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

Question

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Answer 1

Question

Compare Compare Correlation is the measure of the degree of the relationship between the variables. In regression, the relationship between the variables to predict one by another is assessed. In correlation there is no cause and effect between the variables, whereas in regression there is a cause and effect between the variables. By using correlation, we cannot predict anything, but regression is a predictive tool. Coefficients are symmetrical in correlation but in regression they are asymmetrical. Correlation is independent of change in origin and scale, but regression is not independent of change in scale.

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

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

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

EBK INTRODUCTION TO THE PRACTICE OF STA, Chapter 2.5, Problem 112E , additional homework tip 1

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

EBK INTRODUCTION TO THE PRACTICE OF STA, Chapter 2.5, Problem 112E , additional homework tip 2

The residual plot versus x for Dataset C:

EBK INTRODUCTION TO THE PRACTICE OF STA, Chapter 2.5, Problem 112E , additional homework tip 3

The residual plot versus x for Dataset D:

EBK INTRODUCTION TO THE PRACTICE OF STA, Chapter 2.5, Problem 112E , additional homework tip 4

(c)

To determine

To explain: The summary for the residuals.

(c)

Expert Solution

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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Answer 2

Question

Compare Compare Correlation is the measure of the degree of the relationship between the variables. In regression, the relationship between the variables to predict one by another is assessed. In correlation there is no cause and effect between the variables, whereas in regression there is a cause and effect between the variables. By using correlation, we cannot predict anything, but regression is a predictive tool. Coefficients are symmetrical in correlation but in regression they are asymmetrical. Correlation is independent of change in origin and scale, but regression is not independent of change in scale.

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

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

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

EBK INTRODUCTION TO THE PRACTICE OF STA, Chapter 2.5, Problem 112E , additional homework tip 1

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

EBK INTRODUCTION TO THE PRACTICE OF STA, Chapter 2.5, Problem 112E , additional homework tip 2

The residual plot versus x for Dataset C:

EBK INTRODUCTION TO THE PRACTICE OF STA, Chapter 2.5, Problem 112E , additional homework tip 3

The residual plot versus x for Dataset D:

EBK INTRODUCTION TO THE PRACTICE OF STA, Chapter 2.5, Problem 112E , additional homework tip 4

(c)

To determine

To explain: The summary for the residuals.

(c)

Expert Solution

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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Answer 3

Question

Compare Compare Correlation is the measure of the degree of the relationship between the variables. In regression, the relationship between the variables to predict one by another is assessed. In correlation there is no cause and effect between the variables, whereas in regression there is a cause and effect between the variables. By using correlation, we cannot predict anything, but regression is a predictive tool. Coefficients are symmetrical in correlation but in regression they are asymmetrical. Correlation is independent of change in origin and scale, but regression is not independent of change in scale.

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

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

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

EBK INTRODUCTION TO THE PRACTICE OF STA, Chapter 2.5, Problem 112E , additional homework tip 1

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

EBK INTRODUCTION TO THE PRACTICE OF STA, Chapter 2.5, Problem 112E , additional homework tip 2

The residual plot versus x for Dataset C:

EBK INTRODUCTION TO THE PRACTICE OF STA, Chapter 2.5, Problem 112E , additional homework tip 3

The residual plot versus x for Dataset D:

EBK INTRODUCTION TO THE PRACTICE OF STA, Chapter 2.5, Problem 112E , additional homework tip 4

(c)

To determine

To explain: The summary for the residuals.

(c)

Expert Solution

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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Answer 4

Question

Compare Compare Correlation is the measure of the degree of the relationship between the variables. In regression, the relationship between the variables to predict one by another is assessed. In correlation there is no cause and effect between the variables, whereas in regression there is a cause and effect between the variables. By using correlation, we cannot predict anything, but regression is a predictive tool. Coefficients are symmetrical in correlation but in regression they are asymmetrical. Correlation is independent of change in origin and scale, but regression is not independent of change in scale.

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

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

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

EBK INTRODUCTION TO THE PRACTICE OF STA, Chapter 2.5, Problem 112E , additional homework tip 1

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

EBK INTRODUCTION TO THE PRACTICE OF STA, Chapter 2.5, Problem 112E , additional homework tip 2

The residual plot versus x for Dataset C:

EBK INTRODUCTION TO THE PRACTICE OF STA, Chapter 2.5, Problem 112E , additional homework tip 3

The residual plot versus x for Dataset D:

EBK INTRODUCTION TO THE PRACTICE OF STA, Chapter 2.5, Problem 112E , additional homework tip 4

(c)

To determine

To explain: The summary for the residuals.

(c)

Expert Solution

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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Answer 5

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

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

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

EBK INTRODUCTION TO THE PRACTICE OF STA, Chapter 2.5, Problem 112E , additional homework tip 1

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

EBK INTRODUCTION TO THE PRACTICE OF STA, Chapter 2.5, Problem 112E , additional homework tip 2

The residual plot versus x for Dataset C:

EBK INTRODUCTION TO THE PRACTICE OF STA, Chapter 2.5, Problem 112E , additional homework tip 3

The residual plot versus x for Dataset D:

EBK INTRODUCTION TO THE PRACTICE OF STA, Chapter 2.5, Problem 112E , additional homework tip 4

(c)

To determine

To explain: The summary for the residuals.

(c)

Expert Solution

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.

Answer 6

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

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.

Answer 7

Chapter 2.5, Problem 112E

(a)

To determine

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

Answer 8

(a)

Expert Solution

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

Answer 9

(a)

Expert Solution

Answer 10

(a)

Expert Solution

Answer 11

Expert Solution

Answer 12

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.

Answer 13

(b)

To determine

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

(b)

Expert Solution

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

EBK INTRODUCTION TO THE PRACTICE OF STA, Chapter 2.5, Problem 112E , additional homework tip 1

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

EBK INTRODUCTION TO THE PRACTICE OF STA, Chapter 2.5, Problem 112E , additional homework tip 2

The residual plot versus x for Dataset C:

EBK INTRODUCTION TO THE PRACTICE OF STA, Chapter 2.5, Problem 112E , additional homework tip 3

The residual plot versus x for Dataset D:

EBK INTRODUCTION TO THE PRACTICE OF STA, Chapter 2.5, Problem 112E , additional homework tip 4

Answer 14

(b)

To determine

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

Answer 15

(b)

Expert Solution

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

EBK INTRODUCTION TO THE PRACTICE OF STA, Chapter 2.5, Problem 112E , additional homework tip 1

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

EBK INTRODUCTION TO THE PRACTICE OF STA, Chapter 2.5, Problem 112E , additional homework tip 2

The residual plot versus x for Dataset C:

EBK INTRODUCTION TO THE PRACTICE OF STA, Chapter 2.5, Problem 112E , additional homework tip 3

The residual plot versus x for Dataset D:

EBK INTRODUCTION TO THE PRACTICE OF STA, Chapter 2.5, Problem 112E , additional homework tip 4

Answer 16

(b)

Expert Solution

Answer 17

(b)

Expert Solution

Answer 18

Expert Solution

Answer 19

(c)

To determine

To explain: The summary for the residuals.

(c)

Expert Solution

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.

Answer 20

(c)

To determine

To explain: The summary for the residuals.

Answer 21

(c)

Expert Solution

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.

Answer 22

(c)

Expert Solution

Answer 23

(c)

Expert Solution

Answer 24

Expert Solution

Answer 25

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.