee depends on how many years that employee has been with the company and how he/she scored on a business aptitude test.A random sample of 38 employees was selected to collect data on their number of sales, number of years with the company and scores on a business aptitude test.Which of the following would you perform to draw conclusion on the belief?

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 the correct null hypothesis 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?

A quality control manager at a plant that produces O-rings is concerned about whether the diameter of the O-rings that are produced is conformable to the specification.She has calculated that the average diameter of the O-rings is 4.2 centimeters.She also knows that approximately 95% of the O-rings have diameters fall between 3.2 and 5.2 centimeters and almost all of the O-rings have diameters between 2.7 and 5.7 centimeters.When modeling the diameters of the O-rings, which distribution should the scientists use?

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 and using both Model 1 and Model 2, the null hypothesis 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 should be rejected 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 should be the decision ('reject' or 'do not reject')on the null hypothesis when testing whether Attitude makes a significant contribution to the model in the presence of the other independent variables at a 0.05 level of significance?