Create a scatterplot investigating the relationship between the amount of money major league baseball teams spend on their players and the number of wins they have in a season. Here is the data for the payroll amounts for MLB teams in 2018 (rounded to the nearest million) and the number of wins they had that season.
Team
2018 Payroll (million $)
2018 Wins
Cubs
212
95
Yankees
205
100
Nationals
204
82
Red Sox
204
108
Giants
200
73
Angels
177
80
Dodgers
171
92
Astros
166
103
Cardinals
165
88
Mariners
153
89
Rockies
151
91
Mets
149
77
Phillies
145
80
Reds
134
67
Brewers
128
96
Indians
123
91
Braves
118
90
Twins
115
78
Diamondbacks
108
82
Rangers
107
67
Tigers
105
64
Royals
103
58
Athletics
103
97
White Sox
91
62
Orioles
80
47
Pirates
76
82
Padres
76
66
Blue Jays
71
73
Marlins
71
63
Rays
53
90
Create a scatterplot for this data. Place the explanatory on the horizontal axis and response variable on the vertical axis. Label the axes and identify the scale on each axis
Calculate the correlation value, r, using the formula:
????=????(∑????????)−(∑????)(∑????)[????(∑????2)(∑????)2][????(∑????2)−(∑????)2]√r=n(∑xy)−(∑x)(∑y)[n(∑x2)(∑x)2][n(∑y2)−(∑y)2]
Select two points and use them to define the line of best fit, . Identify these points and sketch the line on the scatterplot.
Use the line you defined to estimate the number of wins $150 million would buy in 2018. How does this compare to the Rockies and Mets performance that year.
Identify any outliers on the scatterplot. For this case, an outlier is defined as any team that is more than 15 wins away from the predicted value from the line of best fit.
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