The following is a chart of 25 baseball players' salaries and statistics from 2019. Player Name RBI's HR's AVG Salary (in millions) Eugenio Suarez 103 49 0.271 7.286 Khris Davis 73 23 0.221 16.500 Kyle Seager 63 23 0.237 19.500 Dexter Fowler 67 19 0.238 16.500
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 is a chart of 25 baseball players' salaries and statistics from 2019.
| Player Name | RBI's | HR's | AVG | Salary (in millions) |
|---|---|---|---|---|
| Eugenio Suarez | 103 | 49 | 0.271 | 7.286 |
| Khris Davis | 73 | 23 | 0.221 | 16.500 |
| Kyle Seager | 63 | 23 | 0.237 | 19.500 |
| Dexter Fowler | 67 | 19 | 0.238 | 16.500 |
| Russell Martin | 20 | 6 | 0.220 | 20.000 |
| Brandon Crawford | 59 | 11 | 0.228 | 15.200 |
| JD Martinez | 105 | 36 | 0.304 | 23.750 |
| Gordon Beckham | 15 | 6 | 0.215 | 0.700 |
| Roberto Perez | 63 | 24 | 0.239 | 2.625 |
| Eloy Jimenez | 79 | 31 | 0.267 | 1.833 |
| Randal Grichuk | 80 | 31 | 0.232 | 8.000 |
| Carlos Santana | 93 | 34 | 0.281 | 20.333 |
| Xander Bogaerts | 117 | 33 | 0.309 | 12.000 |
| Brock Holt | 31 | 3 | 0.297 | 3.575 |
| Josh Reddick | 56 | 14 | 0.275 | 13.000 |
| Tucker Barnhart | 40 | 11 | 0.231 | 2.938 |
| Ozzie Albies | 86 | 24 | 0.295 | 1.000 |
| Adam Jones | 67 | 16 | 0.260 | 4.500 |
| DJ LeMahieu | 102 | 26 | 0.327 | 12.000 |
| Brian Dozier | 50 | 20 | 0.238 | 9.000 |
| Starling Marte | 82 | 23 | 0.295 | 10.333 |
| Yulieski Gurriel | 104 | 31 | 0.298 | 10.400 |
| Gerardo Parra | 48 | 9 | 0.234 | 0.555 |
| Albert Pujols | 93 | 23 | 0.244 | 28.000 |
| Cameron Maybin | 32 | 11 | 0.285 | 0.555 |
In order to have
(Round to three decimal places for all answers on this assignment.)
RBI vs. Salary
Complete a correlation analysis, using RBI's as the x-value and salary as the y-value.
Regression Equation: y=y=
Do you have significant correlation?
HR vs. Salary
Complete a correlation analysis, using HR's as the x-value and salary as the y-value.
Correlation coefficient:
Regression Equation: y=y=
Do you have significant correlation?
AVG vs. Salary
Complete a correlation analysis, using AVG as the x-value and salary as the y-value.
Correlation coefficient:
Regression Equation: y=y=
Do you have significant correlation?
Prediction
Based on your analysis, if you had to predict a player's salary, which method would be the best?
Using that method, predict the salary for Jose Altuve. His stats were:
RBI: 74
HR: 31
AVG: 0.298
Based on your analysis, his predicted salary would be: $ million
His actual salary was $9.500 million.
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