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 10.1, Problem 19E

(a)

Section 1:

To determine

To graph: A scatterplot.

(a)

Section 1:

Expert Solution
Check Mark

Explanation of Solution

Graph: Construct a scatterplot using Minitab as follows:

Step 1: Enter the data in Minitab.

Step 2: Click on Graph --> Scatterplot. Select scatterplot with regression.

Step 3: Double click on ‘Number of tornadoes’ to move it to Y variable and ‘Year’ to move it to X variable column.

Step 4: Click ‘Ok’ twice to obtain the graph.

Introduction to the Practice of Statistics, Chapter 10.1, Problem 19E , additional homework tip  1

Section 2:

To determine

To explain: The relationship between two variables seems linear.

Section 2:

Expert Solution
Check Mark

Answer to Problem 19E

Solution: The variables are in linear relationship.

Explanation of Solution

From the graph obtained in the above section 1, it can be seen that all the points lie near the trend line. So, it can be concluded that the variables are linearly related.

Section 3:

To determine

To explain: Whether there are any outliers or unusual pattern.

Section 3:

Expert Solution
Check Mark

Answer to Problem 19E

Solution: There are no outliers.

Explanation of Solution

Outlier is a value that seems to be out on their own from the rest of the data. From the graph obtained in the above section 1, it can be seen that there are no outliers or any unusual patterns in the scatterplot.

(b)

To determine

To find: The least square regression line.

(b)

Expert Solution
Check Mark

Answer to Problem 19E

Solution: The regression line is:

Number of tornadoes=24517+12.8Year

Explanation of Solution

Calculation: Obtain the regression line using Minitab as follows:

Step 1: Enter the data in Minitab.

Step 2: Click on Stat --> Regression --> Regression.

Step 3: Double click on ‘Number of tornadoes’ to move it to Y variable and ‘Year’ to move it to X variable column.

Step 4: Click on ‘Storage’ and check the box for residuals.

Step 5: Click ‘Ok’ twice to obtain the result.

Hence, the obtained regression line is

Number of tornadoes=24517+12.8Year

(c)

To determine

To explain: The intercept of regression equation.

(c)

Expert Solution
Check Mark

Answer to Problem 19E

Solution: The fit is correct because intercept is only used when x=0.

Explanation of Solution

The fit is correct because the intercept only describes the model when x=0 that in this case is far outside the range of the provided data of annual number of tornadoes in the United States between 1953 and 2014.

(d)

Section 1:

To determine

To find: The residuals.

(d)

Section 1:

Expert Solution
Check Mark

Answer to Problem 19E

Solution: The residuals are as follows:

Years

Number of tornadoes

Residuals

1953

421

-127.661

1954

550

-11.495

1955

593

18.670

1956

504

-83.164

1957

856

256.001

1958

564

-48.833

1959

604

-21.668

1960

616

-22.502

1961

697

45.663

1962

657

-7.171

1963

464

-213.006

1964

704

14.160

1965

906

203.325

1966

585

-130.509

1967

926

197.656

1968

660

-81.178

1969

608

-146.013

1970

653

-113.847

1971

888

108.318

1972

741

-51.516

1973

1102

296.649

1974

947

128.815

1975

920

88.980

1976

835

-8.854

1977

852

-4.689

1978

788

-81.523

1979

852

-30.358

1980

866

-29.192

1981

783

-125.027

1982

1046

125.139

1983

931

-2.696

1984

907

-39.530

1985

684

-275.365

1986

764

-208.199

1987

656

-329.034

1988

702

-295.868

1989

856

-154.703

1990

1133

109.463

1991

1132

95.628

1992

1298

248.794

1993

1176

113.959

1994

1082

7.125

1995

1235

147.290

1996

1173

72.456

1997

1148

34.621

1998

1449

322.787

1999

1340

200.952

2000

1075

-76.882

2001

1215

50.283

2002

934

-243.551

2003

1374

183.614

2004

1817

613.780

2005

1265

48.945

2006

1103

-125.889

2007

1096

-145.724

2008

1692

437.442

2009

1156

-111.393

2010

1282

1.773

2011

1691

397.938

2012

938

-367.896

2013

907

-411.731

2014

888

-443.565

Explanation of Solution

Calculation: Obtain the residuals using Minitab as follows:

Step 1: Enter the data in Minitab.

Step 2: Click on Stat --> Regression --> Regression.

Step 3: Double click on ‘Number of tornadoes’ to move it response column and ‘Year’ to move it to predictor column.

Step 4: Click on ‘Storage’ and check the box for residuals.

Step 5: Click ‘Ok’ to obtain the result.

Hence, the obtained residuals are shown below:

Years

Number of tornadoes

Residuals

1953

421

-127.661

1954

550

-11.495

1955

593

18.670

1956

504

-83.164

1957

856

256.001

1958

564

-48.833

1959

604

-21.668

1960

616

-22.502

1961

697

45.663

1962

657

-7.171

1963

464

-213.006

1964

704

14.160

1965

906

203.325

1966

585

-130.509

1967

926

197.656

1968

660

-81.178

1969

608

-146.013

1970

653

-113.847

1971

888

108.318

1972

741

-51.516

1973

1102

296.649

1974

947

128.815

1975

920

88.980

1976

835

-8.854

1977

852

-4.689

1978

788

-81.523

1979

852

-30.358

1980

866

-29.192

1981

783

-125.027

1982

1046

125.139

1983

931

-2.696

1984

907

-39.530

1985

684

-275.365

1986

764

-208.199

1987

656

-329.034

1988

702

-295.868

1989

856

-154.703

1990

1133

109.463

1991

1132

95.628

1992

1298

248.794

1993

1176

113.959

1994

1082

7.125

1995

1235

147.290

1996

1173

72.456

1997

1148

34.621

1998

1449

322.787

1999

1340

200.952

2000

1075

-76.882

2001

1215

50.283

2002

934

-243.551

2003

1374

183.614

2004

1817

613.780

2005

1265

48.945

2006

1103

-125.889

2007

1096

-145.724

2008

1692

437.442

2009

1156

-111.393

2010

1282

1.773

2011

1691

397.938

2012

938

-367.896

2013

907

-411.731

2014

888

-443.565

Section 2:

To determine

To graph: The scatterplot of residual versus year.

Section 2:

Expert Solution
Check Mark

Explanation of Solution

Graph: Construct a scatterplot using Minitab as follows:

Step 1: Enter the data in Minitab.

Step 2: Click on Graph --> Scatterplot. Select scatterplot with regression.

Step 3: Double click on ‘Residuals’ to move it to Y variable and ‘Year’ to move it to X variable column.

Step 4: Click ‘Ok’ to obtain the graph.

Introduction to the Practice of Statistics, Chapter 10.1, Problem 19E , additional homework tip  2

From the scatter plot, it is clear that the residual plot looks mostly random

(e)

To determine

To explain: That residuals are normal or not.

(e)

Expert Solution
Check Mark

Answer to Problem 19E

Solution: The residuals are normally distributed.

Explanation of Solution

Graph: Construct the probability plot for residuals to test for the normality using Minitab as follows:

Step 1: Click on Stat --> Descriptive statistics --> Normality test.

Step 2: Double click on ‘Residuals’ to move it to the variable column.

Step 3: Click ‘OK’ to obtain the graph.

Hence, the obtained graph is shown below:

Introduction to the Practice of Statistics, Chapter 10.1, Problem 19E , additional homework tip  3

Interpretation: All the points lie near the trend line. Therefore, it can be concluded that residuals are normally distributed.

(f)

To determine

To explain: The accuracy of inference based on residual checks.

(f)

Expert Solution
Check Mark

Answer to Problem 19E

Solution: The inference can be made based on residuals.

Explanation of Solution

From the graph obtained in part (e), it is clear that the residuals of the regression follow normal distribution, so it satisfies the assumption of regression equation. Therefore, inference can be made based on residual checks.

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