Description
Complete the problems below .
- Chapter 13 – Problem 63
- Chapter 13 – Problem 64
- Chapter 14 – Problem 35
- Chapter 14 Case A – Century National Bank
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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...
