Unit 8: Term Project Report

Purpose Statement and Model

1) In the introductory paragraph, state why the dependent variable has been chosen for analysis. Then make a general statement about the model:

"The dependent variable _______ is determined by variables ________, ________, ________, and ________."

2) In the second paragraph, identify the primary independent variable and defend why it is important.

"The most important variable in this analysis is ________ because _________." In this paragraph, cite and discuss the two research sources that support the thesis, i.e., the model.

3) Write the general form of the regression model (less intercept and coefficients), with the variables named appropriately so reader can identify each variable at a glance:

Dep_Var = Ind_Var_1 + Ind_Var_2 + Ind_Var_3

For instance, a typical model would be written:

Price_of_Home = Square_Footage + Number_Bedrooms + Lot_Size

Where

Price_of_Home: brief definition of dependent variable

Square_Footage: brief definition of first independent variable

Number_Bedrooms: brief definition of second independent variable

Lot_Size: brief definition of third independent variable

[Note: student of course replaces these variable names with his/her own variable names.]

Definition of Variables

4) 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.

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?

Data Description

5) In one paragraph, describe the data and identify the data sources.

• From which general sources and from which specific tables are the data taken? (Citing a website is not acceptable.)
• Which year or years were the data collected?
• Are there any data limitations?

Presentation and Interpretation of Results

6) Write the regression (prediction) equation:

Dep_Var = Intercept + c1 * Ind_Var_1 + c2 * Ind_Var_2 + c3* Ind_Var_3

7) Identify and interpret the adjusted R2 (one paragraph):

• Define "adjusted R2."
• What does the value of the adjusted R2 reveal about the model?
• If the adjusted R2 is low, how has the choice of independent variables created this result?

8) Identify and interpret the F test (one paragraph):

• Using the p-value approach, is the null hypothesis for the F test rejected or not rejected? Why or why not?
• Interpret the implications of these findings for the model.

9) Identify and interpret the t tests for each of the coefficients (one separate paragraph for each variable, in numerical order):

• Are the signs of the coefficients as expected? If not, why not?
• For each of the coefficients, interpret the numerical value.
• Using the p-value approach, is the null hypothesis for the t test rejected or not rejected for each coefficient? Why or why not?
• Interpret the implications of these findings for the variable.
• Identify the variable with the greatest significance.

10) Analyze multicollinearity of the independent variables (one paragraph):

• Generate the correlation matrix.
• Define multicollinearity.
• Are any of the independent variables highly correlated with each other? If so, identify the variables and explain why they are correlated.
• State the implications of multicollinearity (if found) for the model.

11) Other (not required):

• If any additional techniques for improving results are employed, discuss these at the end of the paper.

Works Cited Page

12) Use the proper format to list the works cited under two headings:

Research: two sources

Data: a separate citation for each of the variables used in the paper.

Research Paper

MG315

May 10, 2020

Purpose Statement and Model

The dependent variable success of the player is determined by independent variables runs of player, strikeout rate of player, number of pitches, and number of matches played. The reason the dependent variable has been chosen for this analysis is because it is the most important variable in this assessment. The most important independent variable in this relationship is strikeout rate of player because strikeout rate provides the average performance of the player and it would be more significant variable.

Dependent Variable: Players Annual Pay ($M).

Independent Variables: Runs allowed (RA), strikeout rate (SO), number of pitches (P), and number of matches played (G).

($M) = RA + SO + P + G.

This variable value is dependent on another independent variable. If the value of independent variable is increased, then dependent variable also increases. In this example the price of players is depend on his performance how he played and overall averages. This variable is not dependent on another variable and it can affect the dependent variable. In this example, strikeout rate of the player, how many strikeouts he obtains, how many matches he played are the independent variables and this will either increase or decrease the player's price tag.

Definition of Variables / Data Description

Players Annual Pay (Y) refers to the "yearly statistics to try and account for the yearly salary of a given player for that season (Magel, R., & Hoffman, M.)". The models which considered yearly production statistics could be used to determine whether a player was underperforming in comparison to his salary for that year. This data is given by Major League Baseball (MLB) statistical department. Since it has zero significance in salary or pay, it is a measurement of ratio scale.

(x1) Runs allowed. Runs Allowed is the total of runs that are recorded against a pitcher. This consist of earned runs and unearned runs.

(x2) Strikeout rate. "Strikeout rate represents the frequency with which a pitcher strikes out hitters, as determined by total strikeouts divided by total batters faced. The K rate leaderboards are generally made up of the game's best pitchers. However, plenty of pitchers have succeeded with lower strikeout rates, generally because they are able to induce weak contact. (MLB Advanced Media, LP)".

(x3) Number of pitches. "A pitcher's total number of pitches is determined by all the pitches he throws in live game action, including strikes, unintentional balls and intentional balls (MLB Advanced Media, LP)".

(x4) Number of matches played. For every time a player has played even one second of a game, it counts as a matched played. Total number of matches played is added by all time stats.

Data has been provided by Overall Baseball Leaders & Baseball Records. Data on this website has been collected from 2000-2020. The only data limitation is the data that has not been documented before the year 2000.

Presentation and Interpretation of Results

Multiple linear regression (MLR) is a statistical test used to establish the best set of forecaster variables for a dependent variable.In baseball, we can use the same hypothesis and apply it to pitchers' value.We can use MLR to determine the best set of variables to determine a dependent variable. This will determine if the value of the player correlates with Runs allowed (RA), strikeout rate (SO), number of pitches (P), and number of matches played (G).

References:

Lind, D. A., Marchal, W. G., & Wathen, S. A. (2019). Basic statistics for business and economics. New York, NY: McGraw-Hill Education.

Magel, R., & Hoffman, M. (2015, May 2). Predicting Salaries of Major League Baseball Players. Retrieved April 4, 2020, from http://article.sapub.org/10.5923.j.sports.20150502.02.html

MLB Advanced Media, LP. (2020). What is a Strikeout Rate (K%)?: Glossary. Retrieved April 4, 2020, from http://m.mlb.com/glossary/advanced-stats/strikeout-rate

Sports Reference LLC. (2000). MLB & Baseball Leaders & Records. Retrieved April 4, 2020, from https://www.baseball-reference.com/leaders/

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