Question

Define and defend all variables, including the dependent variable, in a single paragraph for each variable. Also, state the expectations for each independent variable. These paragraphs should be in numerical order, i.e., dependent variable, X1, then X2, etc.

Dependent Variable: Players Annual Pay
Independent Variables: Batting average, Stolen bases, Home Runs, and RBIs.

In each paragraph, the following should be addressed:
How is the variable defined in the data source?
Which unit of measurement is used?
For the independent variables: why does the variable determine Y?
What sign is expected for the independent variable's coefficient, positive or negative? Why?

Answer 1

• Players Annual Pay (Y) refers to the “yearly statistics to try and account for the yearly salary of a given player for that season. The models which considered yearly production statistics could be used to determine whether or not a player was underperforming in comparison to his salary for that year.This data is given by Major League Baseball (MLB) department.Since 0 has significance in salary So it is a measurement of ratio scale.

• Batting average (X1) is “the average score of a batsman or batter, in cricket a batsman's runs scored per completed innings, and in baseball a batter's safe hits per official times at bat.” as defined by MLB data. Since Batting average is in terms of percentage it is a measurementof ratio scale. Also that players with higher OBP’s generally are paid more, and it is affecting the team budgets and whether or not the trend continues at the team level.
• Stolen bases(X2) “is credited to a baserunner when he successfully advances to the next base while the pitcher is throwing the ball to home plate.” as defined by MLB data. Since Stolen bases is in termsof per 100s it is a measurement of interval scale.This will look at how owners evaluate players and examine contract determination from the perspective of the teams.
• Home Runs(X3) “a hit that allows the batter to make a complete circuit of the bases and score a run.” as defined by MLB data. Since Home runs has a significant 0 it is a measurement of ratio scale. It has correlation with salary and Home run pay isn't always a good thing.
• RBIs(X4) “run batted in (RBI), is a statistic in baseball and softball that credits a batter for making a play that allows a run to be scored ” as defined by MLB data. Since RBIs is in termsof per 100s it is a measurement of interval scale. It has correlation with salary.