Statistics are widely used in Major League Baseball. Are the number of runs batted in (RBI) correlated to a hitter's batting average (AVG)? The following is a chart of 25 baseball players' statistics from 2016. Let the explanatory variable xx = RBI and the response variable y = AVG. Player RBI HR AVG Salary (in millions) Justin Turner 90 27 0.277 5.100 Chris Iannetta 24 7 0.210 4.550 Coco Crisp 55 13 0.231 11.000 Adam Jones 83 29 0.265 16.000 Adrian Gonzalez 90 18 0.285 21.857 Jason Heyward 49 7 0.230 21.667 Jayson Werth 70 21 0.244 21.571 Evan Gattis 72 32 0.251 3.300 Jorge Soler 31 12 0.238 3.667 Brian McCann 58 20 0.242 17.000 David Ortiz 127 38 0.315 16.000 Chris Davis 84 38 0.221 21.119 Matt Wieters 66 17 0.243 15.800 J.D. Martinez 68 22 0.307 6.750 Leonys Martin 47 15 0.245 4.150 Hunter Pence 57 13 0.289 18.500 Aaron Hill 38 10 0.262 12.000 Jean Segura 64 20 0.320 2.600 Shin-Soo Choo 17 7 0.242 20.000 Mike Trout 100 29 0.315 16.083 Ben Zobrist 76 18 0.272 10.500 Curtis Granderson 59 30 0.237 16.000 Joe Mauer 49 11 0.261 23.000 Ryan Braun 91 31 0.305 20.000 Jacoby Ellsbury 56 9 0.263 21.143 Determine the correlation coefficient. (Round your answer to 4 decimal places.) 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.) y^ = For a batter with 28 RBIs, determine the hitter's predicted batting average. (Round to 3 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.
Statistics are widely used in Major League Baseball. Are the number of runs batted in (RBI) correlated to a hitter's batting average (AVG)? The following is a chart of 25 baseball players' statistics from 2016. Let the explanatory variable xx = RBI and the response variable y = AVG.
| Player | RBI | HR | AVG | Salary (in millions) |
|---|---|---|---|---|
| Justin Turner | 90 | 27 | 0.277 | 5.100 |
| Chris Iannetta | 24 | 7 | 0.210 | 4.550 |
| Coco Crisp | 55 | 13 | 0.231 | 11.000 |
| Adam Jones | 83 | 29 | 0.265 | 16.000 |
| Adrian Gonzalez | 90 | 18 | 0.285 | 21.857 |
| Jason Heyward | 49 | 7 | 0.230 | 21.667 |
| Jayson Werth | 70 | 21 | 0.244 | 21.571 |
| Evan Gattis | 72 | 32 | 0.251 | 3.300 |
| Jorge Soler | 31 | 12 | 0.238 | 3.667 |
| Brian McCann | 58 | 20 | 0.242 | 17.000 |
| David Ortiz | 127 | 38 | 0.315 | 16.000 |
| Chris Davis | 84 | 38 | 0.221 | 21.119 |
| Matt Wieters | 66 | 17 | 0.243 | 15.800 |
| J.D. Martinez | 68 | 22 | 0.307 | 6.750 |
| Leonys Martin | 47 | 15 | 0.245 | 4.150 |
| Hunter Pence | 57 | 13 | 0.289 | 18.500 |
| Aaron Hill | 38 | 10 | 0.262 | 12.000 |
| Jean Segura | 64 | 20 | 0.320 | 2.600 |
| Shin-Soo Choo | 17 | 7 | 0.242 | 20.000 |
| Mike Trout | 100 | 29 | 0.315 | 16.083 |
| Ben Zobrist | 76 | 18 | 0.272 | 10.500 |
| Curtis Granderson | 59 | 30 | 0.237 | 16.000 |
| Joe Mauer | 49 | 11 | 0.261 | 23.000 |
| Ryan Braun | 91 | 31 | 0.305 | 20.000 |
| Jacoby Ellsbury | 56 | 9 | 0.263 | 21.143 |
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.)
y^ =
For a batter with 28 RBIs, determine the hitter's predicted batting average.
(Round to 3 decimal places.)
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