The following is a chart of baseball players' salaries and statistics from 2016. RBI's HR's Salary (in millions) Player Name Miquel Cabrera Yoenis Cespedes 108 38 28.050 86 31 27.500 Ryan Howard 59 25 25.000 Albert Pujols 119 31 25.000 Robinson Cano 103 39 24.050 Mark Teixeira 44 15 23.125 Joe Mauer 49 11 23.000 Hanley Ramirez Justin Upton 111 30 22.750 87 31 22.125
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
 alt="The following is a chart of baseball players' salaries and
statistics from 2016.
Salary (in
millions)
Player Name
RBI's
HR's
Miquel Cabrera
108
38
28.050
Yoenis Cespedes
86
31
27.500
Ryan Howard
59
25
25.000
Albert Pujols
119
31
25.000
Robinson Cano
103
39
24.050
Mark Teixeira
44
15
23.125
Joe Mauer
49
11
23.000
Hanley Ramirez
Justin Upton
111
30
22.750
87
31
22.125
Adrian Gonzalez
90
18
21.857
Jason Heyward
49
7
21.667
Jayson Werth
70
21
21.571
Matt Kemp
108
35
21.500
Jacoby Ellsbury
56
9.
21.143
Chris Davis
84
38
21.119
Buster Posey
80
14
20.802
Shin-Soo Choo
17
7
20.000
Troy Tulowitzki
Ryan Braun
79
24
20.000
91
31
20.000
Joey Votto
97
29
20.000
Hunter Pence
57
13
18.500
Prince Fielder
44
8
18.000
Adrian Beltre
104
32
18.000
Victor Martinez
86
27
18.000
Carlos Gonzalez
100
25
17.454
Matt Holliday
62
20
17.000
Brian McCann
58
20
17.000
Mike Trout
100
29
16.083
David Ortiz
127
38
16.000
Adam Jones
83
29
16.000
Curtis
59
30
16.000
Granderson
Colby Rasmus
54
15
15.800
Matt Wieters
66
17
15.800
J.D. Martinez
68
22
6.750
Brandon
84
12
6.000
Crawford
Rajai Davis
48
12
5.950
Aaron Hill
38
10
12.000
Сосо Crisp
55
13
11.000
Ben Zobrist
76
18
10.500
Justin Turner
90
27
5.100
Denard Span
53
11
5.000
Chris lannetta
24
7
4.550
Leonys Martin
47
15
4.150
Justin Smoak
34
14
3.900
Jorge Soler
31
12
3.667
Evan Gattis
72
32
3.300
Logan Forsythe
Jean Segura
52
20
2.750
64
20
2.600
a) Use software to find the multiple linear regression
equation. Enter the coefficients rounded to 4 decimal
places.
21 +
x2
b) Use the multiple linear regression equation to predict
the salary for a baseball player with an RBI of 34 and HR of
20. Round your answer to 1 decimal place, do not convert
numbers to dollars.
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