Linear 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 “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. 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. salary.
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...
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