The four residuals for the data provided on the counts over different times.

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Answer 1

Question

Chapter 2.5, Problem 96E

(a)

To determine

To find: The four residuals for the data provided on the counts over different times.

(a)

Expert Solution

Answer to Problem 96E

Solution: The residuals for the four counts are obtained as 49.9 _, −61.7_, −26.3_, and 38.1_.

Explanation of Solution

Calculation: The regression equation for the provided data set is as follows:

Count=602.8−(74.7×Time)

Here, the response variable (represented as y) is ‘count,’ and the explanatory variable (represented as ″x″) is ‘time.’ The estimated counts are obtained by substituting the respective values of time (1, 3, 5 and 7) in the regression equation.

For time x1=1, the value of count (represented as y^1 ) is calculated as follows:

Count=602.8−(74.7×Time)=602.8−(74.7×1)y^1=528.1

For time x2=3, the value of count (represented as y^2 ) is calculated as follows:

Count=602.8−(74.7×Time)=602.8−(74.7×3)y^2=378.7

For time x3=5, the value of count (represented as y^3 ) is calculated as follows:

count=602.8−(74.7×time)=602.8−(74.7×5)y^3=229.3

For time x4=7, the value of count (represented as y^4 ) is calculated as follows:

Count=602.8−(74.7×Time)=602.8−(74.7×7)y^4=79.9

The observed y values have been provided in the data and are written below:

y1=578y2=317y3=203y4=118

The residuals (represented as ei ) are the difference between the observed y values and predicted y values. The residuals for the above four observed and predicted values are calculated as follows:

For y1, the residual e1 is calculated as follows:

e1=Observed y1−Predicted y1=y1−y^1=578−528.1=49.9

For y2, the residual e2 is calculated as follows:

e2=Observed y2−Predicted y2=y2−y^2=317−378.7=−61.7

For y3, the residual e3 is calculated as follows:

e3=Observed y3−Predicted y3=y3−y^3=203−229.3=−26.3

For y4, the residual e4 is calculated as follows:

e4=Observed y4−Predicted y4=y4−y^4=118−79.9=38.1

Hence, the four residuals obtained are

e1=49.9

e2=−61.7

e3=−26.3

e4=38.1

(b)

To determine

To graph: The model for residual versus time plot.

(b)

Expert Solution

Explanation of Solution

Graph: The residual versus time plot is obtained using the Minitab software by following the steps below:

Step 1: Enter the data in the Minitab worksheet.

Step 2: Go to Stat and select Regression and then select Regression again.

Step 3: Enter the response variable as ‘Count’ and Predictors as ‘Time.’

Step 4: Under Graphs option, choose Residuals versus order.

Step 5: Fill in Residual versus the variables as ‘Time.’

Step 6: Click on Ok.

The resultant graph is obtained as follows:

Introduction to the Practice of Statistics, Chapter 2.5, Problem 96E

(c)

To determine

To explain: Interpretation of the obtained residual plot.

(c)

Expert Solution

Answer to Problem 96E

Solution: Since there is no pattern observed in the residuals versus time plot, it can be concluded that the provided model is appropriate to estimate the count variable.

Explanation of Solution

The residual plot has no specific pattern. The plot seems to be scattered and nonlinear. The two residuals, e1 as 49.9 and e4 as 38.1, are positive, and the two residuals e2 as −61.7 and e3 as −26.3 are negative. This implies that the residuals are scattered above as well as below the x- axis. The uniform scattering of the residuals represents a good sign. Thus, it can be said that the provided regression model is suitable to predict the count variable.

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Answer 2

Question

Chapter 2.5, Problem 96E

(a)

To determine

To find: The four residuals for the data provided on the counts over different times.

(a)

Expert Solution

Answer to Problem 96E

Solution: The residuals for the four counts are obtained as 49.9 _, −61.7_, −26.3_, and 38.1_.

Explanation of Solution

Calculation: The regression equation for the provided data set is as follows:

Count=602.8−(74.7×Time)

Here, the response variable (represented as y) is ‘count,’ and the explanatory variable (represented as ″x″) is ‘time.’ The estimated counts are obtained by substituting the respective values of time (1, 3, 5 and 7) in the regression equation.

For time x1=1, the value of count (represented as y^1 ) is calculated as follows:

Count=602.8−(74.7×Time)=602.8−(74.7×1)y^1=528.1

For time x2=3, the value of count (represented as y^2 ) is calculated as follows:

Count=602.8−(74.7×Time)=602.8−(74.7×3)y^2=378.7

For time x3=5, the value of count (represented as y^3 ) is calculated as follows:

count=602.8−(74.7×time)=602.8−(74.7×5)y^3=229.3

For time x4=7, the value of count (represented as y^4 ) is calculated as follows:

Count=602.8−(74.7×Time)=602.8−(74.7×7)y^4=79.9

The observed y values have been provided in the data and are written below:

y1=578y2=317y3=203y4=118

The residuals (represented as ei ) are the difference between the observed y values and predicted y values. The residuals for the above four observed and predicted values are calculated as follows:

For y1, the residual e1 is calculated as follows:

e1=Observed y1−Predicted y1=y1−y^1=578−528.1=49.9

For y2, the residual e2 is calculated as follows:

e2=Observed y2−Predicted y2=y2−y^2=317−378.7=−61.7

For y3, the residual e3 is calculated as follows:

e3=Observed y3−Predicted y3=y3−y^3=203−229.3=−26.3

For y4, the residual e4 is calculated as follows:

e4=Observed y4−Predicted y4=y4−y^4=118−79.9=38.1

Hence, the four residuals obtained are

e1=49.9

e2=−61.7

e3=−26.3

e4=38.1

(b)

To determine

To graph: The model for residual versus time plot.

(b)

Expert Solution

Explanation of Solution

Graph: The residual versus time plot is obtained using the Minitab software by following the steps below:

Step 1: Enter the data in the Minitab worksheet.

Step 2: Go to Stat and select Regression and then select Regression again.

Step 3: Enter the response variable as ‘Count’ and Predictors as ‘Time.’

Step 4: Under Graphs option, choose Residuals versus order.

Step 5: Fill in Residual versus the variables as ‘Time.’

Step 6: Click on Ok.

The resultant graph is obtained as follows:

Introduction to the Practice of Statistics, Chapter 2.5, Problem 96E

(c)

To determine

To explain: Interpretation of the obtained residual plot.

(c)

Expert Solution

Answer to Problem 96E

Solution: Since there is no pattern observed in the residuals versus time plot, it can be concluded that the provided model is appropriate to estimate the count variable.

Explanation of Solution

The residual plot has no specific pattern. The plot seems to be scattered and nonlinear. The two residuals, e1 as 49.9 and e4 as 38.1, are positive, and the two residuals e2 as −61.7 and e3 as −26.3 are negative. This implies that the residuals are scattered above as well as below the x- axis. The uniform scattering of the residuals represents a good sign. Thus, it can be said that the provided regression model is suitable to predict the count variable.

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Answer 3

Question

Chapter 2.5, Problem 96E

(a)

To determine

To find: The four residuals for the data provided on the counts over different times.

(a)

Expert Solution

Answer to Problem 96E

Solution: The residuals for the four counts are obtained as 49.9 _, −61.7_, −26.3_, and 38.1_.

Explanation of Solution

Calculation: The regression equation for the provided data set is as follows:

Count=602.8−(74.7×Time)

Here, the response variable (represented as y) is ‘count,’ and the explanatory variable (represented as ″x″) is ‘time.’ The estimated counts are obtained by substituting the respective values of time (1, 3, 5 and 7) in the regression equation.

For time x1=1, the value of count (represented as y^1 ) is calculated as follows:

Count=602.8−(74.7×Time)=602.8−(74.7×1)y^1=528.1

For time x2=3, the value of count (represented as y^2 ) is calculated as follows:

Count=602.8−(74.7×Time)=602.8−(74.7×3)y^2=378.7

For time x3=5, the value of count (represented as y^3 ) is calculated as follows:

count=602.8−(74.7×time)=602.8−(74.7×5)y^3=229.3

For time x4=7, the value of count (represented as y^4 ) is calculated as follows:

Count=602.8−(74.7×Time)=602.8−(74.7×7)y^4=79.9

The observed y values have been provided in the data and are written below:

y1=578y2=317y3=203y4=118

The residuals (represented as ei ) are the difference between the observed y values and predicted y values. The residuals for the above four observed and predicted values are calculated as follows:

For y1, the residual e1 is calculated as follows:

e1=Observed y1−Predicted y1=y1−y^1=578−528.1=49.9

For y2, the residual e2 is calculated as follows:

e2=Observed y2−Predicted y2=y2−y^2=317−378.7=−61.7

For y3, the residual e3 is calculated as follows:

e3=Observed y3−Predicted y3=y3−y^3=203−229.3=−26.3

For y4, the residual e4 is calculated as follows:

e4=Observed y4−Predicted y4=y4−y^4=118−79.9=38.1

Hence, the four residuals obtained are

e1=49.9

e2=−61.7

e3=−26.3

e4=38.1

(b)

To determine

To graph: The model for residual versus time plot.

(b)

Expert Solution

Explanation of Solution

Graph: The residual versus time plot is obtained using the Minitab software by following the steps below:

Step 1: Enter the data in the Minitab worksheet.

Step 2: Go to Stat and select Regression and then select Regression again.

Step 3: Enter the response variable as ‘Count’ and Predictors as ‘Time.’

Step 4: Under Graphs option, choose Residuals versus order.

Step 5: Fill in Residual versus the variables as ‘Time.’

Step 6: Click on Ok.

The resultant graph is obtained as follows:

Introduction to the Practice of Statistics, Chapter 2.5, Problem 96E

(c)

To determine

To explain: Interpretation of the obtained residual plot.

(c)

Expert Solution

Answer to Problem 96E

Solution: Since there is no pattern observed in the residuals versus time plot, it can be concluded that the provided model is appropriate to estimate the count variable.

Explanation of Solution

The residual plot has no specific pattern. The plot seems to be scattered and nonlinear. The two residuals, e1 as 49.9 and e4 as 38.1, are positive, and the two residuals e2 as −61.7 and e3 as −26.3 are negative. This implies that the residuals are scattered above as well as below the x- axis. The uniform scattering of the residuals represents a good sign. Thus, it can be said that the provided regression model is suitable to predict the count variable.

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Answer 4

Question

Chapter 2.5, Problem 96E

(a)

To determine

To find: The four residuals for the data provided on the counts over different times.

(a)

Expert Solution

Answer to Problem 96E

Solution: The residuals for the four counts are obtained as 49.9 _, −61.7_, −26.3_, and 38.1_.

Explanation of Solution

Calculation: The regression equation for the provided data set is as follows:

Count=602.8−(74.7×Time)

Here, the response variable (represented as y) is ‘count,’ and the explanatory variable (represented as ″x″) is ‘time.’ The estimated counts are obtained by substituting the respective values of time (1, 3, 5 and 7) in the regression equation.

For time x1=1, the value of count (represented as y^1 ) is calculated as follows:

Count=602.8−(74.7×Time)=602.8−(74.7×1)y^1=528.1

For time x2=3, the value of count (represented as y^2 ) is calculated as follows:

Count=602.8−(74.7×Time)=602.8−(74.7×3)y^2=378.7

For time x3=5, the value of count (represented as y^3 ) is calculated as follows:

count=602.8−(74.7×time)=602.8−(74.7×5)y^3=229.3

For time x4=7, the value of count (represented as y^4 ) is calculated as follows:

Count=602.8−(74.7×Time)=602.8−(74.7×7)y^4=79.9

The observed y values have been provided in the data and are written below:

y1=578y2=317y3=203y4=118

The residuals (represented as ei ) are the difference between the observed y values and predicted y values. The residuals for the above four observed and predicted values are calculated as follows:

For y1, the residual e1 is calculated as follows:

e1=Observed y1−Predicted y1=y1−y^1=578−528.1=49.9

For y2, the residual e2 is calculated as follows:

e2=Observed y2−Predicted y2=y2−y^2=317−378.7=−61.7

For y3, the residual e3 is calculated as follows:

e3=Observed y3−Predicted y3=y3−y^3=203−229.3=−26.3

For y4, the residual e4 is calculated as follows:

e4=Observed y4−Predicted y4=y4−y^4=118−79.9=38.1

Hence, the four residuals obtained are

e1=49.9

e2=−61.7

e3=−26.3

e4=38.1

(b)

To determine

To graph: The model for residual versus time plot.

(b)

Expert Solution

Explanation of Solution

Graph: The residual versus time plot is obtained using the Minitab software by following the steps below:

Step 1: Enter the data in the Minitab worksheet.

Step 2: Go to Stat and select Regression and then select Regression again.

Step 3: Enter the response variable as ‘Count’ and Predictors as ‘Time.’

Step 4: Under Graphs option, choose Residuals versus order.

Step 5: Fill in Residual versus the variables as ‘Time.’

Step 6: Click on Ok.

The resultant graph is obtained as follows:

Introduction to the Practice of Statistics, Chapter 2.5, Problem 96E

(c)

To determine

To explain: Interpretation of the obtained residual plot.

(c)

Expert Solution

Answer to Problem 96E

Solution: Since there is no pattern observed in the residuals versus time plot, it can be concluded that the provided model is appropriate to estimate the count variable.

Explanation of Solution

The residual plot has no specific pattern. The plot seems to be scattered and nonlinear. The two residuals, e1 as 49.9 and e4 as 38.1, are positive, and the two residuals e2 as −61.7 and e3 as −26.3 are negative. This implies that the residuals are scattered above as well as below the x- axis. The uniform scattering of the residuals represents a good sign. Thus, it can be said that the provided regression model is suitable to predict the count variable.

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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 2.5, Problem 96E

(a)

To determine

To find: The four residuals for the data provided on the counts over different times.

(a)

Expert Solution

Answer to Problem 96E

Solution: The residuals for the four counts are obtained as 49.9 _, −61.7_, −26.3_, and 38.1_.

Explanation of Solution

Calculation: The regression equation for the provided data set is as follows:

Count=602.8−(74.7×Time)

Here, the response variable (represented as y) is ‘count,’ and the explanatory variable (represented as ″x″) is ‘time.’ The estimated counts are obtained by substituting the respective values of time (1, 3, 5 and 7) in the regression equation.

For time x1=1, the value of count (represented as y^1 ) is calculated as follows:

Count=602.8−(74.7×Time)=602.8−(74.7×1)y^1=528.1

For time x2=3, the value of count (represented as y^2 ) is calculated as follows:

Count=602.8−(74.7×Time)=602.8−(74.7×3)y^2=378.7

For time x3=5, the value of count (represented as y^3 ) is calculated as follows:

count=602.8−(74.7×time)=602.8−(74.7×5)y^3=229.3

For time x4=7, the value of count (represented as y^4 ) is calculated as follows:

Count=602.8−(74.7×Time)=602.8−(74.7×7)y^4=79.9

The observed y values have been provided in the data and are written below:

y1=578y2=317y3=203y4=118

The residuals (represented as ei ) are the difference between the observed y values and predicted y values. The residuals for the above four observed and predicted values are calculated as follows:

For y1, the residual e1 is calculated as follows:

e1=Observed y1−Predicted y1=y1−y^1=578−528.1=49.9

For y2, the residual e2 is calculated as follows:

e2=Observed y2−Predicted y2=y2−y^2=317−378.7=−61.7

For y3, the residual e3 is calculated as follows:

e3=Observed y3−Predicted y3=y3−y^3=203−229.3=−26.3

For y4, the residual e4 is calculated as follows:

e4=Observed y4−Predicted y4=y4−y^4=118−79.9=38.1

Hence, the four residuals obtained are

e1=49.9

e2=−61.7

e3=−26.3

e4=38.1

(b)

To determine

To graph: The model for residual versus time plot.

(b)

Expert Solution

Explanation of Solution

Graph: The residual versus time plot is obtained using the Minitab software by following the steps below:

Step 1: Enter the data in the Minitab worksheet.

Step 2: Go to Stat and select Regression and then select Regression again.

Step 3: Enter the response variable as ‘Count’ and Predictors as ‘Time.’

Step 4: Under Graphs option, choose Residuals versus order.

Step 5: Fill in Residual versus the variables as ‘Time.’

Step 6: Click on Ok.

The resultant graph is obtained as follows:

Introduction to the Practice of Statistics, Chapter 2.5, Problem 96E

(c)

To determine

To explain: Interpretation of the obtained residual plot.

(c)

Expert Solution

Answer to Problem 96E

Solution: Since there is no pattern observed in the residuals versus time plot, it can be concluded that the provided model is appropriate to estimate the count variable.

Explanation of Solution

The residual plot has no specific pattern. The plot seems to be scattered and nonlinear. The two residuals, e1 as 49.9 and e4 as 38.1, are positive, and the two residuals e2 as −61.7 and e3 as −26.3 are negative. This implies that the residuals are scattered above as well as below the x- axis. The uniform scattering of the residuals represents a good sign. Thus, it can be said that the provided regression model is suitable to predict the count variable.

Answer 6

Chapter 2.5, Problem 96E

(a)

To determine

To find: The four residuals for the data provided on the counts over different times.

(a)

Expert Solution

Answer to Problem 96E

Solution: The residuals for the four counts are obtained as 49.9 _, −61.7_, −26.3_, and 38.1_.

Explanation of Solution

Calculation: The regression equation for the provided data set is as follows:

Count=602.8−(74.7×Time)

Here, the response variable (represented as y) is ‘count,’ and the explanatory variable (represented as ″x″) is ‘time.’ The estimated counts are obtained by substituting the respective values of time (1, 3, 5 and 7) in the regression equation.

For time x1=1, the value of count (represented as y^1 ) is calculated as follows:

Count=602.8−(74.7×Time)=602.8−(74.7×1)y^1=528.1

For time x2=3, the value of count (represented as y^2 ) is calculated as follows:

Count=602.8−(74.7×Time)=602.8−(74.7×3)y^2=378.7

For time x3=5, the value of count (represented as y^3 ) is calculated as follows:

count=602.8−(74.7×time)=602.8−(74.7×5)y^3=229.3

For time x4=7, the value of count (represented as y^4 ) is calculated as follows:

Count=602.8−(74.7×Time)=602.8−(74.7×7)y^4=79.9

The observed y values have been provided in the data and are written below:

y1=578y2=317y3=203y4=118

The residuals (represented as ei ) are the difference between the observed y values and predicted y values. The residuals for the above four observed and predicted values are calculated as follows:

For y1, the residual e1 is calculated as follows:

e1=Observed y1−Predicted y1=y1−y^1=578−528.1=49.9

For y2, the residual e2 is calculated as follows:

e2=Observed y2−Predicted y2=y2−y^2=317−378.7=−61.7

For y3, the residual e3 is calculated as follows:

e3=Observed y3−Predicted y3=y3−y^3=203−229.3=−26.3

For y4, the residual e4 is calculated as follows:

e4=Observed y4−Predicted y4=y4−y^4=118−79.9=38.1

Hence, the four residuals obtained are

e1=49.9

e2=−61.7

e3=−26.3

e4=38.1

Answer 7

Chapter 2.5, Problem 96E

(a)

To determine

To find: The four residuals for the data provided on the counts over different times.

Answer 8

(a)

Expert Solution

Answer to Problem 96E

Solution: The residuals for the four counts are obtained as 49.9 _, −61.7_, −26.3_, and 38.1_.

Answer 9

(a)

Expert Solution

Answer 10

(a)

Expert Solution

Answer 11

Expert Solution

Answer 12

Explanation of Solution

Calculation: The regression equation for the provided data set is as follows:

Count=602.8−(74.7×Time)

Here, the response variable (represented as y) is ‘count,’ and the explanatory variable (represented as ″x″) is ‘time.’ The estimated counts are obtained by substituting the respective values of time (1, 3, 5 and 7) in the regression equation.

For time x1=1, the value of count (represented as y^1 ) is calculated as follows:

Count=602.8−(74.7×Time)=602.8−(74.7×1)y^1=528.1

For time x2=3, the value of count (represented as y^2 ) is calculated as follows:

Count=602.8−(74.7×Time)=602.8−(74.7×3)y^2=378.7

For time x3=5, the value of count (represented as y^3 ) is calculated as follows:

count=602.8−(74.7×time)=602.8−(74.7×5)y^3=229.3

For time x4=7, the value of count (represented as y^4 ) is calculated as follows:

Count=602.8−(74.7×Time)=602.8−(74.7×7)y^4=79.9

The observed y values have been provided in the data and are written below:

y1=578y2=317y3=203y4=118

The residuals (represented as ei ) are the difference between the observed y values and predicted y values. The residuals for the above four observed and predicted values are calculated as follows:

For y1, the residual e1 is calculated as follows:

e1=Observed y1−Predicted y1=y1−y^1=578−528.1=49.9

For y2, the residual e2 is calculated as follows:

e2=Observed y2−Predicted y2=y2−y^2=317−378.7=−61.7

For y3, the residual e3 is calculated as follows:

e3=Observed y3−Predicted y3=y3−y^3=203−229.3=−26.3

For y4, the residual e4 is calculated as follows:

e4=Observed y4−Predicted y4=y4−y^4=118−79.9=38.1

Hence, the four residuals obtained are

e1=49.9

e2=−61.7

e3=−26.3

e4=38.1

Answer 13

(b)

To determine

To graph: The model for residual versus time plot.

(b)

Expert Solution

Explanation of Solution

Graph: The residual versus time plot is obtained using the Minitab software by following the steps below:

Step 1: Enter the data in the Minitab worksheet.

Step 2: Go to Stat and select Regression and then select Regression again.

Step 3: Enter the response variable as ‘Count’ and Predictors as ‘Time.’

Step 4: Under Graphs option, choose Residuals versus order.

Step 5: Fill in Residual versus the variables as ‘Time.’

Step 6: Click on Ok.

The resultant graph is obtained as follows:

Introduction to the Practice of Statistics, Chapter 2.5, Problem 96E

Answer 14

(b)

To determine

To graph: The model for residual versus time plot.

Answer 15

(b)

Expert Solution

Explanation of Solution

Graph: The residual versus time plot is obtained using the Minitab software by following the steps below:

Step 1: Enter the data in the Minitab worksheet.

Step 2: Go to Stat and select Regression and then select Regression again.

Step 3: Enter the response variable as ‘Count’ and Predictors as ‘Time.’

Step 4: Under Graphs option, choose Residuals versus order.

Step 5: Fill in Residual versus the variables as ‘Time.’

Step 6: Click on Ok.

The resultant graph is obtained as follows:

Introduction to the Practice of Statistics, Chapter 2.5, Problem 96E

Answer 16

(b)

Expert Solution

Answer 17

(b)

Expert Solution

Answer 18

Expert Solution

Answer 19

(c)

To determine

To explain: Interpretation of the obtained residual plot.

(c)

Expert Solution

Answer to Problem 96E

Solution: Since there is no pattern observed in the residuals versus time plot, it can be concluded that the provided model is appropriate to estimate the count variable.

Explanation of Solution

The residual plot has no specific pattern. The plot seems to be scattered and nonlinear. The two residuals, e1 as 49.9 and e4 as 38.1, are positive, and the two residuals e2 as −61.7 and e3 as −26.3 are negative. This implies that the residuals are scattered above as well as below the x- axis. The uniform scattering of the residuals represents a good sign. Thus, it can be said that the provided regression model is suitable to predict the count variable.

Answer 20

(c)

To determine

To explain: Interpretation of the obtained residual plot.

Answer 21

(c)

Expert Solution

Answer to Problem 96E

Solution: Since there is no pattern observed in the residuals versus time plot, it can be concluded that the provided model is appropriate to estimate the count variable.

Answer 22

(c)

Expert Solution

Answer 23

(c)

Expert Solution

Answer 24

Expert Solution

Answer 25

Explanation of Solution

The residual plot has no specific pattern. The plot seems to be scattered and nonlinear. The two residuals, e1 as 49.9 and e4 as 38.1, are positive, and the two residuals e2 as −61.7 and e3 as −26.3 are negative. This implies that the residuals are scattered above as well as below the x- axis. The uniform scattering of the residuals represents a good sign. Thus, it can be said that the provided regression model is suitable to predict the count variable.