## Description

Complete the problems below .

- Chapter 13 – Problem 63
- Chapter 13 – Problem 64
- Chapter 14 – Problem 35
- Chapter 14 Case A – Century National Bank

For problems requiring computations, please ensure that your Excel file includes the associated cell computations and/or statistics output.

Submit output in one Excel file.

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## Explanation & Answer

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Regression Statistics

Multiple R 0,670871

R Square

0,450067

Adjusted R Square

0,409332

Standard Error0,49352

Observations

30

ANOVA

df

Regression

Residual

Total

SS

MS

F

Significance F

2 5,381973 2,690987 11,04846 0,000312

27 6,576177 0,243562

29 11,95815

Coefficients

Standard Error t Stat

P-value Lower 95% Upper 95%

Intercept

-5,95268 2,004201

-2,9701 0,006182

-10,065

-1,8404

BA

36,27043 7,741811 4,685006

7,1E-05 20,38555 52,15531

ERA

-0,19441 0,184681 -1,05268 0,301817 -0,57334 0,184524

Team

Attendance

BA

ERA

Arizona Diamondbacks

2,18

0,259

3,93

Atlanta Braves

2,42

0,247

3,42

2,1

0,247

3,9

Boston Red Sox

3,04

0,26

4,7

Chicago Cubs

2,88

0,24

4,51

Chicago White Sox

1,97

0,255

4,02

Cincinnati Reds

2,35

0,251

3,34

Cleveland Indians

1,6

0,251

4,78

Colorado Rockies

2,63

0,274

5,22

Detroit Tigers

3,03

0,268

3,75

Houston Astros

1,61

0,236

4,56

Kansas City Royals

1,74

0,265

4,3

Los Angeles Angels

3,06

0,274

4,02

Los Angeles Dodgers

3,32

0,252

3,34

Miami Marlins

2,22

0,244

4,09

Milwaukee Brewers

Minnesota Twins

2,83

2,78

0,259

0,26

4,22

4,77

New York Mets

2,24

0,249

4,09

New York Yankees

3,54

0,265

3,85

Oakland Athletics

1,68

0,238

3,48

Philadelphia Phillies

3,57

0,255

3,83

Pittsburgh Pirates

2,09

0,243

3,86

San Diego Padres

2,12

0,247

4,01

San Francisco Giants

3,38

0,269

3,68

Seattle Mariners

1,72

0,234

3,76

St. Louis Cardinals

3,26

0,271

3,71

Tampa Bay Rays

1,56

0,24

3,19

Texas Rangers

3,46

0,273

3,99

2,1

0,245

4,64

2,37

0,261

3,33

Baltimore Orioles

Toronto Blue Jays

Washington Nationals

Attendance

Attendance

BA

ERA

BA

1

0,653832474

1

-0,054837543 0,143525677

Average Salary

1990

$578.930

1991

$891.188

1992

$1.084.408

1993

$1.120.254

1994

$1.188.679

1995

$1.071.029

1996

$1.176.967

1997

$1.383.578

1998

$1.441.406

1999

$1.720.050

2000

$1.988.034

2001

$2.264.403

2002

$2.383.235

2003

$2.555.476

2004

$2.486.609

2005

$2.632.655

$2.866.544

$2.944.556

$3.154.845

$3.240.206

ERA

1

2010

$3.297.828

2011

$3.305.393

2012

$3.440.000

Team

Salary 2012

Attendance

X1

X5

X7

Arizona Diamondbacks

74,3

2,18

Atlanta Braves

83,3

2,42

Baltimore Orioles

81,4

2,1

173,2

3,04

Chicago Cubs

88,2

2,88

Chicago White Sox

96,9

1,97

Cincinnati Reds

82,2

2,35

Cleveland Indians

78,4

1,6

Colorado Rockies

78,1

2,63

Detroit Tigers

132,3

3,03

Houston Astros

60,7

1,61

Kansas City Royals

60,9

1,74

Los Angeles Angels

154,5

3,06

Los Angeles Dodgers

95,1

3,32

Miami Marlins

118,1

2,22

Milwaukee Brewers

Minnesota Twins

97,7

94,1

2,83

2,78

New York Mets

93,4

2,24

New York Yankees

198

3,54

Oakland Athletics

55,4

1,68

Philadelphia Phillies

174,5

3,57

Pittsburgh Pirates

63,4

2,09

San Diego Padres

55,2

2,12

San Francisco Giants

117,6

3,38

82

1,72

St. Louis Cardinals

110,3

3,26

Tampa Bay Rays

64,2

1,56

Texas Rangers

120,5

3,46

Toronto Blue Jays

75,5

2,1

Washington Nationals

81,3

2,37

Boston Red Sox

Seattle Mariners

Scatter diagram showing relationship between Salary and

Attendance

4

3,5

Attendance

3

2,5

2

Series1

1,5

1

0,5

0

0

50

100

150

Salary

200

250

Average Salary

1989

$512.930

1990

$578.930

1991

$891.188

1992

$1.084.408

1993

$1.120.254

1994

$1.188.679

1995

$1.071.029

1996

$1.176.967

1997

$1.383.578

1998

$1.441.406

1999

$1.720.050

2000

$1.988.034

2001

$2.264.403

2002

$2.383.235

2003

$2.555.476

2004

$2.486.609

2005

2006

$2.632.655

$2.866.544

2007

$2.944.556

2008

$3.154.845

2009

$3.240.206

2010

$3.297.828

2011

$3.305.393

2012

$3.440.000

SUMMARY OUTPUT

Regression Statistics

Multiple R

0,770317814

R Square

0,593389535

Adjusted R Square

0,578867732

Standard Error

0,416717999

Observations

30

ANOVA

df

Regression

Residual

Total

Intercept

X Variable 1

SS

MS

F

Significance F

1 7,095841 7,095841 40,86198 6,41E-07

28 4,862309 0,173654

29 11,95815

CoefficientsStandard Error t Stat

P-value Lower 95% Upper 95%Lower 95.0%

1,178554138 0,219546 5,368153 1,01E-05 0,728835 1,628273 0,728835

0,013429923 0,002101 6,392337 6,41E-07 0,009126 0,017734 0,009126

PROBABILITY OUTPUT

Percentile

1,666666667

5

8,333333333

11,66666667

15

18,33333333

21,66666667

25

28,33333333

31,66666667

35

38,33333333

41,66666667

45

48,33333333

51,66666667

55

58,33333333

61,66666667

65

68,33333333

71,66666667

Y

1,56

1,6

1,61

1,68

1,72

1,74

1,97

2,09

2,1

2,1

2,12

2,18

2,22

2,24

2,35

2,37

2,42

2,63

2,78

2,83

2,88

3,03

75

78,33333333

81,66666667

85

88,33333333

91,66666667

95

98,33333333

3,04

3,06

3,26

3,32

3,38

3,46

3,54

3,57

Upper 95.0%

1,628273

0,017734

Regression Equation: y = 1.179 + 0.0134x

a)

Scatter Diagram

Scatter diagram showing relationship between Salary and

Attendance

4

3,5

Attendance

3

2,5

2

Series1

1,5

1

0,5

0

0

50

100

150

200

250

Salary

From the scatter diagram above, the relationship between salary and attendance although not strong is direct.

b)

Expected attendance for a team with a salary of $80.0 million

y = 1.179 + 0.0134x

y = 1.179 + 0.0134 (80)

y = 2.251

c)

Expected addition in attendance for an additional $30 million pay by owners

y = [1.179 + 0.0134(110)] - [1.179 + 0.0134 (80)]

y = 2.653 - 2.251

y = 0.402

Therefore the attendance will be more by 402 people.

d)

Hypothesis test to conclude that the slope of the regression line is positive at 0.05 significance level

Null hypothesis (Ho) will be that the slope is not positive while the alternative hypothesis (Hi) will be that the sl

is positive

The slope is the x-intercept.

From the regression output, the p-value for x-intercept is less than 0.05 and therefore we reject the null hypothes

Therefore, we can conclude that the slope of the regression line is indeed positive.

e)

Percentage of variations in attendance accounted for by salary

From the regression analysis output, R-squared is used to determine the variation in y-variable

accounted for by the x-variable.

Therefore 59.34% of the variation in attendance is accounted for by salary.

f)

Correlation

Attendance

Attendance

1

BA

0,65

ERA

-0,05

BA

1

0,14

ERA

1

The correlation between batting average and attendance is stronger than that between ERA and attendance

Hypothesis testing

Intercept

BA

ERA

Coefficients

Standard Error t Stat

P-value Lower 95% Upper 95%

-5,95268 2,004201

-2,9701 0,006...