Exam 17: Getting Ready to Analyze Data

A quality control engineer is in charge of the manufacture of computer disks. Two different processes can be used to manufacture the disks. He suspects that the Kohler method produces a Greater proportion of defects than the Russell method. He samples 150 of the Kohler and 200 of The Russell disks and finds that 27 and 18 of them, respectively, are defective. If Kohler is Designated as "Group 1" and Russell is designated as "Group 2," which of the following tests will You use to find out if the Kohler method is worse than the Russell method?

SCENARIO 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. -Referring to Scenario 17-9, ________ of the variation in Accel Time can be explained by Cargo Vol while controlling for the other independent variables.

SCENARIO 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). The Minitab output is given below: -Referring to Scenario 17-11, there is not enough evidence to conclude that the model is not a good-fitting model at a 0.05 level of significance.

Data on the amount of money made in a year by 1000 families in a small town were collected. You want to know the difference in the amount of money made in that year by the middle 50% of The 1,000 families. Which of the following would you compute?

SCENARIO 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 $\left( X _ { 1 } \right)$ , the amount of insulation in inches $\left( X _ { 2 } \right)$ , the number of windows in the house $\left( X _ { 3 } \right)$ , and the age of the furnace in years $\left( X _ { 4 } \right)$ . Given below are the EXCEL outputs of two regression models. Model 1 Regression Statistics R Square 0.8080 Adjusted R Square 0.7568 Observations 20 $\text { ANOVA }$ df SS MS F Significance F Regression 4 169503.4241 42375.86 15.7874 0.0000 Residual 15 40262.3259 2684.155 Total 19 209765.75 Coefficients Standard Error t Stat P-value Lower 90.0\% Upper 90.0\% Intereept 421.4277 77.8614 5.4125 0.0000 284.9327 557.9227 (Temperature) -4.5098 0.8129 -5.5476 0.0000 -5.9349 -3.0847 (Insulation) -14.9029 5.0508 -2.9505 0.0099 -23.7573 -6.0485 (Windows) 0.2151 4.8675 0.0442 0.9653 -8.3181 8.7484 (Furnace Age) 6.3780 4.1026 1.5546 0.1408 -0.8140 13.5702 $\text { Model } 2$ Regression Statistics R Square 0.7768 Adjusted R Square 0.7506 Observations 20 $\text { ANOVA }$ Coefficients Standard Error t Stat P-value Lower 95\% Upper 95\% Intercept 489.3227 43.9826 11.1253 0.0000 396.5273 582.1180 (Temperature) -5.1103 0.6951 -7.3515 0.0000 -6.5769 -3.6437 (Insulation) -14.7195 4.8864 -3.0123 0.0078 -25.0290 -4.4099 -Referring to Scenario 17-2, what are the degrees of freedom of the partial F test for $H _ { 0 } : \beta _ { 3 } = \beta _ { 4 } = 0 \quad \text { vs. } H _ { 1 } : \text { At least one } \beta _ { \mathrm { j } } \neq 0 , j = 3,4$ ?

SCENARIO 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: SUMMARY OUTPUT Regression Statistics Multiple R 0.865 R Square 0.748 Adjusted R Square 0.726 Standard Error 5.195 Observations 50 ANOVA df SS MS F Signif F Regression 3605.7736 1201.9245 0.0000 Residual 1214.2264 26.3962 Total 49 4820.0000 Coeff StdError t Stat P -value Intercept -1.6335 5.8078 -0.281 0.7798 Income 0.4485 0.1137 3.9545 0.0003 Size 4.2615 0.8062 5.286 0.0001 School -0.6517 0.4319 -1.509 0.1383 -Referring to Scenario 17-1, suppose the builder wants to test whether the coefficient on School is significantly different from 0. What is the value of the relevant t-statistic?

Data mining is used mostly in the mining industry.

SCENARIO 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. -Referring to Scenario 17-9, what is the correct interpretation for the estimated coefficient for HP?

SCENARIO 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, $X _ { 1 } = \%$ Attendance, $X _ { 2 } =$ Salaries and $X _ { 3 } =$ Spending: Regression Statistics Multiple R 0.7930 R Square 0.6288 Adjusted R 0.6029 Square Standard 10.4570 Error Observations 47 ANOVA Coefficients Standard Error t Stat P-value Lower 95\% Upper 95\% Intercept -753.4225 101.1149 -7.4511 0.0000 -957.3401 -549.5050 \% Attendance 8.5014 1.0771 7.8929 0.0000 6.3292 10.6735 Salary 0.000000685 0.0006 0.0011 0.9991 -0.0013 0.0013 Spending 0.0060 0.0046 1.2879 0.2047 -0.0034 0.0153 -Referring to Scenario 17-8, predict the percentage of students passing the proficiency test for a school which has a daily mean of 95% of students attending class, a mean teacher salary of 40,000 dollars, and an instructional spending per pupil of 2,000 dollars.

SCENARIO 17-14 The treemap below shows the amounts (size) measured in billions of US dollars and percentage changes from prior year (color) of business-to-consumer ecommerce sales last year for North America, Asia Pacific, Western Europe, Central & Eastern Europe, Latin America, and Middle East & Africa. -Referring to Scenario 17-14, which region has the fastest growth in business-to-consumer ecommerce sales last year?

Successful implementation of a classification tree requires rules for splitting the data at each node based on an independent variable.

SCENARIO 17-15 The tree diagram below shows the results of the classification tree model that has been constructed to predict the probability of a cable company's customers who will switch ("Yes" or "No") into its bundled program offering based on the price ($30, $40, $50, $60) and whether the customer spends more than 5 hours a day watching TV ("Yes" or "No") using the data set of 100 customers collected from a survey. -Referring to Scenario 17-15, the highest probability of switching is predicted to occur among customers who do not watch more than 5 hours of TV a day and are offered the bundled price of lower than $50.

Which of the following explores business activities that have occurred or are occurring in the present moment?

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 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 $\left( X _ { 1 } \right)$ , the amount of insulation in inches $\left( X _ { 2 } \right)$ , the number of windows in the house $\left( X _ { 3 } \right)$ , and the age of the furnace in years $\left( X _ { 4 } \right)$ . Given below are the EXCEL outputs of two regression models. Model 1 Regression Statistics R Square 0.8080 Adjusted R Square 0.7568 Observations 20 $\text { ANOVA }$ df SS MS F Significance F Regression 4 169503.4241 42375.86 15.7874 0.0000 Residual 15 40262.3259 2684.155 Total 19 209765.75 Coefficients Standard Error t Stat P-value Lower 90.0\% Upper 90.0\% Intereept 421.4277 77.8614 5.4125 0.0000 284.9327 557.9227 (Temperature) -4.5098 0.8129 -5.5476 0.0000 -5.9349 -3.0847 (Insulation) -14.9029 5.0508 -2.9505 0.0099 -23.7573 -6.0485 (Windows) 0.2151 4.8675 0.0442 0.9653 -8.3181 8.7484 (Furnace Age) 6.3780 4.1026 1.5546 0.1408 -0.8140 13.5702 $\text { Model } 2$ Regression Statistics R Square 0.7768 Adjusted R Square 0.7506 Observations 20 $\text { ANOVA }$ Coefficients Standard Error t Stat P-value Lower 95\% Upper 95\% Intercept 489.3227 43.9826 11.1253 0.0000 396.5273 582.1180 (Temperature) -5.1103 0.6951 -7.3515 0.0000 -6.5769 -3.6437 (Insulation) -14.7195 4.8864 -3.0123 0.0078 -25.0290 -4.4099 -Referring to Scenario 17-2, what is your decision and conclusion for the test $H _ { 0 } : \beta _ { 2 } = 0 \text { vs. } H _ { 1 } : \beta _ { 2 } < 0 \text { at the } \alpha = 0.01$ level of significance using Model 1?

SCENARIO 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, $X _ { 1 } = \%$ Attendance, $X _ { 2 } =$ Salaries and $X _ { 3 } =$ Spending: Regression Statistics Multiple R 0.7930 R Square 0.6288 Adjusted R 0.6029 Square Standard 10.4570 Error Observations 47 ANOVA Coefficients Standard Error t Stat P-value Lower 95\% Upper 95\% Intercept -753.4225 101.1149 -7.4511 0.0000 -957.3401 -549.5050 \% Attendance 8.5014 1.0771 7.8929 0.0000 6.3292 10.6735 Salary 0.000000685 0.0006 0.0011 0.9991 -0.0013 0.0013 Spending 0.0060 0.0046 1.2879 0.2047 -0.0034 0.0153 -Referring to Scenario 17-8, what are the numerator and denominator degrees of freedom, respectively, for the test statistic to determine whether there is a significant relationship between percentage of students passing the proficiency test and the entire set of explanatory variables?

SCENARIO 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 ( $R _ { \mathrm { y } } ^ { 2 }$ (All raiables excopt $j$ ) ) of each of the 6 predictors are, respectively, $0.2807$ , $0.0386,0.0317,0.0141,0.0958$ , and $0.1201$ . Regression Statistics Multiple R 0.7035 R Square 0.4949 Adjusted R 0.4030 Square Standard 18.4861 Error Observations 40 $\text { ANOVA }$ Coefficients Standard Error t Stat P-value Lower 95\% Upper 95\% Intercept 32.6595 23.18302 1.4088 0.1683 -14.5067 79.8257 Age 1.2915 0.3599 3.5883 0.0011 0.5592 2.0238 Edu -1.3537 1.1766 -1.1504 0.2582 -3.7476 1.0402 Job Yr 0.6171 0.5940 1.0389 0.3064 -0.5914 1.8257 Married -5.2189 7.6068 -0.6861 0.4974 -20.6950 10.2571 Head -14.2978 7.6479 -1.8695 0.0704 -29.8575 1.2618 Manager -24.8203 11.6932 -2.1226 0.0414 -48.6102 -1.0303 -Referring to Scenario 17-10 Model 1, you 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 5% level of significance if we use only the information of the 95% confidence interval estimate for?2 .

SCENARIO 17-5 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 Statistics Multiple R 0.63 R Square 0.40 Adjusted R Square 0.23 Standard Error 50.00 Observations 15.00 ANOVA df SS MS F Significance F Regression 3 5994.24 2.40 0.12 Residual 11 27496.82 Total 45479.54 Coefficients Standard Error t Stat P-value Lower 99.0\% Upper 99.0\% Intercept 123.80 48.71 2.54 0.03 -27.47 275.07 AGE -0.82 0.87 -0.95 0.36 -3.51 1.87 TICKETS 21.25 10.66 1.99 0.07 -11.86 54.37 DENSITY -3.14 6.46 -0.49 0.64 -23.19 16.91 AGE -0.82 0.87 -0.95 0.36 -3.51 1.87 TICKETS 21.25 10.66 1.99 0.07 -11.86 54.37 DENSITY -3.14 6.46 -0.49 0.64 -23.19 16.91 -Referring to Scenario 17-5, the residual mean squares (MSE) that are missing in the ANOVA table should be _____.

SCENARIO 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). The Minitab output is given below: -Referring to Scenario 17-11, which of the following is the correct interpretation for the Tofel500 slope coefficient?

SCENARIO 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 $\left( X _ { 1 } \right)$ , the amount of insulation in inches $\left( X _ { 2 } \right)$ , the number of windows in the house $\left( X _ { 3 } \right)$ , and the age of the furnace in years $\left( X _ { 4 } \right)$ . Given below are the EXCEL outputs of two regression models. Model 1 Regression Statistics R Square 0.8080 Adjusted R Square 0.7568 Observations 20 $\text { ANOVA }$ df SS MS F Significance F Regression 4 169503.4241 42375.86 15.7874 0.0000 Residual 15 40262.3259 2684.155 Total 19 209765.75 Coefficients Standard Error t Stat P-value Lower 90.0\% Upper 90.0\% Intereept 421.4277 77.8614 5.4125 0.0000 284.9327 557.9227 (Temperature) -4.5098 0.8129 -5.5476 0.0000 -5.9349 -3.0847 (Insulation) -14.9029 5.0508 -2.9505 0.0099 -23.7573 -6.0485 (Windows) 0.2151 4.8675 0.0442 0.9653 -8.3181 8.7484 (Furnace Age) 6.3780 4.1026 1.5546 0.1408 -0.8140 13.5702 $\text { Model } 2$ Regression Statistics R Square 0.7768 Adjusted R Square 0.7506 Observations 20 $\text { ANOVA }$ Coefficients Standard Error t Stat P-value Lower 95\% Upper 95\% Intercept 489.3227 43.9826 11.1253 0.0000 396.5273 582.1180 (Temperature) -5.1103 0.6951 -7.3515 0.0000 -6.5769 -3.6437 (Insulation) -14.7195 4.8864 -3.0123 0.0078 -25.0290 -4.4099 -Referring to Scenario 17-2, the estimated value of the partial regression parameter $\beta _ { 1 }$ in Model 1 means that