To graph: The scatterplot .

Question

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Answer 1

Question

Chapter 2, Problem 144E

(a)

To determine

To graph: The scatterplot.

(a)

Expert Solution

Explanation of Solution

Graph: To draw the scatterplot for the provided data set, the below steps are followed in Minitab software.

Step 1: Open the “MEIS” file in Minitab software.

Step 2: Go to Graph → Scatterplot.

Step 3: Choose the option “Simple” and click “OK”.

Step 4: Select “Sales” as Y variables and “Dwellpermit” as X variables.

Step 5: Click “OK” twice.

The scatterplot is obtained as:

Introduction to the Practice of Statistics, Chapter 2, Problem 144E , additional homework tip 1

To determine

To explain: The relationship between the variables and the presence of the outliers.

Expert Solution

Answer to Problem 144E

Solution: Though the relationship between the variables is very weak, but there is no outlier in the data set.

Explanation of Solution

The scatterplot obtained in part (a) shows that the data are very much scattered. That is there is very weak relationship between the response variable sales and the explanatory variable, issued permits. But there is no outlier present in the data set.

(b)

To determine

To find: The least-squares regression line for the data.

(b)

Expert Solution

Answer to Problem 144E

Solution: The least-squares regression line is obtained as Sales=109.8+0.1263DwellPermit, which is shown in the below diagram.

Introduction to the Practice of Statistics, Chapter 2, Problem 144E , additional homework tip 2

Explanation of Solution

Calculation: To draw the regression line and obtain the sketch of the regression line, the below steps are followed in the Minitab software.

Step 1: Right click on the obtained graph in the part (a).

Step 2: Go to Add → Regression Fit.

Step 3: Click on “Linear” under the menu “Model Order” and tick the “Fit intercept”.

Step 4: Click on “OK” to obtain the regression line.

The obtained regression equation is Sales=109.8+0.1263DwellPermit.

Graph: The below graph shows the regression line.

Introduction to the Practice of Statistics, Chapter 2, Problem 144E , additional homework tip 3

(c)

To determine

To explain: The slope of the obtained line.

(c)

Expert Solution

Answer to Problem 144E

Solution: The slope can be interpreted as if there is an increase of 1unit of the variable, issued permit for dwelling then there is an increase of 0.1263 units in the value of the variable sales.

Explanation of Solution

The slope of the least-square regression line indicates the amount of increase (decrease) in the response variable due to the 1-unit increase (decrease) in the value of the explanatory variable. In the provided equation, the amount of increase in the value of the response variable, sales is 0.1263 due to the 1-unit increase in the value of the variable issued permit for dwelling.

(d)

To determine

To explain: The intercept of the line.

(d)

Expert Solution

Answer to Problem 144E

Solution: The intercept can be interpreted as the value of the response variable when the value of the explanatory variable is zero. As the value of the response variable is 109.8 for the zero issued permits, it is appropriate to use the intercept for explaining the relationship between the variables.

Explanation of Solution

The intercept of the least-squares linear regression provided the value of the response variable when the value of the explanatory variable is zero. The explanatory variable can be zero because the index of issued permits for new dwelling can be zero and the value of the response variable for zero issued permit is 109.8. Therefore, it is appropriate to use the intercept for explaining the relationship between the variables.

(e)

To determine

The sales for an index of 224 dwelling permits.

(e)

Expert Solution

Answer to Problem 144E

Solution: The predicted value of the sales is 138.0912.

Explanation of Solution

The predicted value of the sales can be obtained by substituting the value of the index of dwelling permit in the least-squares linear regression equation.

The predicted value can be calculated as:

Sales=109.8+0.1263DwellPermit=109.8+0.1263×224=138.0912

(f)

To determine

To find: The residual value for Canada.

(f)

Expert Solution

Answer to Problem 144E

Solution: The obtained value of the residual is −8.0912_.

Explanation of Solution

Calculation: The sale for the Canada is provided as 122. The residual value for the sales for Canada whose index of dwelling permits is 224 is calculated as:

Residual=Observed Sales−Predicted Sales=122−138.0912=−16.0912

(g)

To determine

The percentage of variability in sales is explained by dwelling permit.

(g)

Expert Solution

Answer to Problem 144E

Solution: The explained percentage of variability in sales is 10.30%.

Explanation of Solution

The variability is explained by r2 which indicates that how better the model fits the data. The value of r2 is obtained along with the regression line when the line is added to the obtained scatterplot in the Minitab software in part (b). The value is obtained as 10.30%.

Therefore, the proportion of variation that is explained by the explanatory variables of the model is 10.30%.

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Answer 2

Question

Chapter 2, Problem 144E

(a)

To determine

To graph: The scatterplot.

(a)

Expert Solution

Explanation of Solution

Graph: To draw the scatterplot for the provided data set, the below steps are followed in Minitab software.

Step 1: Open the “MEIS” file in Minitab software.

Step 2: Go to Graph → Scatterplot.

Step 3: Choose the option “Simple” and click “OK”.

Step 4: Select “Sales” as Y variables and “Dwellpermit” as X variables.

Step 5: Click “OK” twice.

The scatterplot is obtained as:

Introduction to the Practice of Statistics, Chapter 2, Problem 144E , additional homework tip 1

To determine

To explain: The relationship between the variables and the presence of the outliers.

Expert Solution

Answer to Problem 144E

Solution: Though the relationship between the variables is very weak, but there is no outlier in the data set.

Explanation of Solution

The scatterplot obtained in part (a) shows that the data are very much scattered. That is there is very weak relationship between the response variable sales and the explanatory variable, issued permits. But there is no outlier present in the data set.

(b)

To determine

To find: The least-squares regression line for the data.

(b)

Expert Solution

Answer to Problem 144E

Solution: The least-squares regression line is obtained as Sales=109.8+0.1263DwellPermit, which is shown in the below diagram.

Introduction to the Practice of Statistics, Chapter 2, Problem 144E , additional homework tip 2

Explanation of Solution

Calculation: To draw the regression line and obtain the sketch of the regression line, the below steps are followed in the Minitab software.

Step 1: Right click on the obtained graph in the part (a).

Step 2: Go to Add → Regression Fit.

Step 3: Click on “Linear” under the menu “Model Order” and tick the “Fit intercept”.

Step 4: Click on “OK” to obtain the regression line.

The obtained regression equation is Sales=109.8+0.1263DwellPermit.

Graph: The below graph shows the regression line.

Introduction to the Practice of Statistics, Chapter 2, Problem 144E , additional homework tip 3

(c)

To determine

To explain: The slope of the obtained line.

(c)

Expert Solution

Answer to Problem 144E

Solution: The slope can be interpreted as if there is an increase of 1unit of the variable, issued permit for dwelling then there is an increase of 0.1263 units in the value of the variable sales.

Explanation of Solution

The slope of the least-square regression line indicates the amount of increase (decrease) in the response variable due to the 1-unit increase (decrease) in the value of the explanatory variable. In the provided equation, the amount of increase in the value of the response variable, sales is 0.1263 due to the 1-unit increase in the value of the variable issued permit for dwelling.

(d)

To determine

To explain: The intercept of the line.

(d)

Expert Solution

Answer to Problem 144E

Solution: The intercept can be interpreted as the value of the response variable when the value of the explanatory variable is zero. As the value of the response variable is 109.8 for the zero issued permits, it is appropriate to use the intercept for explaining the relationship between the variables.

Explanation of Solution

The intercept of the least-squares linear regression provided the value of the response variable when the value of the explanatory variable is zero. The explanatory variable can be zero because the index of issued permits for new dwelling can be zero and the value of the response variable for zero issued permit is 109.8. Therefore, it is appropriate to use the intercept for explaining the relationship between the variables.

(e)

To determine

The sales for an index of 224 dwelling permits.

(e)

Expert Solution

Answer to Problem 144E

Solution: The predicted value of the sales is 138.0912.

Explanation of Solution

The predicted value of the sales can be obtained by substituting the value of the index of dwelling permit in the least-squares linear regression equation.

The predicted value can be calculated as:

Sales=109.8+0.1263DwellPermit=109.8+0.1263×224=138.0912

(f)

To determine

To find: The residual value for Canada.

(f)

Expert Solution

Answer to Problem 144E

Solution: The obtained value of the residual is −8.0912_.

Explanation of Solution

Calculation: The sale for the Canada is provided as 122. The residual value for the sales for Canada whose index of dwelling permits is 224 is calculated as:

Residual=Observed Sales−Predicted Sales=122−138.0912=−16.0912

(g)

To determine

The percentage of variability in sales is explained by dwelling permit.

(g)

Expert Solution

Answer to Problem 144E

Solution: The explained percentage of variability in sales is 10.30%.

Explanation of Solution

The variability is explained by r2 which indicates that how better the model fits the data. The value of r2 is obtained along with the regression line when the line is added to the obtained scatterplot in the Minitab software in part (b). The value is obtained as 10.30%.

Therefore, the proportion of variation that is explained by the explanatory variables of the model is 10.30%.

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Answer 3

Question

Chapter 2, Problem 144E

(a)

To determine

To graph: The scatterplot.

(a)

Expert Solution

Explanation of Solution

Graph: To draw the scatterplot for the provided data set, the below steps are followed in Minitab software.

Step 1: Open the “MEIS” file in Minitab software.

Step 2: Go to Graph → Scatterplot.

Step 3: Choose the option “Simple” and click “OK”.

Step 4: Select “Sales” as Y variables and “Dwellpermit” as X variables.

Step 5: Click “OK” twice.

The scatterplot is obtained as:

Introduction to the Practice of Statistics, Chapter 2, Problem 144E , additional homework tip 1

To determine

To explain: The relationship between the variables and the presence of the outliers.

Expert Solution

Answer to Problem 144E

Solution: Though the relationship between the variables is very weak, but there is no outlier in the data set.

Explanation of Solution

The scatterplot obtained in part (a) shows that the data are very much scattered. That is there is very weak relationship between the response variable sales and the explanatory variable, issued permits. But there is no outlier present in the data set.

(b)

To determine

To find: The least-squares regression line for the data.

(b)

Expert Solution

Answer to Problem 144E

Solution: The least-squares regression line is obtained as Sales=109.8+0.1263DwellPermit, which is shown in the below diagram.

Introduction to the Practice of Statistics, Chapter 2, Problem 144E , additional homework tip 2

Explanation of Solution

Calculation: To draw the regression line and obtain the sketch of the regression line, the below steps are followed in the Minitab software.

Step 1: Right click on the obtained graph in the part (a).

Step 2: Go to Add → Regression Fit.

Step 3: Click on “Linear” under the menu “Model Order” and tick the “Fit intercept”.

Step 4: Click on “OK” to obtain the regression line.

The obtained regression equation is Sales=109.8+0.1263DwellPermit.

Graph: The below graph shows the regression line.

Introduction to the Practice of Statistics, Chapter 2, Problem 144E , additional homework tip 3

(c)

To determine

To explain: The slope of the obtained line.

(c)

Expert Solution

Answer to Problem 144E

Solution: The slope can be interpreted as if there is an increase of 1unit of the variable, issued permit for dwelling then there is an increase of 0.1263 units in the value of the variable sales.

Explanation of Solution

The slope of the least-square regression line indicates the amount of increase (decrease) in the response variable due to the 1-unit increase (decrease) in the value of the explanatory variable. In the provided equation, the amount of increase in the value of the response variable, sales is 0.1263 due to the 1-unit increase in the value of the variable issued permit for dwelling.

(d)

To determine

To explain: The intercept of the line.

(d)

Expert Solution

Answer to Problem 144E

Solution: The intercept can be interpreted as the value of the response variable when the value of the explanatory variable is zero. As the value of the response variable is 109.8 for the zero issued permits, it is appropriate to use the intercept for explaining the relationship between the variables.

Explanation of Solution

The intercept of the least-squares linear regression provided the value of the response variable when the value of the explanatory variable is zero. The explanatory variable can be zero because the index of issued permits for new dwelling can be zero and the value of the response variable for zero issued permit is 109.8. Therefore, it is appropriate to use the intercept for explaining the relationship between the variables.

(e)

To determine

The sales for an index of 224 dwelling permits.

(e)

Expert Solution

Answer to Problem 144E

Solution: The predicted value of the sales is 138.0912.

Explanation of Solution

The predicted value of the sales can be obtained by substituting the value of the index of dwelling permit in the least-squares linear regression equation.

The predicted value can be calculated as:

Sales=109.8+0.1263DwellPermit=109.8+0.1263×224=138.0912

(f)

To determine

To find: The residual value for Canada.

(f)

Expert Solution

Answer to Problem 144E

Solution: The obtained value of the residual is −8.0912_.

Explanation of Solution

Calculation: The sale for the Canada is provided as 122. The residual value for the sales for Canada whose index of dwelling permits is 224 is calculated as:

Residual=Observed Sales−Predicted Sales=122−138.0912=−16.0912

(g)

To determine

The percentage of variability in sales is explained by dwelling permit.

(g)

Expert Solution

Answer to Problem 144E

Solution: The explained percentage of variability in sales is 10.30%.

Explanation of Solution

The variability is explained by r2 which indicates that how better the model fits the data. The value of r2 is obtained along with the regression line when the line is added to the obtained scatterplot in the Minitab software in part (b). The value is obtained as 10.30%.

Therefore, the proportion of variation that is explained by the explanatory variables of the model is 10.30%.

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Answer 4

Question

Chapter 2, Problem 144E

(a)

To determine

To graph: The scatterplot.

(a)

Expert Solution

Explanation of Solution

Graph: To draw the scatterplot for the provided data set, the below steps are followed in Minitab software.

Step 1: Open the “MEIS” file in Minitab software.

Step 2: Go to Graph → Scatterplot.

Step 3: Choose the option “Simple” and click “OK”.

Step 4: Select “Sales” as Y variables and “Dwellpermit” as X variables.

Step 5: Click “OK” twice.

The scatterplot is obtained as:

Introduction to the Practice of Statistics, Chapter 2, Problem 144E , additional homework tip 1

To determine

To explain: The relationship between the variables and the presence of the outliers.

Expert Solution

Answer to Problem 144E

Solution: Though the relationship between the variables is very weak, but there is no outlier in the data set.

Explanation of Solution

The scatterplot obtained in part (a) shows that the data are very much scattered. That is there is very weak relationship between the response variable sales and the explanatory variable, issued permits. But there is no outlier present in the data set.

(b)

To determine

To find: The least-squares regression line for the data.

(b)

Expert Solution

Answer to Problem 144E

Solution: The least-squares regression line is obtained as Sales=109.8+0.1263DwellPermit, which is shown in the below diagram.

Introduction to the Practice of Statistics, Chapter 2, Problem 144E , additional homework tip 2

Explanation of Solution

Calculation: To draw the regression line and obtain the sketch of the regression line, the below steps are followed in the Minitab software.

Step 1: Right click on the obtained graph in the part (a).

Step 2: Go to Add → Regression Fit.

Step 3: Click on “Linear” under the menu “Model Order” and tick the “Fit intercept”.

Step 4: Click on “OK” to obtain the regression line.

The obtained regression equation is Sales=109.8+0.1263DwellPermit.

Graph: The below graph shows the regression line.

Introduction to the Practice of Statistics, Chapter 2, Problem 144E , additional homework tip 3

(c)

To determine

To explain: The slope of the obtained line.

(c)

Expert Solution

Answer to Problem 144E

Solution: The slope can be interpreted as if there is an increase of 1unit of the variable, issued permit for dwelling then there is an increase of 0.1263 units in the value of the variable sales.

Explanation of Solution

The slope of the least-square regression line indicates the amount of increase (decrease) in the response variable due to the 1-unit increase (decrease) in the value of the explanatory variable. In the provided equation, the amount of increase in the value of the response variable, sales is 0.1263 due to the 1-unit increase in the value of the variable issued permit for dwelling.

(d)

To determine

To explain: The intercept of the line.

(d)

Expert Solution

Answer to Problem 144E

Solution: The intercept can be interpreted as the value of the response variable when the value of the explanatory variable is zero. As the value of the response variable is 109.8 for the zero issued permits, it is appropriate to use the intercept for explaining the relationship between the variables.

Explanation of Solution

The intercept of the least-squares linear regression provided the value of the response variable when the value of the explanatory variable is zero. The explanatory variable can be zero because the index of issued permits for new dwelling can be zero and the value of the response variable for zero issued permit is 109.8. Therefore, it is appropriate to use the intercept for explaining the relationship between the variables.

(e)

To determine

The sales for an index of 224 dwelling permits.

(e)

Expert Solution

Answer to Problem 144E

Solution: The predicted value of the sales is 138.0912.

Explanation of Solution

The predicted value of the sales can be obtained by substituting the value of the index of dwelling permit in the least-squares linear regression equation.

The predicted value can be calculated as:

Sales=109.8+0.1263DwellPermit=109.8+0.1263×224=138.0912

(f)

To determine

To find: The residual value for Canada.

(f)

Expert Solution

Answer to Problem 144E

Solution: The obtained value of the residual is −8.0912_.

Explanation of Solution

Calculation: The sale for the Canada is provided as 122. The residual value for the sales for Canada whose index of dwelling permits is 224 is calculated as:

Residual=Observed Sales−Predicted Sales=122−138.0912=−16.0912

(g)

To determine

The percentage of variability in sales is explained by dwelling permit.

(g)

Expert Solution

Answer to Problem 144E

Solution: The explained percentage of variability in sales is 10.30%.

Explanation of Solution

The variability is explained by r2 which indicates that how better the model fits the data. The value of r2 is obtained along with the regression line when the line is added to the obtained scatterplot in the Minitab software in part (b). The value is obtained as 10.30%.

Therefore, the proportion of variation that is explained by the explanatory variables of the model is 10.30%.

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Answer 5

Chapter 2, Problem 144E

(a)

To determine

To graph: The scatterplot.

(a)

Expert Solution

Explanation of Solution

Graph: To draw the scatterplot for the provided data set, the below steps are followed in Minitab software.

Step 1: Open the “MEIS” file in Minitab software.

Step 2: Go to Graph → Scatterplot.

Step 3: Choose the option “Simple” and click “OK”.

Step 4: Select “Sales” as Y variables and “Dwellpermit” as X variables.

Step 5: Click “OK” twice.

The scatterplot is obtained as:

Introduction to the Practice of Statistics, Chapter 2, Problem 144E , additional homework tip 1

To determine

To explain: The relationship between the variables and the presence of the outliers.

Expert Solution

Answer to Problem 144E

Solution: Though the relationship between the variables is very weak, but there is no outlier in the data set.

Explanation of Solution

The scatterplot obtained in part (a) shows that the data are very much scattered. That is there is very weak relationship between the response variable sales and the explanatory variable, issued permits. But there is no outlier present in the data set.

(b)

To determine

To find: The least-squares regression line for the data.

(b)

Expert Solution

Answer to Problem 144E

Solution: The least-squares regression line is obtained as Sales=109.8+0.1263DwellPermit, which is shown in the below diagram.

Introduction to the Practice of Statistics, Chapter 2, Problem 144E , additional homework tip 2

Explanation of Solution

Calculation: To draw the regression line and obtain the sketch of the regression line, the below steps are followed in the Minitab software.

Step 1: Right click on the obtained graph in the part (a).

Step 2: Go to Add → Regression Fit.

Step 3: Click on “Linear” under the menu “Model Order” and tick the “Fit intercept”.

Step 4: Click on “OK” to obtain the regression line.

The obtained regression equation is Sales=109.8+0.1263DwellPermit.

Graph: The below graph shows the regression line.

Introduction to the Practice of Statistics, Chapter 2, Problem 144E , additional homework tip 3

(c)

To determine

To explain: The slope of the obtained line.

(c)

Expert Solution

Answer to Problem 144E

Solution: The slope can be interpreted as if there is an increase of 1unit of the variable, issued permit for dwelling then there is an increase of 0.1263 units in the value of the variable sales.

Explanation of Solution

The slope of the least-square regression line indicates the amount of increase (decrease) in the response variable due to the 1-unit increase (decrease) in the value of the explanatory variable. In the provided equation, the amount of increase in the value of the response variable, sales is 0.1263 due to the 1-unit increase in the value of the variable issued permit for dwelling.

(d)

To determine

To explain: The intercept of the line.

(d)

Expert Solution

Answer to Problem 144E

Solution: The intercept can be interpreted as the value of the response variable when the value of the explanatory variable is zero. As the value of the response variable is 109.8 for the zero issued permits, it is appropriate to use the intercept for explaining the relationship between the variables.

Explanation of Solution

The intercept of the least-squares linear regression provided the value of the response variable when the value of the explanatory variable is zero. The explanatory variable can be zero because the index of issued permits for new dwelling can be zero and the value of the response variable for zero issued permit is 109.8. Therefore, it is appropriate to use the intercept for explaining the relationship between the variables.

(e)

To determine

The sales for an index of 224 dwelling permits.

(e)

Expert Solution

Answer to Problem 144E

Solution: The predicted value of the sales is 138.0912.

Explanation of Solution

The predicted value of the sales can be obtained by substituting the value of the index of dwelling permit in the least-squares linear regression equation.

The predicted value can be calculated as:

Sales=109.8+0.1263DwellPermit=109.8+0.1263×224=138.0912

(f)

To determine

To find: The residual value for Canada.

(f)

Expert Solution

Answer to Problem 144E

Solution: The obtained value of the residual is −8.0912_.

Explanation of Solution

Calculation: The sale for the Canada is provided as 122. The residual value for the sales for Canada whose index of dwelling permits is 224 is calculated as:

Residual=Observed Sales−Predicted Sales=122−138.0912=−16.0912

(g)

To determine

The percentage of variability in sales is explained by dwelling permit.

(g)

Expert Solution

Answer to Problem 144E

Solution: The explained percentage of variability in sales is 10.30%.

Explanation of Solution

The variability is explained by r2 which indicates that how better the model fits the data. The value of r2 is obtained along with the regression line when the line is added to the obtained scatterplot in the Minitab software in part (b). The value is obtained as 10.30%.

Therefore, the proportion of variation that is explained by the explanatory variables of the model is 10.30%.

Answer 6

Chapter 2, Problem 144E

(a)

To determine

To graph: The scatterplot.

(a)

Expert Solution

Explanation of Solution

Graph: To draw the scatterplot for the provided data set, the below steps are followed in Minitab software.

Step 1: Open the “MEIS” file in Minitab software.

Step 2: Go to Graph → Scatterplot.

Step 3: Choose the option “Simple” and click “OK”.

Step 4: Select “Sales” as Y variables and “Dwellpermit” as X variables.

Step 5: Click “OK” twice.

The scatterplot is obtained as:

Introduction to the Practice of Statistics, Chapter 2, Problem 144E , additional homework tip 1

Answer 7

Chapter 2, Problem 144E

(a)

To determine

To graph: The scatterplot.

Answer 8

(a)

Expert Solution

Explanation of Solution

Graph: To draw the scatterplot for the provided data set, the below steps are followed in Minitab software.

Step 1: Open the “MEIS” file in Minitab software.

Step 2: Go to Graph → Scatterplot.

Step 3: Choose the option “Simple” and click “OK”.

Step 4: Select “Sales” as Y variables and “Dwellpermit” as X variables.

Step 5: Click “OK” twice.

The scatterplot is obtained as:

Introduction to the Practice of Statistics, Chapter 2, Problem 144E , additional homework tip 1

Answer 9

(a)

Expert Solution

Answer 10

(a)

Expert Solution

Answer 11

Expert Solution

Answer 12

To determine

To explain: The relationship between the variables and the presence of the outliers.

Expert Solution

Answer to Problem 144E

Solution: Though the relationship between the variables is very weak, but there is no outlier in the data set.

Explanation of Solution

The scatterplot obtained in part (a) shows that the data are very much scattered. That is there is very weak relationship between the response variable sales and the explanatory variable, issued permits. But there is no outlier present in the data set.

Answer 13

To determine

To explain: The relationship between the variables and the presence of the outliers.

Answer 14

Expert Solution

Answer to Problem 144E

Solution: Though the relationship between the variables is very weak, but there is no outlier in the data set.

Answer 15

Expert Solution

Answer 16

Expert Solution

Answer 17

Expert Solution

Answer 18

Explanation of Solution

The scatterplot obtained in part (a) shows that the data are very much scattered. That is there is very weak relationship between the response variable sales and the explanatory variable, issued permits. But there is no outlier present in the data set.

Answer 19

(b)

To determine

To find: The least-squares regression line for the data.

(b)

Expert Solution

Answer to Problem 144E

Solution: The least-squares regression line is obtained as Sales=109.8+0.1263DwellPermit, which is shown in the below diagram.

Introduction to the Practice of Statistics, Chapter 2, Problem 144E , additional homework tip 2

Explanation of Solution

Calculation: To draw the regression line and obtain the sketch of the regression line, the below steps are followed in the Minitab software.

Step 1: Right click on the obtained graph in the part (a).

Step 2: Go to Add → Regression Fit.

Step 3: Click on “Linear” under the menu “Model Order” and tick the “Fit intercept”.

Step 4: Click on “OK” to obtain the regression line.

The obtained regression equation is Sales=109.8+0.1263DwellPermit.

Graph: The below graph shows the regression line.

Introduction to the Practice of Statistics, Chapter 2, Problem 144E , additional homework tip 3

Answer 20

(b)

To determine

To find: The least-squares regression line for the data.

Answer 21

(b)

Expert Solution

Answer to Problem 144E

Solution: The least-squares regression line is obtained as Sales=109.8+0.1263DwellPermit, which is shown in the below diagram.

Introduction to the Practice of Statistics, Chapter 2, Problem 144E , additional homework tip 2

Answer 22

(b)

Expert Solution

Answer 23

(b)

Expert Solution

Answer 24

Expert Solution

Answer 25

Explanation of Solution

Calculation: To draw the regression line and obtain the sketch of the regression line, the below steps are followed in the Minitab software.

Step 1: Right click on the obtained graph in the part (a).

Step 2: Go to Add → Regression Fit.

Step 3: Click on “Linear” under the menu “Model Order” and tick the “Fit intercept”.

Step 4: Click on “OK” to obtain the regression line.

The obtained regression equation is Sales=109.8+0.1263DwellPermit.

Graph: The below graph shows the regression line.

Introduction to the Practice of Statistics, Chapter 2, Problem 144E , additional homework tip 3

Answer 26

(c)

To determine

To explain: The slope of the obtained line.

(c)

Expert Solution

Answer to Problem 144E

Solution: The slope can be interpreted as if there is an increase of 1unit of the variable, issued permit for dwelling then there is an increase of 0.1263 units in the value of the variable sales.

Explanation of Solution

The slope of the least-square regression line indicates the amount of increase (decrease) in the response variable due to the 1-unit increase (decrease) in the value of the explanatory variable. In the provided equation, the amount of increase in the value of the response variable, sales is 0.1263 due to the 1-unit increase in the value of the variable issued permit for dwelling.

Answer 27

(c)

To determine

To explain: The slope of the obtained line.

Answer 28

(c)

Expert Solution

Answer to Problem 144E

Solution: The slope can be interpreted as if there is an increase of 1unit of the variable, issued permit for dwelling then there is an increase of 0.1263 units in the value of the variable sales.

Answer 29

(c)

Expert Solution

Answer 30

(c)

Expert Solution

Answer 31

Expert Solution

Answer 32

Explanation of Solution

The slope of the least-square regression line indicates the amount of increase (decrease) in the response variable due to the 1-unit increase (decrease) in the value of the explanatory variable. In the provided equation, the amount of increase in the value of the response variable, sales is 0.1263 due to the 1-unit increase in the value of the variable issued permit for dwelling.

Answer 33

(d)

To determine

To explain: The intercept of the line.

(d)

Expert Solution

Answer to Problem 144E

Solution: The intercept can be interpreted as the value of the response variable when the value of the explanatory variable is zero. As the value of the response variable is 109.8 for the zero issued permits, it is appropriate to use the intercept for explaining the relationship between the variables.

Explanation of Solution

The intercept of the least-squares linear regression provided the value of the response variable when the value of the explanatory variable is zero. The explanatory variable can be zero because the index of issued permits for new dwelling can be zero and the value of the response variable for zero issued permit is 109.8. Therefore, it is appropriate to use the intercept for explaining the relationship between the variables.

Answer 34

(d)

To determine

To explain: The intercept of the line.

Answer 35

(d)

Expert Solution

Answer to Problem 144E

Solution: The intercept can be interpreted as the value of the response variable when the value of the explanatory variable is zero. As the value of the response variable is 109.8 for the zero issued permits, it is appropriate to use the intercept for explaining the relationship between the variables.

Answer 36

(d)

Expert Solution

Answer 37

(d)

Expert Solution

Answer 38

Expert Solution

Answer 39

Explanation of Solution

The intercept of the least-squares linear regression provided the value of the response variable when the value of the explanatory variable is zero. The explanatory variable can be zero because the index of issued permits for new dwelling can be zero and the value of the response variable for zero issued permit is 109.8. Therefore, it is appropriate to use the intercept for explaining the relationship between the variables.

Answer 40

(e)

To determine

The sales for an index of 224 dwelling permits.

(e)

Expert Solution

Answer to Problem 144E

Solution: The predicted value of the sales is 138.0912.

Explanation of Solution

The predicted value of the sales can be obtained by substituting the value of the index of dwelling permit in the least-squares linear regression equation.

The predicted value can be calculated as:

Sales=109.8+0.1263DwellPermit=109.8+0.1263×224=138.0912

Answer 41

(e)

To determine

The sales for an index of 224 dwelling permits.

Answer 42

(e)

Expert Solution

Answer to Problem 144E

Solution: The predicted value of the sales is 138.0912.

Answer 43

(e)

Expert Solution

Answer 44

(e)

Expert Solution

Answer 45

Expert Solution

Answer 46

Explanation of Solution

The predicted value of the sales can be obtained by substituting the value of the index of dwelling permit in the least-squares linear regression equation.

The predicted value can be calculated as:

Sales=109.8+0.1263DwellPermit=109.8+0.1263×224=138.0912

Answer 47

(f)

To determine

To find: The residual value for Canada.

(f)

Expert Solution

Answer to Problem 144E

Solution: The obtained value of the residual is −8.0912_.

Explanation of Solution

Calculation: The sale for the Canada is provided as 122. The residual value for the sales for Canada whose index of dwelling permits is 224 is calculated as:

Residual=Observed Sales−Predicted Sales=122−138.0912=−16.0912

Answer 48

(f)

To determine

To find: The residual value for Canada.

Answer 49

(f)

Expert Solution

Answer to Problem 144E

Solution: The obtained value of the residual is −8.0912_.

Answer 50

(f)

Expert Solution

Answer 51

(f)

Expert Solution

Answer 52

Expert Solution

Answer 53

Explanation of Solution

Calculation: The sale for the Canada is provided as 122. The residual value for the sales for Canada whose index of dwelling permits is 224 is calculated as:

Residual=Observed Sales−Predicted Sales=122−138.0912=−16.0912

Answer 54

(g)

To determine

The percentage of variability in sales is explained by dwelling permit.

(g)

Expert Solution

Answer to Problem 144E

Solution: The explained percentage of variability in sales is 10.30%.

Explanation of Solution

The variability is explained by r2 which indicates that how better the model fits the data. The value of r2 is obtained along with the regression line when the line is added to the obtained scatterplot in the Minitab software in part (b). The value is obtained as 10.30%.

Therefore, the proportion of variation that is explained by the explanatory variables of the model is 10.30%.

Answer 55

(g)

To determine

The percentage of variability in sales is explained by dwelling permit.

Answer 56

(g)

Expert Solution

Answer to Problem 144E

Solution: The explained percentage of variability in sales is 10.30%.

Answer 57

(g)

Expert Solution

Answer 58

(g)

Expert Solution

Answer 59

Expert Solution

Answer 60

Explanation of Solution

The variability is explained by r2 which indicates that how better the model fits the data. The value of r2 is obtained along with the regression line when the line is added to the obtained scatterplot in the Minitab software in part (b). The value is obtained as 10.30%.

Therefore, the proportion of variation that is explained by the explanatory variables of the model is 10.30%.