Statistics are widely used in Major League Baseball. Does a baseball player's batting average (AVG) determine their salary? The following is a chart of 25 baseball players' statistics from 2016. Let the explanatory variable x = AVG and the response variable y= Salary.
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.
Statistics are widely used in Major League Baseball. Does a baseball player's batting average (AVG) determine their salary? The following is a chart of 25 baseball players' statistics from 2016. Let the explanatory variable x = AVG and the response variable y= Salary.
| Player | RBI | HR | AVG | Salary (in millions) |
|---|---|---|---|---|
| Buster Posey | 80 | 14 | 0.288 | 20.802 |
| Mark Teixeira | 44 | 15 | 0.204 | 23.125 |
| Aaron Hill | 38 | 10 | 0.262 | 12.000 |
| Hunter Pence | 57 | 13 | 0.289 | 18.500 |
| Coco Crisp | 55 | 13 | 0.231 | 11.000 |
| Jacoby Ellsbury | 56 | 9 | 0.263 | 21.143 |
| Chris Davis | 84 | 38 | 0.221 | 21.119 |
| Jean Segura | 64 | 20 | 0.320 | 2.600 |
| Troy Tulowitzki | 79 | 24 | 0.256 | 20.000 |
| Justin Smoak | 34 | 14 | 0.217 | 3.900 |
| Leonys Martin | 47 | 15 | 0.245 | 4.150 |
| Hanley Ramirez | 111 | 30 | 0.286 | 22.750 |
| Adrian Beltre | 104 | 32 | 0.300 | 18.000 |
| Adrian Gonzalez | 90 | 18 | 0.285 | 21.857 |
| Adam Jones | 83 | 29 | 0.265 | 16.000 |
| Joe Mauer | 49 | 11 | 0.261 | 23.000 |
| Chris Iannetta | 24 | 7 | 0.210 | 4.550 |
| Curtis Granderson | 59 | 30 | 0.237 | 16.000 |
| Jason Heyward | 49 | 7 | 0.230 | 21.667 |
| Prince Fielder | 44 | 8 | 0.212 | 18.000 |
| Carlos Gonzalez | 100 | 25 | 0.298 | 17.454 |
| Jayson Werth | 70 | 21 | 0.244 | 21.571 |
| Matt Holliday | 62 | 20 | 0.246 | 17.000 |
| Joey Votto | 97 | 29 | 0.326 | 20.000 |
| Mike Trout | 100 | 29 | 0.315 | 16.083 |
Determine the
Find the slope, y-intercept, and equation of the least-squares line ˆy=a+bxy^=a+bx .
a = (Round to 4 decimal places.)
b = (Round to 4 decimal places.)
ˆy =
For a batter with a batting average of 0.254, determine the player's predicted Salary.
millions (Round to one decimal place.)
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