The equation of the fitted least-squares line

Question

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Answer 1

Question

Chapter 13, Problem 13.25SE

a.

To determine

To find: The equation of the fitted least-squares line

a.

Expert Solution

Explanation of Solution

Given:

The Minitab output is:

Introduction to Probability and Statistics, Chapter 13, Problem 13.25SE , additional homework tip 1

Plot is:

Introduction to Probability and Statistics, Chapter 13, Problem 13.25SE , additional homework tip 2

From the provided output, the equation of the regression line is:

y=8.585+3.88208x−0.21663x2

a.

To determine

To interpret: The value of R2 and comment on the fit of the model.

a.

Expert Solution

Explanation of Solution

From the provided output, the coefficient of determination is 0.944. It means that 99.8% of the variation in the model is explained. Since, the value is large enough it means that the provided model is fit enough.

c.

To determine

To find: Whether the model is significant at 5% level of significance.

c.

Expert Solution

Explanation of Solution

From the provided excel output; the p -value is equal to 0.000 which implies that the regression model is highly significant.

c.

To determine

To find: Whether there is sufficient evidence to show that the quadratic model provides a better fir to the data than a simple linear model.

c.

Expert Solution

Explanation of Solution

The prediction equation relating y^ and x1 when x2=4 can be calculated as:

Y=−28.4+1.46x1+3.84(4)=−28.4+1.46x1

d.

To determine

To find: The number of defective items produced for an operator whose average output per hour is 25 and whose machine was serviced 3 weeks ago.

d.

Expert Solution

Explanation of Solution

Since, the p -value is less than the level of significance. Thus, it could be said that the quadratic model provided a better fit than a simple linear model

e.

To determine

To explain: Whether normality assumptions have been violated using the residual plot.

e.

Expert Solution

Explanation of Solution

From the provided residual plot, it could be said that there is no violation of normality assumptions. It means that model is well fitted.

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Answer 2

Question

Chapter 13, Problem 13.25SE

a.

To determine

To find: The equation of the fitted least-squares line

a.

Expert Solution

Explanation of Solution

Given:

The Minitab output is:

Introduction to Probability and Statistics, Chapter 13, Problem 13.25SE , additional homework tip 1

Plot is:

Introduction to Probability and Statistics, Chapter 13, Problem 13.25SE , additional homework tip 2

From the provided output, the equation of the regression line is:

y=8.585+3.88208x−0.21663x2

a.

To determine

To interpret: The value of R2 and comment on the fit of the model.

a.

Expert Solution

Explanation of Solution

From the provided output, the coefficient of determination is 0.944. It means that 99.8% of the variation in the model is explained. Since, the value is large enough it means that the provided model is fit enough.

c.

To determine

To find: Whether the model is significant at 5% level of significance.

c.

Expert Solution

Explanation of Solution

From the provided excel output; the p -value is equal to 0.000 which implies that the regression model is highly significant.

c.

To determine

To find: Whether there is sufficient evidence to show that the quadratic model provides a better fir to the data than a simple linear model.

c.

Expert Solution

Explanation of Solution

The prediction equation relating y^ and x1 when x2=4 can be calculated as:

Y=−28.4+1.46x1+3.84(4)=−28.4+1.46x1

d.

To determine

To find: The number of defective items produced for an operator whose average output per hour is 25 and whose machine was serviced 3 weeks ago.

d.

Expert Solution

Explanation of Solution

Since, the p -value is less than the level of significance. Thus, it could be said that the quadratic model provided a better fit than a simple linear model

e.

To determine

To explain: Whether normality assumptions have been violated using the residual plot.

e.

Expert Solution

Explanation of Solution

From the provided residual plot, it could be said that there is no violation of normality assumptions. It means that model is well fitted.

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Answer 3

Question

Chapter 13, Problem 13.25SE

a.

To determine

To find: The equation of the fitted least-squares line

a.

Expert Solution

Explanation of Solution

Given:

The Minitab output is:

Introduction to Probability and Statistics, Chapter 13, Problem 13.25SE , additional homework tip 1

Plot is:

Introduction to Probability and Statistics, Chapter 13, Problem 13.25SE , additional homework tip 2

From the provided output, the equation of the regression line is:

y=8.585+3.88208x−0.21663x2

a.

To determine

To interpret: The value of R2 and comment on the fit of the model.

a.

Expert Solution

Explanation of Solution

From the provided output, the coefficient of determination is 0.944. It means that 99.8% of the variation in the model is explained. Since, the value is large enough it means that the provided model is fit enough.

c.

To determine

To find: Whether the model is significant at 5% level of significance.

c.

Expert Solution

Explanation of Solution

From the provided excel output; the p -value is equal to 0.000 which implies that the regression model is highly significant.

c.

To determine

To find: Whether there is sufficient evidence to show that the quadratic model provides a better fir to the data than a simple linear model.

c.

Expert Solution

Explanation of Solution

The prediction equation relating y^ and x1 when x2=4 can be calculated as:

Y=−28.4+1.46x1+3.84(4)=−28.4+1.46x1

d.

To determine

To find: The number of defective items produced for an operator whose average output per hour is 25 and whose machine was serviced 3 weeks ago.

d.

Expert Solution

Explanation of Solution

Since, the p -value is less than the level of significance. Thus, it could be said that the quadratic model provided a better fit than a simple linear model

e.

To determine

To explain: Whether normality assumptions have been violated using the residual plot.

e.

Expert Solution

Explanation of Solution

From the provided residual plot, it could be said that there is no violation of normality assumptions. It means that model is well fitted.

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

Answer 4

Question

Chapter 13, Problem 13.25SE

a.

To determine

To find: The equation of the fitted least-squares line

a.

Expert Solution

Explanation of Solution

Given:

The Minitab output is:

Introduction to Probability and Statistics, Chapter 13, Problem 13.25SE , additional homework tip 1

Plot is:

Introduction to Probability and Statistics, Chapter 13, Problem 13.25SE , additional homework tip 2

From the provided output, the equation of the regression line is:

y=8.585+3.88208x−0.21663x2

a.

To determine

To interpret: The value of R2 and comment on the fit of the model.

a.

Expert Solution

Explanation of Solution

From the provided output, the coefficient of determination is 0.944. It means that 99.8% of the variation in the model is explained. Since, the value is large enough it means that the provided model is fit enough.

c.

To determine

To find: Whether the model is significant at 5% level of significance.

c.

Expert Solution

Explanation of Solution

From the provided excel output; the p -value is equal to 0.000 which implies that the regression model is highly significant.

c.

To determine

To find: Whether there is sufficient evidence to show that the quadratic model provides a better fir to the data than a simple linear model.

c.

Expert Solution

Explanation of Solution

The prediction equation relating y^ and x1 when x2=4 can be calculated as:

Y=−28.4+1.46x1+3.84(4)=−28.4+1.46x1

d.

To determine

To find: The number of defective items produced for an operator whose average output per hour is 25 and whose machine was serviced 3 weeks ago.

d.

Expert Solution

Explanation of Solution

Since, the p -value is less than the level of significance. Thus, it could be said that the quadratic model provided a better fit than a simple linear model

e.

To determine

To explain: Whether normality assumptions have been violated using the residual plot.

e.

Expert Solution

Explanation of Solution

From the provided residual plot, it could be said that there is no violation of normality assumptions. It means that model is well fitted.

Want to see more full solutions like this?

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

Answer 5

Chapter 13, Problem 13.25SE

a.

To determine

To find: The equation of the fitted least-squares line

a.

Expert Solution

Explanation of Solution

Given:

The Minitab output is:

Introduction to Probability and Statistics, Chapter 13, Problem 13.25SE , additional homework tip 1

Plot is:

Introduction to Probability and Statistics, Chapter 13, Problem 13.25SE , additional homework tip 2

From the provided output, the equation of the regression line is:

y=8.585+3.88208x−0.21663x2

a.

To determine

To interpret: The value of R2 and comment on the fit of the model.

a.

Expert Solution

Explanation of Solution

From the provided output, the coefficient of determination is 0.944. It means that 99.8% of the variation in the model is explained. Since, the value is large enough it means that the provided model is fit enough.

c.

To determine

To find: Whether the model is significant at 5% level of significance.

c.

Expert Solution

Explanation of Solution

From the provided excel output; the p -value is equal to 0.000 which implies that the regression model is highly significant.

c.

To determine

To find: Whether there is sufficient evidence to show that the quadratic model provides a better fir to the data than a simple linear model.

c.

Expert Solution

Explanation of Solution

The prediction equation relating y^ and x1 when x2=4 can be calculated as:

Y=−28.4+1.46x1+3.84(4)=−28.4+1.46x1

d.

To determine

To find: The number of defective items produced for an operator whose average output per hour is 25 and whose machine was serviced 3 weeks ago.

d.

Expert Solution

Explanation of Solution

Since, the p -value is less than the level of significance. Thus, it could be said that the quadratic model provided a better fit than a simple linear model

e.

To determine

To explain: Whether normality assumptions have been violated using the residual plot.

e.

Expert Solution

Explanation of Solution

From the provided residual plot, it could be said that there is no violation of normality assumptions. It means that model is well fitted.

Answer 6

Chapter 13, Problem 13.25SE

a.

To determine

To find: The equation of the fitted least-squares line

a.

Expert Solution

Explanation of Solution

Given:

The Minitab output is:

Introduction to Probability and Statistics, Chapter 13, Problem 13.25SE , additional homework tip 1

Plot is:

Introduction to Probability and Statistics, Chapter 13, Problem 13.25SE , additional homework tip 2

From the provided output, the equation of the regression line is:

y=8.585+3.88208x−0.21663x2

Answer 7

Chapter 13, Problem 13.25SE

a.

To determine

To find: The equation of the fitted least-squares line

Answer 8

a.

Expert Solution

Explanation of Solution

Given:

The Minitab output is:

Introduction to Probability and Statistics, Chapter 13, Problem 13.25SE , additional homework tip 1

Plot is:

Introduction to Probability and Statistics, Chapter 13, Problem 13.25SE , additional homework tip 2

From the provided output, the equation of the regression line is:

y=8.585+3.88208x−0.21663x2

Answer 9

a.

Expert Solution

Answer 10

a.

Expert Solution

Answer 11

Expert Solution

Answer 12

a.

To determine

To interpret: The value of R2 and comment on the fit of the model.

a.

Expert Solution

Explanation of Solution

From the provided output, the coefficient of determination is 0.944. It means that 99.8% of the variation in the model is explained. Since, the value is large enough it means that the provided model is fit enough.

Answer 13

a.

To determine

To interpret: The value of R2 and comment on the fit of the model.

Answer 14

a.

Expert Solution

Explanation of Solution

From the provided output, the coefficient of determination is 0.944. It means that 99.8% of the variation in the model is explained. Since, the value is large enough it means that the provided model is fit enough.

Answer 15

a.

Expert Solution

Answer 16

a.

Expert Solution

Answer 17

Expert Solution

Answer 18

c.

To determine

To find: Whether the model is significant at 5% level of significance.

c.

Expert Solution

Explanation of Solution

From the provided excel output; the p -value is equal to 0.000 which implies that the regression model is highly significant.

Answer 19

c.

To determine

To find: Whether the model is significant at 5% level of significance.

Answer 20

c.

Expert Solution

Explanation of Solution

From the provided excel output; the p -value is equal to 0.000 which implies that the regression model is highly significant.

Answer 21

c.

Expert Solution

Answer 22

c.

Expert Solution

Answer 23

Expert Solution

Answer 24

c.

To determine

To find: Whether there is sufficient evidence to show that the quadratic model provides a better fir to the data than a simple linear model.

c.

Expert Solution

Explanation of Solution

The prediction equation relating y^ and x1 when x2=4 can be calculated as:

Y=−28.4+1.46x1+3.84(4)=−28.4+1.46x1

Answer 25

c.

To determine

To find: Whether there is sufficient evidence to show that the quadratic model provides a better fir to the data than a simple linear model.

Answer 26

c.

Expert Solution

Explanation of Solution

The prediction equation relating y^ and x1 when x2=4 can be calculated as:

Y=−28.4+1.46x1+3.84(4)=−28.4+1.46x1

Answer 27

c.

Expert Solution

Answer 28

c.

Expert Solution

Answer 29

Expert Solution

Answer 30

d.

To determine

To find: The number of defective items produced for an operator whose average output per hour is 25 and whose machine was serviced 3 weeks ago.

d.

Expert Solution

Explanation of Solution

Since, the p -value is less than the level of significance. Thus, it could be said that the quadratic model provided a better fit than a simple linear model

Answer 31

d.

To determine

To find: The number of defective items produced for an operator whose average output per hour is 25 and whose machine was serviced 3 weeks ago.

Answer 32

d.

Expert Solution

Explanation of Solution

Since, the p -value is less than the level of significance. Thus, it could be said that the quadratic model provided a better fit than a simple linear model

Answer 33

d.

Expert Solution

Answer 34

d.

Expert Solution

Answer 35

Expert Solution

Answer 36

e.

To determine

To explain: Whether normality assumptions have been violated using the residual plot.

e.

Expert Solution

Explanation of Solution

From the provided residual plot, it could be said that there is no violation of normality assumptions. It means that model is well fitted.

Answer 37

e.

To determine

To explain: Whether normality assumptions have been violated using the residual plot.

Answer 38

e.

Expert Solution

Explanation of Solution

From the provided residual plot, it could be said that there is no violation of normality assumptions. It means that model is well fitted.

Answer 39

e.

Expert Solution

Answer 40

e.

Expert Solution

Answer 41

Expert Solution

Answer 42

Ch. 13.4 - Prob. 13.1E Ch. 13.4 - Prob. 13.2E Ch. 13.4 - Suppose that you fit the model E(y)=0+1x1+2x2+3x3...Ch. 13.4 - Prob. 13.4E Ch. 13.4 - Prob. 13.5E Ch. 13.4 - Prob. 13.6E Ch. 13.4 - Prob. 13.7E Ch. 13.4 - Prob. 13.8E Ch. 13.4 - Prob. 13.9E Ch. 13.4 - College Textbooks A publisher of college textbooks...

The equation of the fitted least-squares line

Concept explainers

Videos

To find: The equation of the fitted least-squares line

Explanation of Solution

To interpret: The value of R2 and comment on the fit of the model.

Explanation of Solution

To find: Whether the model is significant at 5% level of significance.

Explanation of Solution

To find: Whether there is sufficient evidence to show that the quadratic model provides a better fir to the data than a simple linear model.

Explanation of Solution

To find: The number of defective items produced for an operator whose average output per hour is 25 and whose machine was serviced 3 weeks ago.

Explanation of Solution

To explain: Whether normality assumptions have been violated using the residual plot.

Explanation of Solution

Want to see more full solutions like this?

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