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Quantile Regression - PowerPoint PPT Presentation

Quantile Regression . By: Ashley Nissenbaum. About the Author . Leo H. Kahane Associate Professor at Providence College Research Sport economics, international trade, political science Editor of Journal of Sports Economics. Previous Research . Golf earnings are highly positively skewed

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QuantileRegression

By: Ashley Nissenbaum

• Leo H. Kahane

• Associate Professor at Providence College

• Research

• Sport economics, international trade, political science

• Editor of Journal of Sports Economics

• Golf earnings are highly positively skewed

• Schmanske (1992)

• Value of the marginal product from putting may be in the range of \$500 per hour of practice.

• Alexander and Kern (2005)

• “Drive for show, putt for dough”

• Callan and Thomas (2007)

• Skills determine score, which determines rank and thus earnings

Earnings and Skewness

• Linear Regression

• Focuses on the behavior of the conditional mean of the dependent variable

• Most people make under \$300K per event

Reasons for Skewness

Payout Structure

• Non-linear

• Top 50% after the first two rounds: 1st place receives 18%, 2nd place receives 10.8%, 3rd place receives 6.8%, 4th place – 4.8%, etc

• Extraordinary Talented Golfers

• Tournament wins are spread across a large number of golfers

• Won 185 tournaments

• 14 professional major tournaments, 71 PGA Tour events

• \$500 Million net worth

• Highest paid athlete from 2001 to 2012

• \$132 million from tournaments

Concept of Quantile Regression

• Equation for Quantile Regression:

• Where:

• y(i)= real earnings per PGA event

• Q= Specific quantile associated with the equation

• Β = Vector of coefficients to be estimated

• Ε = Error term

• X(i)= Covariates

• x(i) = covariates expected to explain golf earnings

• Greens in regulation

• The percent of time a player was able to hit the green in regulation (greens hit in regulation / holes played x 100). Positive correlation expected.

• Putting average

• Average number of putts needed to finish a hole per green hit in regulation. Negative correlation expected.

• Save percentage

• Percentage of time a golfer was able to get the ball in the hole in two shots or less following landing in a greenside sand bunker (regardless of score). Positive correlation expected.

• Yards per drive

• Average number of yards per measured drive. Positive correlation expected.

• Driving accuracy

• Percentage of time a tee shot comes to rest in the fairway. Positive correlation expected.

• Simple level OLS (Ordinary Least Squares) regression estimate:

OLS and Quantile Regression Results