The multiple regression for BMI using x 1 and x 2 as explanatory variables.

Question

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Answer 1

Question

Chapter 11, Problem 25E

(a)

To determine

To find: The multiple regression for BMI using x1and x2 as explanatory variables.

(a)

Expert Solution

Answer to Problem 25E

Solution: The required multiple regression model is BMI=23.4−0.682x1+0.102x2_.

Explanation of Solution

Given: The data for the PA and BMI are given below:

Introduction to the Practice of Statistics, Chapter 11, Problem 25E , additional homework tip 1

Calculation: The explanatory variables are x1=(PA−8.614)and x2=(PA−8.614)2

To obtain multiple regression analysis by using Minitab, follow the steps below:

Step 1: Enter the data in Minitab worksheet.

Step 2: Go to Calc>Calculator.

Step 3: Enter x1=PA−8.614 in Store result in variable for Expression.

Step 4: Click OK.

Step 5: Repeat the steps. Enter x2=(PA−8.614)2 in Store result in variable for Expression.

Step 6: Go to Stat > Regression > Regression

Step 7: Select BMI in Response and select x1 and x2 in Predictors.

Step 8: Click OK.

The multiple regression model is obtained as BMI=23.4−0.682x1+0.102x2.

(b)

To determine

To find: The value of R2.

(b)

Expert Solution

Answer to Problem 25E

Solution: The value of R2 17.7%.

Explanation of Solution

It can be seen from part (b) that R2 is obtained as 17.7% which is explained by predictors x1 and x2. The percentage of R2 is very low. It indicates that the model is not good with this quadratic term.

(c)

To determine

To graph: The Normal quantile plot.

(c)

Expert Solution

Explanation of Solution

Graph: To perform the multiple regression by using year and census count as explanatory variables use Minitab. Follow the steps below:

Step 1: Enter the data in Minitab worksheet.

Step 2: Go to Stat> Regression >Regression.

Step 3: Select BMI in Response and select x1 and x2 in Predictors.

Step 4: Click on Graphs and select “Residuals versus fits.”

Step 5: Click OK.

The residual plot is obtained as:

Introduction to the Practice of Statistics, Chapter 11, Problem 25E , additional homework tip 2

Interpretation: From the obtained residual plot, it can be concluded that the plot represents no pattern and the data points are randomly scattered.

(d)

To determine

To test: The hypothesis that coefficient of the variable PA−8.614 is equal to zero.

(d)

Expert Solution

Answer to Problem 25E

Solution: There is enough evidence to conclude that there is no linear increase over time.

Explanation of Solution

Calculation: From the output which is obtained in part (b), the regression equation is BMI=23.4−0.682x1+0.102x2. The standard error is 0.0555. From the equation, it can be seen that the coefficient of x2 is b2=0.102. To test the hypothesis that there is a linear rise over time, the null and alternative hypotheses can be stated as:

H0:β2=0Hα:β2≠0

The level of significance is 0.05. The test statistic under null hypothesis is calculated as:

t=b2sb1=0.1020.05556=1.835

The p-value can be calculated as:

p−value=2P(t≥|tcal|)=2P(t≥1.835)=2(0.034)=0.0678

The p-value is 0.0678.

Conclusion: The obtained p-value is greater than the significance level. Hence, there is enough evidence to conclude that the quadratic term contributes insignificantly to the fit.

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Answer 2

Question

Chapter 11, Problem 25E

(a)

To determine

To find: The multiple regression for BMI using x1and x2 as explanatory variables.

(a)

Expert Solution

Answer to Problem 25E

Solution: The required multiple regression model is BMI=23.4−0.682x1+0.102x2_.

Explanation of Solution

Given: The data for the PA and BMI are given below:

Introduction to the Practice of Statistics, Chapter 11, Problem 25E , additional homework tip 1

Calculation: The explanatory variables are x1=(PA−8.614)and x2=(PA−8.614)2

To obtain multiple regression analysis by using Minitab, follow the steps below:

Step 1: Enter the data in Minitab worksheet.

Step 2: Go to Calc>Calculator.

Step 3: Enter x1=PA−8.614 in Store result in variable for Expression.

Step 4: Click OK.

Step 5: Repeat the steps. Enter x2=(PA−8.614)2 in Store result in variable for Expression.

Step 6: Go to Stat > Regression > Regression

Step 7: Select BMI in Response and select x1 and x2 in Predictors.

Step 8: Click OK.

The multiple regression model is obtained as BMI=23.4−0.682x1+0.102x2.

(b)

To determine

To find: The value of R2.

(b)

Expert Solution

Answer to Problem 25E

Solution: The value of R2 17.7%.

Explanation of Solution

It can be seen from part (b) that R2 is obtained as 17.7% which is explained by predictors x1 and x2. The percentage of R2 is very low. It indicates that the model is not good with this quadratic term.

(c)

To determine

To graph: The Normal quantile plot.

(c)

Expert Solution

Explanation of Solution

Graph: To perform the multiple regression by using year and census count as explanatory variables use Minitab. Follow the steps below:

Step 1: Enter the data in Minitab worksheet.

Step 2: Go to Stat> Regression >Regression.

Step 3: Select BMI in Response and select x1 and x2 in Predictors.

Step 4: Click on Graphs and select “Residuals versus fits.”

Step 5: Click OK.

The residual plot is obtained as:

Introduction to the Practice of Statistics, Chapter 11, Problem 25E , additional homework tip 2

Interpretation: From the obtained residual plot, it can be concluded that the plot represents no pattern and the data points are randomly scattered.

(d)

To determine

To test: The hypothesis that coefficient of the variable PA−8.614 is equal to zero.

(d)

Expert Solution

Answer to Problem 25E

Solution: There is enough evidence to conclude that there is no linear increase over time.

Explanation of Solution

Calculation: From the output which is obtained in part (b), the regression equation is BMI=23.4−0.682x1+0.102x2. The standard error is 0.0555. From the equation, it can be seen that the coefficient of x2 is b2=0.102. To test the hypothesis that there is a linear rise over time, the null and alternative hypotheses can be stated as:

H0:β2=0Hα:β2≠0

The level of significance is 0.05. The test statistic under null hypothesis is calculated as:

t=b2sb1=0.1020.05556=1.835

The p-value can be calculated as:

p−value=2P(t≥|tcal|)=2P(t≥1.835)=2(0.034)=0.0678

The p-value is 0.0678.

Conclusion: The obtained p-value is greater than the significance level. Hence, there is enough evidence to conclude that the quadratic term contributes insignificantly to the fit.

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Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 3

Question

Chapter 11, Problem 25E

(a)

To determine

To find: The multiple regression for BMI using x1and x2 as explanatory variables.

(a)

Expert Solution

Answer to Problem 25E

Solution: The required multiple regression model is BMI=23.4−0.682x1+0.102x2_.

Explanation of Solution

Given: The data for the PA and BMI are given below:

Introduction to the Practice of Statistics, Chapter 11, Problem 25E , additional homework tip 1

Calculation: The explanatory variables are x1=(PA−8.614)and x2=(PA−8.614)2

To obtain multiple regression analysis by using Minitab, follow the steps below:

Step 1: Enter the data in Minitab worksheet.

Step 2: Go to Calc>Calculator.

Step 3: Enter x1=PA−8.614 in Store result in variable for Expression.

Step 4: Click OK.

Step 5: Repeat the steps. Enter x2=(PA−8.614)2 in Store result in variable for Expression.

Step 6: Go to Stat > Regression > Regression

Step 7: Select BMI in Response and select x1 and x2 in Predictors.

Step 8: Click OK.

The multiple regression model is obtained as BMI=23.4−0.682x1+0.102x2.

(b)

To determine

To find: The value of R2.

(b)

Expert Solution

Answer to Problem 25E

Solution: The value of R2 17.7%.

Explanation of Solution

It can be seen from part (b) that R2 is obtained as 17.7% which is explained by predictors x1 and x2. The percentage of R2 is very low. It indicates that the model is not good with this quadratic term.

(c)

To determine

To graph: The Normal quantile plot.

(c)

Expert Solution

Explanation of Solution

Graph: To perform the multiple regression by using year and census count as explanatory variables use Minitab. Follow the steps below:

Step 1: Enter the data in Minitab worksheet.

Step 2: Go to Stat> Regression >Regression.

Step 3: Select BMI in Response and select x1 and x2 in Predictors.

Step 4: Click on Graphs and select “Residuals versus fits.”

Step 5: Click OK.

The residual plot is obtained as:

Introduction to the Practice of Statistics, Chapter 11, Problem 25E , additional homework tip 2

Interpretation: From the obtained residual plot, it can be concluded that the plot represents no pattern and the data points are randomly scattered.

(d)

To determine

To test: The hypothesis that coefficient of the variable PA−8.614 is equal to zero.

(d)

Expert Solution

Answer to Problem 25E

Solution: There is enough evidence to conclude that there is no linear increase over time.

Explanation of Solution

Calculation: From the output which is obtained in part (b), the regression equation is BMI=23.4−0.682x1+0.102x2. The standard error is 0.0555. From the equation, it can be seen that the coefficient of x2 is b2=0.102. To test the hypothesis that there is a linear rise over time, the null and alternative hypotheses can be stated as:

H0:β2=0Hα:β2≠0

The level of significance is 0.05. The test statistic under null hypothesis is calculated as:

t=b2sb1=0.1020.05556=1.835

The p-value can be calculated as:

p−value=2P(t≥|tcal|)=2P(t≥1.835)=2(0.034)=0.0678

The p-value is 0.0678.

Conclusion: The obtained p-value is greater than the significance level. Hence, there is enough evidence to conclude that the quadratic term contributes insignificantly to the fit.

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Answer 4

Question

Chapter 11, Problem 25E

(a)

To determine

To find: The multiple regression for BMI using x1and x2 as explanatory variables.

(a)

Expert Solution

Answer to Problem 25E

Solution: The required multiple regression model is BMI=23.4−0.682x1+0.102x2_.

Explanation of Solution

Given: The data for the PA and BMI are given below:

Introduction to the Practice of Statistics, Chapter 11, Problem 25E , additional homework tip 1

Calculation: The explanatory variables are x1=(PA−8.614)and x2=(PA−8.614)2

To obtain multiple regression analysis by using Minitab, follow the steps below:

Step 1: Enter the data in Minitab worksheet.

Step 2: Go to Calc>Calculator.

Step 3: Enter x1=PA−8.614 in Store result in variable for Expression.

Step 4: Click OK.

Step 5: Repeat the steps. Enter x2=(PA−8.614)2 in Store result in variable for Expression.

Step 6: Go to Stat > Regression > Regression

Step 7: Select BMI in Response and select x1 and x2 in Predictors.

Step 8: Click OK.

The multiple regression model is obtained as BMI=23.4−0.682x1+0.102x2.

(b)

To determine

To find: The value of R2.

(b)

Expert Solution

Answer to Problem 25E

Solution: The value of R2 17.7%.

Explanation of Solution

It can be seen from part (b) that R2 is obtained as 17.7% which is explained by predictors x1 and x2. The percentage of R2 is very low. It indicates that the model is not good with this quadratic term.

(c)

To determine

To graph: The Normal quantile plot.

(c)

Expert Solution

Explanation of Solution

Graph: To perform the multiple regression by using year and census count as explanatory variables use Minitab. Follow the steps below:

Step 1: Enter the data in Minitab worksheet.

Step 2: Go to Stat> Regression >Regression.

Step 3: Select BMI in Response and select x1 and x2 in Predictors.

Step 4: Click on Graphs and select “Residuals versus fits.”

Step 5: Click OK.

The residual plot is obtained as:

Introduction to the Practice of Statistics, Chapter 11, Problem 25E , additional homework tip 2

Interpretation: From the obtained residual plot, it can be concluded that the plot represents no pattern and the data points are randomly scattered.

(d)

To determine

To test: The hypothesis that coefficient of the variable PA−8.614 is equal to zero.

(d)

Expert Solution

Answer to Problem 25E

Solution: There is enough evidence to conclude that there is no linear increase over time.

Explanation of Solution

Calculation: From the output which is obtained in part (b), the regression equation is BMI=23.4−0.682x1+0.102x2. The standard error is 0.0555. From the equation, it can be seen that the coefficient of x2 is b2=0.102. To test the hypothesis that there is a linear rise over time, the null and alternative hypotheses can be stated as:

H0:β2=0Hα:β2≠0

The level of significance is 0.05. The test statistic under null hypothesis is calculated as:

t=b2sb1=0.1020.05556=1.835

The p-value can be calculated as:

p−value=2P(t≥|tcal|)=2P(t≥1.835)=2(0.034)=0.0678

The p-value is 0.0678.

Conclusion: The obtained p-value is greater than the significance level. Hence, there is enough evidence to conclude that the quadratic term contributes insignificantly to the fit.

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Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 5

Chapter 11, Problem 25E

(a)

To determine

To find: The multiple regression for BMI using x1and x2 as explanatory variables.

(a)

Expert Solution

Answer to Problem 25E

Solution: The required multiple regression model is BMI=23.4−0.682x1+0.102x2_.

Explanation of Solution

Given: The data for the PA and BMI are given below:

Introduction to the Practice of Statistics, Chapter 11, Problem 25E , additional homework tip 1

Calculation: The explanatory variables are x1=(PA−8.614)and x2=(PA−8.614)2

To obtain multiple regression analysis by using Minitab, follow the steps below:

Step 1: Enter the data in Minitab worksheet.

Step 2: Go to Calc>Calculator.

Step 3: Enter x1=PA−8.614 in Store result in variable for Expression.

Step 4: Click OK.

Step 5: Repeat the steps. Enter x2=(PA−8.614)2 in Store result in variable for Expression.

Step 6: Go to Stat > Regression > Regression

Step 7: Select BMI in Response and select x1 and x2 in Predictors.

Step 8: Click OK.

The multiple regression model is obtained as BMI=23.4−0.682x1+0.102x2.

(b)

To determine

To find: The value of R2.

(b)

Expert Solution

Answer to Problem 25E

Solution: The value of R2 17.7%.

Explanation of Solution

It can be seen from part (b) that R2 is obtained as 17.7% which is explained by predictors x1 and x2. The percentage of R2 is very low. It indicates that the model is not good with this quadratic term.

(c)

To determine

To graph: The Normal quantile plot.

(c)

Expert Solution

Explanation of Solution

Graph: To perform the multiple regression by using year and census count as explanatory variables use Minitab. Follow the steps below:

Step 1: Enter the data in Minitab worksheet.

Step 2: Go to Stat> Regression >Regression.

Step 3: Select BMI in Response and select x1 and x2 in Predictors.

Step 4: Click on Graphs and select “Residuals versus fits.”

Step 5: Click OK.

The residual plot is obtained as:

Introduction to the Practice of Statistics, Chapter 11, Problem 25E , additional homework tip 2

Interpretation: From the obtained residual plot, it can be concluded that the plot represents no pattern and the data points are randomly scattered.

(d)

To determine

To test: The hypothesis that coefficient of the variable PA−8.614 is equal to zero.

(d)

Expert Solution

Answer to Problem 25E

Solution: There is enough evidence to conclude that there is no linear increase over time.

Explanation of Solution

Calculation: From the output which is obtained in part (b), the regression equation is BMI=23.4−0.682x1+0.102x2. The standard error is 0.0555. From the equation, it can be seen that the coefficient of x2 is b2=0.102. To test the hypothesis that there is a linear rise over time, the null and alternative hypotheses can be stated as:

H0:β2=0Hα:β2≠0

The level of significance is 0.05. The test statistic under null hypothesis is calculated as:

t=b2sb1=0.1020.05556=1.835

The p-value can be calculated as:

p−value=2P(t≥|tcal|)=2P(t≥1.835)=2(0.034)=0.0678

The p-value is 0.0678.

Conclusion: The obtained p-value is greater than the significance level. Hence, there is enough evidence to conclude that the quadratic term contributes insignificantly to the fit.

Answer 6

Chapter 11, Problem 25E

(a)

To determine

To find: The multiple regression for BMI using x1and x2 as explanatory variables.

(a)

Expert Solution

Answer to Problem 25E

Solution: The required multiple regression model is BMI=23.4−0.682x1+0.102x2_.

Explanation of Solution

Given: The data for the PA and BMI are given below:

Introduction to the Practice of Statistics, Chapter 11, Problem 25E , additional homework tip 1

Calculation: The explanatory variables are x1=(PA−8.614)and x2=(PA−8.614)2

To obtain multiple regression analysis by using Minitab, follow the steps below:

Step 1: Enter the data in Minitab worksheet.

Step 2: Go to Calc>Calculator.

Step 3: Enter x1=PA−8.614 in Store result in variable for Expression.

Step 4: Click OK.

Step 5: Repeat the steps. Enter x2=(PA−8.614)2 in Store result in variable for Expression.

Step 6: Go to Stat > Regression > Regression

Step 7: Select BMI in Response and select x1 and x2 in Predictors.

Step 8: Click OK.

The multiple regression model is obtained as BMI=23.4−0.682x1+0.102x2.

Answer 7

Chapter 11, Problem 25E

(a)

To determine

To find: The multiple regression for BMI using x1and x2 as explanatory variables.

Answer 8

(a)

Expert Solution

Answer to Problem 25E

Solution: The required multiple regression model is BMI=23.4−0.682x1+0.102x2_.

Answer 9

(a)

Expert Solution

Answer 10

(a)

Expert Solution

Answer 11

Expert Solution

Answer 12

Explanation of Solution

Given: The data for the PA and BMI are given below:

Introduction to the Practice of Statistics, Chapter 11, Problem 25E , additional homework tip 1

Calculation: The explanatory variables are x1=(PA−8.614)and x2=(PA−8.614)2

To obtain multiple regression analysis by using Minitab, follow the steps below:

Step 1: Enter the data in Minitab worksheet.

Step 2: Go to Calc>Calculator.

Step 3: Enter x1=PA−8.614 in Store result in variable for Expression.

Step 4: Click OK.

Step 5: Repeat the steps. Enter x2=(PA−8.614)2 in Store result in variable for Expression.

Step 6: Go to Stat > Regression > Regression

Step 7: Select BMI in Response and select x1 and x2 in Predictors.

Step 8: Click OK.

The multiple regression model is obtained as BMI=23.4−0.682x1+0.102x2.

Answer 13

(b)

To determine

To find: The value of R2.

(b)

Expert Solution

Answer to Problem 25E

Solution: The value of R2 17.7%.

Explanation of Solution

It can be seen from part (b) that R2 is obtained as 17.7% which is explained by predictors x1 and x2. The percentage of R2 is very low. It indicates that the model is not good with this quadratic term.

Answer 14

(b)

To determine

To find: The value of R2.

Answer 15

(b)

Expert Solution

Answer to Problem 25E

Solution: The value of R2 17.7%.

Answer 16

(b)

Expert Solution

Answer 17

(b)

Expert Solution

Answer 18

Expert Solution

Answer 19

Explanation of Solution

It can be seen from part (b) that R2 is obtained as 17.7% which is explained by predictors x1 and x2. The percentage of R2 is very low. It indicates that the model is not good with this quadratic term.

Answer 20

(c)

To determine

To graph: The Normal quantile plot.

(c)

Expert Solution

Explanation of Solution

Graph: To perform the multiple regression by using year and census count as explanatory variables use Minitab. Follow the steps below:

Step 1: Enter the data in Minitab worksheet.

Step 2: Go to Stat> Regression >Regression.

Step 3: Select BMI in Response and select x1 and x2 in Predictors.

Step 4: Click on Graphs and select “Residuals versus fits.”

Step 5: Click OK.

The residual plot is obtained as:

Introduction to the Practice of Statistics, Chapter 11, Problem 25E , additional homework tip 2

Interpretation: From the obtained residual plot, it can be concluded that the plot represents no pattern and the data points are randomly scattered.

Answer 21

(c)

To determine

To graph: The Normal quantile plot.

Answer 22

(c)

Expert Solution

Explanation of Solution

Graph: To perform the multiple regression by using year and census count as explanatory variables use Minitab. Follow the steps below:

Step 1: Enter the data in Minitab worksheet.

Step 2: Go to Stat> Regression >Regression.

Step 3: Select BMI in Response and select x1 and x2 in Predictors.

Step 4: Click on Graphs and select “Residuals versus fits.”

Step 5: Click OK.

The residual plot is obtained as:

Introduction to the Practice of Statistics, Chapter 11, Problem 25E , additional homework tip 2

Interpretation: From the obtained residual plot, it can be concluded that the plot represents no pattern and the data points are randomly scattered.

Answer 23

(c)

Expert Solution

Answer 24

(c)

Expert Solution

Answer 25

Expert Solution

Answer 26

(d)

To determine

To test: The hypothesis that coefficient of the variable PA−8.614 is equal to zero.

(d)

Expert Solution

Answer to Problem 25E

Solution: There is enough evidence to conclude that there is no linear increase over time.

Explanation of Solution

Calculation: From the output which is obtained in part (b), the regression equation is BMI=23.4−0.682x1+0.102x2. The standard error is 0.0555. From the equation, it can be seen that the coefficient of x2 is b2=0.102. To test the hypothesis that there is a linear rise over time, the null and alternative hypotheses can be stated as:

H0:β2=0Hα:β2≠0

The level of significance is 0.05. The test statistic under null hypothesis is calculated as:

t=b2sb1=0.1020.05556=1.835

The p-value can be calculated as:

p−value=2P(t≥|tcal|)=2P(t≥1.835)=2(0.034)=0.0678

The p-value is 0.0678.

Conclusion: The obtained p-value is greater than the significance level. Hence, there is enough evidence to conclude that the quadratic term contributes insignificantly to the fit.

Answer 27

(d)

To determine

To test: The hypothesis that coefficient of the variable PA−8.614 is equal to zero.

Answer 28

(d)

Expert Solution

Answer to Problem 25E

Solution: There is enough evidence to conclude that there is no linear increase over time.

Answer 29

(d)

Expert Solution

Answer 30

(d)

Expert Solution

Answer 31

Expert Solution

Answer 32

Explanation of Solution

Calculation: From the output which is obtained in part (b), the regression equation is BMI=23.4−0.682x1+0.102x2. The standard error is 0.0555. From the equation, it can be seen that the coefficient of x2 is b2=0.102. To test the hypothesis that there is a linear rise over time, the null and alternative hypotheses can be stated as:

H0:β2=0Hα:β2≠0

The level of significance is 0.05. The test statistic under null hypothesis is calculated as:

t=b2sb1=0.1020.05556=1.835

The p-value can be calculated as:

p−value=2P(t≥|tcal|)=2P(t≥1.835)=2(0.034)=0.0678

The p-value is 0.0678.

Conclusion: The obtained p-value is greater than the significance level. Hence, there is enough evidence to conclude that the quadratic term contributes insignificantly to the fit.