FiltersDone

Question type

Essay

Multiple Choice

Short Answer

True False

Matching

Exam 17: Getting Ready to Analyze Data

Show Answer

Share

---

All types

Filters

Study FlashcardsPractice ExamLearn

Question 21

True/False

Review LaterAdd Note

Review Later

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 $0.1201$ . $\begin{array}{lr}\hline{\text { Regression Statistics }} \\\hline \text { Multiple R } & 0.7035 \\\text { R Square } & 0.4949 \\\text { Adjusted R } & 0.4030 \\\text { Square } & \\\text { Standard } & 18.4861 \\\text { Error } & \\\text { Observations } & 40 \\\hline\end{array}$ $\text { ANOVA }$ $\begin{array}{l}\begin{array} { l r r r r r r } \hline & \text { Coefficients } & \text { Standard Error } & { t \text { Stat } } & \text { P-value } & \text { Lower 95\% } & \text { Upper 95\% } \\\hline \text { Intercept } & 32.6595 & 23.18302 & 1.4088 & 0.1683 & - 14.5067 & 79.8257 \\\text { Age } & 1.2915 & 0.3599 & 3.5883 & 0.0011 & 0.5592 & 2.0238 \\\text { Edu } & - 1.3537 & 1.1766 & - 1.1504 & 0.2582 & - 3.7476 & 1.0402 \\\text { Job Yr } & 0.6171 & 0.5940 & 1.0389 & 0.3064 & - 0.5914 & 1.8257 \\\text { Married } & - 5.2189 & 7.6068 & - 0.6861 & 0.4974 & - 20.6950 & 10.2571 \\\text { Head } & - 14.2978 & 7.6479 & - 1.8695 & 0.0704 & - 29.8575 & 1.2618 \\\text { Manager } & - 24.8203 & 11.6932 & - 2.1226 & 0.0414 & - 48.6102 & - 1.0303 \\\hline\end{array}\end{array}$ -Referring to Scenario 17-10 Model 1, there is sufficient evidence that age has an 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 at a 10% level of significance.

A) True
B) False

Correct Answer

verified

Show Answer

Question 22

True/False

Review LaterAdd Note

Review Later

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, there is enough evidence to conclude that MPG makes a significant contribution to the regression model in the presence of the other independent variables at a 5% level of significance.

A) True
B) False

Correct Answer

verified

Show Answer

Question 23

Multiple Choice

Review LaterAdd Note

Suppose the probability of a power outage at a nuclear power plant on a single day is the same every day of the year. Also the probability of having a power outage on a single day does not Increase or decrease the probability of a power outage on another day. Which of the following Distributions would you use to determine the probability that a power outage will occur next Monday?

Some business analytics involve starting with many variables, followed by filtering the data by exploring specific combinations of categorical values or numerical range. In Excel, this approach is mimicked by using a drill-down.

The probability that a particular brand of smoke alarm will function properly and sound an alarm in the presence of smoke is 0.8. You have 5 such alarms in your home and they operate Independently. Which of the following distributions would you use to determine the probability That all of them will function properly in case of a fire?

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 $0.1201$ . $\begin{array}{lr}\hline{\text { Regression Statistics }} \\\hline \text { Multiple R } & 0.7035 \\\text { R Square } & 0.4949 \\\text { Adjusted R } & 0.4030 \\\text { Square } & \\\text { Standard } & 18.4861 \\\text { Error } & \\\text { Observations } & 40 \\\hline\end{array}$ $\text { ANOVA }$ $\begin{array}{l}\begin{array} { l r r r r r r } \hline & \text { Coefficients } & \text { Standard Error } & { t \text { Stat } } & \text { P-value } & \text { Lower 95\% } & \text { Upper 95\% } \\\hline \text { Intercept } & 32.6595 & 23.18302 & 1.4088 & 0.1683 & - 14.5067 & 79.8257 \\\text { Age } & 1.2915 & 0.3599 & 3.5883 & 0.0011 & 0.5592 & 2.0238 \\\text { Edu } & - 1.3537 & 1.1766 & - 1.1504 & 0.2582 & - 3.7476 & 1.0402 \\\text { Job Yr } & 0.6171 & 0.5940 & 1.0389 & 0.3064 & - 0.5914 & 1.8257 \\\text { Married } & - 5.2189 & 7.6068 & - 0.6861 & 0.4974 & - 20.6950 & 10.2571 \\\text { Head } & - 14.2978 & 7.6479 & - 1.8695 & 0.0704 & - 29.8575 & 1.2618 \\\text { Manager } & - 24.8203 & 11.6932 & - 2.1226 & 0.0414 & - 48.6102 & - 1.0303 \\\hline\end{array}\end{array}$ -Referring to Scenario 17-10 Model 1, what is the p-value of 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 17-12 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 expression for the estimated model? a) $Y = - 70.49 + 0.2868$ Income $+ 1.0647$ LawnSize $- 12.744$ Atitude $- 0.200$ Teenager $+ 1.0792$ Age b) $\begin{aligned} \hat { Y } = & - 70.49 + 0.2868 \text { Income } + 1.0647 \text { LawnSize } - 12.744 \text { Atitude } \\ & - 0.200 \text { Teenager } + 1.0792 \text { Age } \end{aligned}$ c) $\ln ($ odds ratio $) = - 70.49 + 0.2868$ Income $+ 1.0647$ LawnSize $- 12.744$ Atitude $- 0.200$ Teenager $+ 1.0792$ Age d) $\ln ($ estimated odds ratio) $= - 70.49 + 0.2868$ Income $+ 1.0647$ LawnSize $- 12.744$ Atitude $- 0.200$ Teenager $+ 1.0792$ Age

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 $0.1201$ . $\begin{array}{lr}\hline{\text { Regression Statistics }} \\\hline \text { Multiple R } & 0.7035 \\\text { R Square } & 0.4949 \\\text { Adjusted R } & 0.4030 \\\text { Square } & \\\text { Standard } & 18.4861 \\\text { Error } & \\\text { Observations } & 40 \\\hline\end{array}$ $\text { ANOVA }$ $\begin{array}{l}\begin{array} { l r r r r r r } \hline & \text { Coefficients } & \text { Standard Error } & { t \text { Stat } } & \text { P-value } & \text { Lower 95\% } & \text { Upper 95\% } \\\hline \text { Intercept } & 32.6595 & 23.18302 & 1.4088 & 0.1683 & - 14.5067 & 79.8257 \\\text { Age } & 1.2915 & 0.3599 & 3.5883 & 0.0011 & 0.5592 & 2.0238 \\\text { Edu } & - 1.3537 & 1.1766 & - 1.1504 & 0.2582 & - 3.7476 & 1.0402 \\\text { Job Yr } & 0.6171 & 0.5940 & 1.0389 & 0.3064 & - 0.5914 & 1.8257 \\\text { Married } & - 5.2189 & 7.6068 & - 0.6861 & 0.4974 & - 20.6950 & 10.2571 \\\text { Head } & - 14.2978 & 7.6479 & - 1.8695 & 0.0704 & - 29.8575 & 1.2618 \\\text { Manager } & - 24.8203 & 11.6932 & - 2.1226 & 0.0414 & - 48.6102 & - 1.0303 \\\hline\end{array}\end{array}$ -Referring to Scenario 17-10 and using both Model 1 and Model 2, what are the null and alternative hypotheses 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?

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 $0.1201$ . $\begin{array}{lr}\hline{\text { Regression Statistics }} \\\hline \text { Multiple R } & 0.7035 \\\text { R Square } & 0.4949 \\\text { Adjusted R } & 0.4030 \\\text { Square } & \\\text { Standard } & 18.4861 \\\text { Error } & \\\text { Observations } & 40 \\\hline\end{array}$ $\text { ANOVA }$ $\begin{array}{l}\begin{array} { l r r r r r r } \hline & \text { Coefficients } & \text { Standard Error } & { t \text { Stat } } & \text { P-value } & \text { Lower 95\% } & \text { Upper 95\% } \\\hline \text { Intercept } & 32.6595 & 23.18302 & 1.4088 & 0.1683 & - 14.5067 & 79.8257 \\\text { Age } & 1.2915 & 0.3599 & 3.5883 & 0.0011 & 0.5592 & 2.0238 \\\text { Edu } & - 1.3537 & 1.1766 & - 1.1504 & 0.2582 & - 3.7476 & 1.0402 \\\text { Job Yr } & 0.6171 & 0.5940 & 1.0389 & 0.3064 & - 0.5914 & 1.8257 \\\text { Married } & - 5.2189 & 7.6068 & - 0.6861 & 0.4974 & - 20.6950 & 10.2571 \\\text { Head } & - 14.2978 & 7.6479 & - 1.8695 & 0.0704 & - 29.8575 & 1.2618 \\\text { Manager } & - 24.8203 & 11.6932 & - 2.1226 & 0.0414 & - 48.6102 & - 1.0303 \\\hline\end{array}\end{array}$ -Referring to Scenario 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?2 .

A powerful women's group has claimed that men and women differ in attitudes about sexual discrimination. A group of 50 men (group 1) and 40 women (group 2) were asked if they thought Sexual discrimination is a problem in the United States. Of those sampled, 11 of the men and 19 Of the women did believe that sexual discrimination is a problem. Which of the following tests Will you use to find out if there is any difference in attitudes about sexual discrimination?

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: $\begin{array}{lr}\hline{\text { Regression Statistics }} \\\hline \text { Multiple R } & 0.7930 \\\text { R Square } & 0.6288 \\\text { Adjusted R } & 0.6029 \\\text { Square } & \\\text { Standard } & 10.4570 \\\text { Error } & \\\text { Observations } & 47 \\\hline\end{array}$ ANOVA $\begin{array}{lrrrrrr}\hline & \text { Coefficients } & \begin{array}{c}\text { Standard } \\\text { Error }\end{array} & \text { t Stat } & \text { P-value } & \text { Lower 95\% } & \text { Upper 95\% } \\\hline \text { Intercept } & -753.4225 & 101.1149 & -7.4511 & 0.0000 & -957.3401 & -549.5050 \\\text { \% Attendance } & 8.5014 & 1.0771 & 7.8929 & 0.0000 & 6.3292 & 10.6735 \\\text { Salary } & 0.000000685 & 0.0006 & 0.0011 & 0.9991 & -0.0013 & 0.0013 \\\text { Spending } & 0.0060 & 0.0046 & 1.2879 & 0.2047 & -0.0034 & 0.0153 \\\hline\end{array}$ -Referring to Scenario 17-8, the alternative hypothesis $H _ { 1 } \text { : At least one of } \beta _ { j } \neq 0 \text { for } j = 1,2 \text {. }$ , 3 implies that percentage of students passing the proficiency test is related to at least one of the explanatory variables.

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 $\begin{array} { l l } \text { Multiple R } & 0.865 \\ \text { R Square } & 0.748 \\ \text { Adjusted R Square } & 0.726 \\ \text { Standard Error } & 5.195 \\ \text { Observations } & 50 \end{array}$ ANOVA $\begin{array} { l c c c c c } & d f & \text { SS } & \text { MS } & F & \text { Signif } F \\ \text { Regression } & & 3605.7736 & 1201.9245 & & 0.0000 \\ \text { Residual } & & 1214.2264 & 26.3962 & & \\ \text { Total } & 49 & 4820.0000 & & & \end{array}$ $\begin{array} { l c l c c } & \text { Coeff } & \text { StdError } & t \text { Stat } & P \text {-value } \\ \text { Intercept } & - 1.6335 & 5.8078 & - 0.281 & 0.7798 \\ \text { Income } & 0.4485 & 0.1137 & 3.9545 & 0.0003 \\ \text { Size } & 4.2615 & 0.8062 & 5.286 & 0.0001 \\ \text { School } & - 0.6517 & 0.4319 & - 1.509 & 0.1383 \end{array}$ -Referring to Scenario 17-1, what fraction of the variability in house size is explained by income, size of family, and education?

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 p-value of the test statistic to determine whether 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 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 $0.1201$ . $\begin{array}{lr}\hline{\text { Regression Statistics }} \\\hline \text { Multiple R } & 0.7035 \\\text { R Square } & 0.4949 \\\text { Adjusted R } & 0.4030 \\\text { Square } & \\\text { Standard } & 18.4861 \\\text { Error } & \\\text { Observations } & 40 \\\hline\end{array}$ $\text { ANOVA }$ $\begin{array}{l}\begin{array} { l r r r r r r } \hline & \text { Coefficients } & \text { Standard Error } & { t \text { Stat } } & \text { P-value } & \text { Lower 95\% } & \text { Upper 95\% } \\\hline \text { Intercept } & 32.6595 & 23.18302 & 1.4088 & 0.1683 & - 14.5067 & 79.8257 \\\text { Age } & 1.2915 & 0.3599 & 3.5883 & 0.0011 & 0.5592 & 2.0238 \\\text { Edu } & - 1.3537 & 1.1766 & - 1.1504 & 0.2582 & - 3.7476 & 1.0402 \\\text { Job Yr } & 0.6171 & 0.5940 & 1.0389 & 0.3064 & - 0.5914 & 1.8257 \\\text { Married } & - 5.2189 & 7.6068 & - 0.6861 & 0.4974 & - 20.6950 & 10.2571 \\\text { Head } & - 14.2978 & 7.6479 & - 1.8695 & 0.0704 & - 29.8575 & 1.2618 \\\text { Manager } & - 24.8203 & 11.6932 & - 2.1226 & 0.0414 & - 48.6102 & - 1.0303 \\\hline\end{array}\end{array}$ -Referring to Scenario 17-10 and using both Model 1 and Model 2, there is insufficient evidence to conclude that the independent variables that are not significant individually are significant as a group in explaining the variation in the dependent variable at a 5% level of significance?

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 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?

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: $\begin{array}{l}\begin{array}{lr}\hline {\text { Regression Statistics }} \\\hline \text { Multiple R } & 0.63 \\\text { R Square } & 0.40 \\\text { Adjusted R Square } & 0.23 \\\text { Standard Error } & 50.00 \\\text { Observations } & 15.00 \\\hline\end{array}\\\\\text { ANOVA }\\\begin{array}{lrcccr}\hline & d f &{\text { SS }} & \text { MS } & \text { F }&{\text { Significance } F} \\\hline \text { Regression } & 3 & & 5994.24 & 2.40 & 0.12 \\\text { Residual } & 11 & 27496.82 & & & \\\text { Total } & & 45479.54 & & & \\\hline\end{array}\\\\\begin{array}{lrrrrrr}\hline & \text { Coefficients } & \begin{array}{c}\text { Standard } \\\text { Error }\end{array} & \text { t Stat } & \text { P-value } & \text { Lower 99.0\% } & \text { Upper 99.0\% } \\\hline \text { Intercept } & 123.80 & 48.71 & 2.54 & 0.03 & -27.47 & 275.07 \\\text { AGE } & -0.82 & 0.87 & -0.95 & 0.36 & -3.51 & 1.87 \\\text { TICKETS } & 21.25 & 10.66 & 1.99 & 0.07 & -11.86 & 54.37 \\\text { DENSITY } & -3.14 & 6.46 & -0.49 & 0.64 & -23.19 & 16.91 \\\hline\end{array}\end{array}$ 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 regression sum of squares that is missing in the ANOVA table should be ______.

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 $0.1201$ . $\begin{array}{lr}\hline{\text { Regression Statistics }} \\\hline \text { Multiple R } & 0.7035 \\\text { R Square } & 0.4949 \\\text { Adjusted R } & 0.4030 \\\text { Square } & \\\text { Standard } & 18.4861 \\\text { Error } & \\\text { Observations } & 40 \\\hline\end{array}$ $\text { ANOVA }$ $\begin{array}{l}\begin{array} { l r r r r r r } \hline & \text { Coefficients } & \text { Standard Error } & { t \text { Stat } } & \text { P-value } & \text { Lower 95\% } & \text { Upper 95\% } \\\hline \text { Intercept } & 32.6595 & 23.18302 & 1.4088 & 0.1683 & - 14.5067 & 79.8257 \\\text { Age } & 1.2915 & 0.3599 & 3.5883 & 0.0011 & 0.5592 & 2.0238 \\\text { Edu } & - 1.3537 & 1.1766 & - 1.1504 & 0.2582 & - 3.7476 & 1.0402 \\\text { Job Yr } & 0.6171 & 0.5940 & 1.0389 & 0.3064 & - 0.5914 & 1.8257 \\\text { Married } & - 5.2189 & 7.6068 & - 0.6861 & 0.4974 & - 20.6950 & 10.2571 \\\text { Head } & - 14.2978 & 7.6479 & - 1.8695 & 0.0704 & - 29.8575 & 1.2618 \\\text { Manager } & - 24.8203 & 11.6932 & - 2.1226 & 0.0414 & - 48.6102 & - 1.0303 \\\hline\end{array}\end{array}$ -Referring to Scenario 17-10 and using both Model 1 and Model 2, what is the p-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?

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 $0.1201$ . $\begin{array}{lr}\hline{\text { Regression Statistics }} \\\hline \text { Multiple R } & 0.7035 \\\text { R Square } & 0.4949 \\\text { Adjusted R } & 0.4030 \\\text { Square } & \\\text { Standard } & 18.4861 \\\text { Error } & \\\text { Observations } & 40 \\\hline\end{array}$ $\text { ANOVA }$ $\begin{array}{l}\begin{array} { l r r r r r r } \hline & \text { Coefficients } & \text { Standard Error } & { t \text { Stat } } & \text { P-value } & \text { Lower 95\% } & \text { Upper 95\% } \\\hline \text { Intercept } & 32.6595 & 23.18302 & 1.4088 & 0.1683 & - 14.5067 & 79.8257 \\\text { Age } & 1.2915 & 0.3599 & 3.5883 & 0.0011 & 0.5592 & 2.0238 \\\text { Edu } & - 1.3537 & 1.1766 & - 1.1504 & 0.2582 & - 3.7476 & 1.0402 \\\text { Job Yr } & 0.6171 & 0.5940 & 1.0389 & 0.3064 & - 0.5914 & 1.8257 \\\text { Married } & - 5.2189 & 7.6068 & - 0.6861 & 0.4974 & - 20.6950 & 10.2571 \\\text { Head } & - 14.2978 & 7.6479 & - 1.8695 & 0.0704 & - 29.8575 & 1.2618 \\\text { Manager } & - 24.8203 & 11.6932 & - 2.1226 & 0.0414 & - 48.6102 & - 1.0303 \\\hline\end{array}\end{array}$ -Referring to Scenario 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.

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: $\begin{aligned} Y & = \text { Weight-loss (in pounds) } \\ X _ { 1 } & = \text { Length of time in weight-loss program (in months) } \\ X _ { 2 } & = 1 \text { if morning session, } 0 \text { if not } \\ X _ { 3 } & = 1 \text { if afternoon session, } 0 \text { if not } \quad \text { (Base level = evening session) } \end{aligned}$ 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: $\begin{array}{ll}{\text { Regression Statistics }} \\\text { Multiple R } & 0.73514 \\\text { R Square } & 0.540438 \\\text { Adjusted R Square } & 0.157469 \\\text { Standard Error } & 12.4147 \\\text { Observations } & 12\end{array}$ $\text { ANOVA }$ $F=5.41118 \quad \text { Significance } F=0.040201$ $\begin{array}{ccccc} & \text { Coeff } & \text { StdError } & t \text { Stat } & P \text {-value } \\\text { Intercept } & 0.089744 & 14.127 & 0.0060 & 0.9951 \\\text { Length }\left(X_{1}\right) & 6.22538 & 2.43473 & 2.54956 & 0.0479 \\\text { Morn Ses }\left(X_{2}\right) & 2.217272 & 22.1416 & 0.100141 & 0.9235 \\\text { Aft Ses }\left(X_{3}\right) & 11.8233 & 3.1545 & 3.558901 & 0.0165 \\\text { Length*Morn Ses } & 0.77058 & 3.562 & 0.216334 & 0.8359 \\\text { Length"Aft Ses } & -0.54147 & 3.35988 & -0.161158 & 0.8773\end{array}$ -Referring to Scenario 17-6, which of the following statements is supported by the analysis shown? a) There is sufficient evidence (at $\alpha = 0.05$ ) of curvature in the relationship between weight-loss $( Y )$ and months in program $\left( X _ { 1 } \right)$ . b) There is sufficient evidence (at $\alpha = 0.05$ ) to indicate that the relationship between weight-loss $( Y )$ and months in program $\left( X _ { 1 } \right)$ depends on session time. c) There is sufficient evidence (at $\alpha = 0.10$ ) to indicate that the session time (morning, afternoon, evening) affects weight-loss $( Y )$ . d) There is insufficient evidence (at $\alpha = 0.10$ ) to indicate that the relationship between weight-loss $( Y )$ and months in program $\left( X _ { 1 } \right)$ depends on session time.

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 first split occurs at what price?