Linear Modeling Project free essay sample

Modeling Project The purpose of this experiment is to determine whether a player’s statistics in baseball are related to the player’s salary. The sample set was taken out of 30 players who were randomly selected from the top 100 fantasy baseball players in 2007. We displayed the information with a scatter plot, and then determined with a linear equation the line of best fit. Along with the line of best fit we are going to analyze the Pearson Correlation Coefficient. This value is represented as an â€Å"r-value†. The closer this number is to 1 the better the relationship between the two variables being compared. The three statistics that we compared to the player’s salaries are; Homeruns, RBI, (runs batted in), and batting Average. The line of best fit for a players home runs to salary using linear regression is . 0453029808x+6. 586733375. The Pearson Correlation Coefficient, (r-value) is . 0811721504. Based on how the graph looks and the distance of the r-value to 1, it is pretty safe to say that there is not a good relationship between the number of homeruns a player hits and their salary. We will write a custom essay sample on Linear Modeling Project or any similar topic specifically for you Do Not WasteYour Time HIRE WRITER Only 13.90 / page This means that a person’s salary is not based on the number of homeruns that they hit. Next we’ll discuss the relationship between RBI’s and salary. The line of best fit for a players RBI to salary is . 0299088213x+5. 00741382. The r-value is . 1429247937. While this line of best fit is slightly better than homeruns vs. salary based on the r-value it is still not enough to be considered a good relationship between the two. The lack of relationship between RBI and salary means that a player’s salary is not based upon the number of runs batted in. The last stat we’ll discuss is batting average vs. alary. The line of best fit for batting average to salary is 93. 29024715x-19. 57391786. The r-value for this line is . 4644363458. Based on this r-value we are 99% confident in our line of best fit. Looking at the scatter plot and the line of best fit it is not nearly as random and all over as the other two comparisons had been. The relationship between a players batting average to salary simply means that a player will most likely receive a higher salary if they have a higher batting average. Out of the three comparisons we tested only one, batting average vs. alary, can be used for making predictions of a player’s salary. Chipper Jones’s salary for 2008 was $12,333,333 and his batting average was . 364. When this information is plugged into the equation we came up with it shows his salary should be around $14. 4 million. This is pretty close to his actual salary, (when it comes to being a multi-millionaire what’s another couple million? ). Alfonso Soriano’s salary for 2008 was $14 million and he had a batting average of . 280. When the data was entered into the equation it determined that his salary should be around $6. 6 million. He should be a happy man because he is making double, (according to the equation) what he should be. I think the predictions are semi-accurate. There will always be exceptions to the information. From this project I learned that yes you can use math like this in everyday situations. I learned that some baseball players make way too much money! I’ve learned that a baseball player’s salary isn’t necessarily dependent on his homeruns, or RBI’s but is more reliant on his batting average. Also this project helped to cement this information in my head so that I should definitely not miss this question on the test!