Exam 17: Getting Ready to Analyze Data

Which of the following disciplines is typically NOT involved in business analytics?

SCENARIO 17-7 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 $Y _ { i } = \alpha + \beta _ { 1 } X _ { 1 i } + \beta _ { 2 } X _ { 2 i } + \beta _ { 3 } X _ { 3 i } + \varepsilon$ where $Y$ is the meter price $X _ { l }$ is the number of blocks to the quad $X _ { 2 }$ is a dummy variable that takes the value 1 if the meter is located in downtown and off campus and the value 0 otherwise $X _ { 3 }$ 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. Regression Statistics Multiple R 0.9659 R Square 0.9331 Adjusted R Square 0.9294 Standard Error 0.0327 Observations 58 $\text { ANOVA }$ Df SS MS F Significance F Regression 3 0.8094 0.2698 251.1995 0.0000 Residual 54 0.0580 0.0010 Total 57 0.8675 Coefficients Standard Error t Stat P -value Intercept 0.5118 0.0136 37.4675 2.4904 -0.0045 0.0034 -1.3276 0.1898 -0.2392 0.0123 -19.3942 0.0000 -0.0002 0.0123 -0.0214 0.9829 -Referring to Scenario 17-7, predict the meter rate per hour if one parks outside of downtown and off campus 3 blocks from the quad.

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 lower and upper limits of the 95% confidence interval estimate for the effect of a one dollar increase in instructional spending per pupil on the mean percentage of students passing the proficiency test?

SCENARIO 17-3 A financial analyst wanted to examine the relationship between salary (in $\$ 1,000$ ) and 4 variables: age $\left( X _ { 1 } = \mathrm { Age } \right)$ , experience in the field $\left( X _ { 2 } = \right.$ Exper $)$ , number of degrees $\left( X _ { 3 } = \right.$ Degrees $)$ , and number of previous jobs in the field ( $X _ { 4 } =$ Prevjobs). He took a sample of 20 employees and obtained the following Microsoft Excel output: SUMMARY OUTPUT Regression Statistics Multiple R 0.992 R Square 0.984 Adjusted R Square 0.979 Standard Error 2.26743 Observations 20 df SS MS F Signif F Regression 4 4609.83164 1152.45791 224.160 0.0001 Residual 15 77.11836 5.14122 Total 19 4686.95000 Coeff StdError Stat P-value Intercept -9.611198 2.77988638 -3.457 0.0035 Age 1.327695 0.11491930 11.553 0.0001 Exper -0.106705 0.14265559 -0.748 0.4660 Degrees 7.311332 0.80324187 9.102 0.0001 Prevjobs -0.504168 0.44771573 -1.126 0.2778 -Referring to Scenario 17-3, the estimate of the unit change in the mean of Y per unit change in $X _ { 4 }$ , taking into account the effects of the other 3 variables, is ________.

Suppose that past history shows that 60% of college students prefer Coca-Cola. A sample of 10 students is to be selected. Which of the following distributions would you use to figure out the Probability that at least half of them will prefer Coca-Cola?

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?

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, the alternative hypothesis $H _ { 1 } : \text { At least one of } \beta _ { j } \neq 0 \text { for } j = 1,2$ , 3 implies that percentage of students passing the proficiency test is related to all of the explanatory variables.

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, there is sufficient evidence that all of the explanatory variables are related to the percentage of students passing the proficiency test at a 5% level of significance.

At a meeting of information systems officers for regional offices of a national company, a survey was taken to determine the number of employees the officers supervise in the operation of their departments, where X is the number of employees overseen by each information systems officer. A stem-and-leaf display can be used to present this information.

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, which of the following is a correct statement?

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, what is the p-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 17-12 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 (Atitude 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 17-12, which of the following is the correct interpretation for the Income slope coefficient?

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. Which of the following tests will be the most appropriate To find out if the primary specialty and the origin of medical school degree interact to affect the Charges?

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 watch more than 5 hours of TV a day and are offered the bundled price of higher than $40.

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, 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) $H _ { 0 } : \beta _ { 0 } = \beta _ { 1 } = \beta _ { 2 } = \beta _ { 3 } = \beta _ { 4 } = \beta _ { 5 } = \beta _ { 6 } = 0$ b) $H _ { 0 } : \beta _ { 1 } = \beta _ { 2 } = \beta _ { 3 } = \beta _ { 4 } = \beta _ { 5 } = \beta _ { 6 } = 0$ c) $H _ { 0 } : \beta _ { 0 } = \beta _ { 1 } = \beta _ { 2 } = \beta _ { 3 } = \beta _ { 4 } = \beta _ { 5 } = \beta _ { 6 }$ d) $H _ { 0 } : \beta _ { 1 } = \beta _ { 2 } = \beta _ { 3 } = \beta _ { 4 } = \beta _ { 5 } = \beta _ { 6 }$

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, what are the numerator and denominator degrees of freedom, respectively, for 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 17-6 A weight-loss clinic wants to use regression analysis to build a model for weight-loss of a client (measured in pounds). Two variables thought to affect weight-loss are client's length of time on the weight loss program and time of session. These variables are described below: Y = Weight-loss (in pounds) = Length of time in weight-loss program (in months) =1 if morning session, 0 if not =1 if afternoon session, 0 if not (Base level = evening session) Data for 12 clients on a weight-loss program at the clinic were collected and used to fit the interaction model: $\quad Y = \beta _ { 0 } + \beta _ { 1 } X _ { 1 } + \beta _ { 2 } X _ { 2 } + \beta _ { 3 } X _ { 3 } + \beta _ { 4 } X _ { 1 } X _ { 2 } + \beta _ { 5 } X _ { 1 } X _ { 3 } + \varepsilon$ Partial output from Microsoft Excel follows: Regression Statistics Multiple R 0.73514 R Square 0.540438 Adjusted R Square 0.157469 Standard Error 12.4147 Observations 12 $\text { ANOVA }$ $F=5.41118 \quad \text { Significance } F=0.040201$ Coeff StdError t Stat P -value Intercept 0.089744 14.127 0.0060 0.9951 Length 6.22538 2.43473 2.54956 0.0479 Morn Ses 2.217272 22.1416 0.100141 0.9235 Aft Ses 11.8233 3.1545 3.558901 0.0165 Length*Morn Ses 0.77058 3.562 0.216334 0.8359 Length"Aft Ses -0.54147 3.35988 -0.161158 0.8773 -Referring to Scenario 17-6, in terms of the ?s in the model, give the mean change in weight- loss (Y) for every 1 month increase in time in the program (X1) when attending the afternoon Session.

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 standard error of the estimate is _________.

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, the null hypothesis should be rejected at a 5% level of significance when testing whether instructional spending per pupil has any effect on percentage of students passing the proficiency test, taking into account the effect of all the other independent variables.

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 slowest growth in business-to-consumer ecommerce sales last year?