Introduction to the Practice of Statistics
Introduction to the Practice of Statistics
9th Edition
ISBN: 9781319013387
Author: David S. Moore, George P. McCabe, Bruce A. Craig
Publisher: W. H. Freeman
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Chapter 2.5, Problem 112E

(a)

To determine

To find: The predicted values and residuals for each of the four regression equation.

(a)

Expert Solution
Check Mark

Answer to Problem 112E

Solution: The predicted values and residuals for Data set A is given below:

xA

yA

Predicted values

Residual

10

8.04

8.001

0.039

8

6.95

7.001

0.051

13

7.58

9.501

1.921

9

8.81

7.501

1.309

11

8.33

8.501

0.171

14

9.96

10.001

0.041

6

7.24

6.001

1.239

4

4.26

5.000

0.740

12

10.84

9.001

1.839

7

4.82

6.501

1.681

5

5.68

5.501

0.179

The predicted values and residuals for Data set B is given below:

xB

yB

Predicted values

Residual

10

9.14

8.001

1.139

8

8.14

7.001

1.139

13

8.74

9.501

0.761

9

8.77

7.501

1.269

11

9.26

8.501

0.759

14

8.10

10.001

1.901

6

6.13

6.001

0.129

4

3.10

5.000

1.901

12

9.13

9.001

0.129

7

7.26

6.501

0.759

5

4.74

5.501

0.761

The predicted values and residuals for Data set C is given below:

xC

yC

Predicted values

Residual

10

7.46

7.999

0.540

8

6.77

7.000

0.230

13

12.74

9.499

3.241

9

7.11

7.50

0.390

11

7.81

8.499

0.689

14

8.84

9.999

1.159

6

6.08

6.001

0.079

4

5.39

5.001

0.389

12

8.15

8.999

0.849

7

6.42

6.501

0.081

5

5.73

5.501

0.229

The predicted values and residuals for Data set D is given below:

xD

yD

Predicted values

Residual

8

6.58

7.001

0.421

8

5.76

7.001

1.241

8

7.71

7.001

0.709

8

8.84

7.001

1.839

8

8.47

7.001

1.469

8

7.04

7.001

0.039

8

5.25

7.001

1.751

8

5.56

7.001

1.441

8

7.91

7.001

0.909

8

6.89

7.001

0.111

19

12.50

12.5

0.000

Explanation of Solution

Calculation: To predict y for Data set A, Minitab is used. The steps to be followed are:

Step 1: Go to the Minitab worksheet.

Step 2: Go to Stat > Regression > Regression.

Step 3: Enter the variable yA in the response and enter the variable xA in the predictor column.

Step 4: Go to results and select “The table of fits and residuals.”

Step 5: Click OK.

Hence, the result is

xA

yA

Predicted values

Residual

10

8.04

8.001

0.039

8

6.95

7.001

0.051

13

7.58

9.501

1.921

9

8.81

7.501

1.309

11

8.33

8.501

0.171

14

9.96

10.001

0.041

6

7.24

6.001

1.239

4

4.26

5.000

0.740

12

10.84

9.001

1.839

7

4.82

6.501

1.681

5

5.68

5.501

0.179

To predict y for Data set B, Minitab is used. The steps to be followed are:

Step 1: Go to the Minitab worksheet.

Step 2: Go to Stat > Regression > Regression.

Step 3: Enter the variable yB in the response and enter the variable xB in the predictor column.

Step 4: Go to results and select “The table of fits and residuals.”

Step 5: Click OK.

Hence, the result is

xB

yB

Predicted values

Residual

10

9.14

8.001

1.139

8

8.14

7.001

1.139

13

8.74

9.501

0.761

9

8.77

7.501

1.269

11

9.26

8.501

0.759

14

8.10

10.001

1.901

6

6.13

6.001

0.129

4

3.10

5.000

1.901

12

9.13

9.001

0.129

7

7.26

6.501

0.759

5

4.74

5.501

0.761

To predict y for Data set C, Minitab is used. The steps to be followed are:

Step 1: Go to the Minitab worksheet.

Step 2: Go to Stat > Regression > Regression.

Step 3: Enter the variable yC in the response and enter the variable xC in the predictor column.

Step 4: Go to results and select “The table of fits and residuals.”

Step 5: Click OK.

Hence, the result is

xC

yC

Predicted values

Residual

10

7.46

7.999

0.540

8

6.77

7.000

0.230

13

12.74

9.499

3.241

9

7.11

7.50

0.390

11

7.81

8.499

0.689

14

8.84

9.999

1.159

6

6.08

6.001

0.079

4

5.39

5.001

0.389

12

8.15

8.999

0.849

7

6.42

6.501

0.081

5

5.73

5.501

0.229

To predict y for Data set D, Minitab is used. The steps to be followed are:

Step 1: Go to the Minitab worksheet.

Step 2: Go to Stat > Regression > Regression.

Step 3: Enter the variable yD in the response and enter the variable xD in the predictor column.

Step 4: Go to results and select “The table of fits and residuals.”

Step 5: Click OK.

Hence, the result is

xD

yD

Predicted values

Residual

8

6.58

7.001

0.421

8

5.76

7.001

1.241

8

7.71

7.001

0.709

8

8.84

7.001

1.839

8

8.47

7.001

1.469

8

7.04

7.001

0.039

8

5.25

7.001

1.751

8

5.56

7.001

1.441

8

7.91

7.001

0.909

8

6.89

7.001

0.111

19

12.50

12.5

0.000

Interpretation: The residual values are the differences of observed value and the predicted value.

(b)

To determine

To graph: The residual versus x for each of the four datasets.

(b)

Expert Solution
Check Mark

Explanation of Solution

Graph: To plot the residual versus x for each of the four datasets, Minitab is used. The steps to be followed are:

Step 1: Go to the Minitab worksheet.

Step 2: Go to Stat > Regression > Regression.

Step 3: Enter the variable yA in the response and enter the variable xA in the predictor column.

Step 4: Go to graph and select Residual versus fits.

Step 5: Click OK.

Hence, the obtained graph is

Introduction to the Practice of Statistics, Chapter 2.5, Problem 112E , additional homework tip  1

Similarly, repeat the steps for the residual plot versus x for Dataset B:

Introduction to the Practice of Statistics, Chapter 2.5, Problem 112E , additional homework tip  2

The residual plot versus x for Dataset C:

Introduction to the Practice of Statistics, Chapter 2.5, Problem 112E , additional homework tip  3

The residual plot versus x for Dataset D:

Introduction to the Practice of Statistics, Chapter 2.5, Problem 112E , additional homework tip  4

(c)

To determine

To explain: The summary for the residuals.

(c)

Expert Solution
Check Mark

Answer to Problem 112E

Solution: The regression lines for datasets A and C fit the data quite well. The residual plot for dataset C shows strong correlation between the variables.

Explanation of Solution

For the Data set A, the residual plot has no correlation around a zero residual and this line fits the data quite well. For Data set B, the residual plot is in the form of arc and shows no correlation. This regression line is not a good representation of the data. For the Data set C, there is a strong correlation between the variables. So, the regression line fits well in the data and shows one outlier. For the Data set D, the residual plot is vertical. This is not a good prediction equation and there is one outlier.

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Introduction to the Practice of Statistics

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