Compute the coefficient of determination, ρ2, with percentage of games won as the dependent variable. (Note that this data set belongs to a population.) Carry out all calculations exactly, and round the final answer to three decimal places.
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.
The following table gives the 2012 total payroll (in millions of dollars) and the percentage of games won during the 2012 season by each of the National League baseball teams.
|
Team |
Total Payroll (millions of dollars) |
Percentage of Games Won |
|---|---|---|
|
Arizona Diamondbacks |
83 |
46 |
|
Atlanta Braves |
89 |
35 |
|
Chicago Cubs |
110 |
57 |
|
Cincinnati Reds |
111 |
34 |
|
Colorado Rockies |
93 |
39 |
|
Los Angeles Dodgers |
264 |
51 |
|
Miami Marlins |
59 |
38 |
|
Milwaukee Brewers |
99 |
39 |
|
New York Mets |
95 |
53 |
|
Philadelphia Phillies |
127 |
33 |
|
Pittsburgh Pirates |
82 |
58 |
|
San Diego Padres |
92 |
40 |
|
San Francisco Giants |
164 |
46 |
|
St. Louis Cardinals |
112 |
59 |
|
Washington Nationals |
156 |
45 |
Compute the coefficient of determination, ρ2, with percentage of games won as the dependent variable. (Note that this data set belongs to a population.)
Carry out all calculations exactly, and round the final answer to three decimal places.
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