Business Statistics Essay

Technology has brought to the sport of golf a revolution in golf equipment. Clubs swing faster and the balls fly higher and further. The average driving distance of golf pros has gone from 260 yards in 1992 to 286 yards in 2003. However, with all of these improvements in distance, it is not all that clear whether players have improved their accuracy or whether their scores have gotten better. The Professional Golfers Association (PGA) has collected performance data on the 125 top-earning PGA Tour pros. The task of this analysis is to determine whether there exists any relationship between certain aspects of the game such as driving distance, accuracy and overall performance, among others. Description of the data is as follows: Money refers to the total earnings in PGA Tour events. Scoring Average is the average a golfer scores per round. DrDist refers to the average driving distance measured in yards per drive. This measurement is composed of two drives measured on different wholes with opposing wind directions and with no regard to accuracy. DrAccuracy is the percentage of times that a drive lands on the fairway. Every drive is measured with the exception of par 3’s. GIR, or Greens in Regulation refers to the percentage of times that the golfer was able to hit the green in regulation. Hitting the green in regulation consists of getting the ball to the green in par minus 2 strokes. This analysis will study whether there exits any relationship between: driving distance and scoring average; driving accuracy and scoring average; GIR and scoring average; driving accuracy and driving distance. This analysis will also determine which of these variables is most significant in terms of scoring average. Descriptive Statistics The data used in this report consists of information regarding the top 125 players in the PGA Tour based on earnings. The data includes the total amount earned in PGA Tour events, the average number of strokes per completed round, the average number of yards per measured drive, the percentage of time a tee shot comes to rest in the fairway, and the percentage of time a player was able to hit the green in regulation. Care was used in collection of the data to ensure a proper sample. For the average number of yards per measured drive (DrDist), the selection of two holes facing opposite directions to counteract the effect of the wind was used to limit outside factors. Also the point where the ball came to rest was measured regardless of whether or not it was on the fairway. Driving accuracy (DrAccu) was measured on every hole with the exception of par 3’s. For the percentage of time a player was able to hit the green in regulation (GIR), the stroke was determined by subtracting two from par. The data collected was then summarized both numerically and graphically to determine if any relationship exists improvements in technology and golfers performance. Appendix A depicts both graphically and numerically the summary of all data. The mean amount earned is $1791113 and the mean scoring average is 71. 03. For the data the mean distance is 288. Appendix B shows the relationship between scoring average and driving distance. The use of regression analysis shows an F of . 608 and a p-value of . 437. With a p-value ≠¥ .01 the null hypothesis is to be accepted. While accepting the hypothesis recognizes statistical significance, it is necessary to investigate further whether a relationship between scoring average and driving distance exists. Regression analysis was also used to find a relationship between scoring average and driving accuracy. Appendix C shows that an F of 5. 91 and a p-value of . 016. With a p-value ? .01 the null hypothesis is to be accepted in this case. The relationship between scoring average and greens in regulation was also investigated using regression analysis. The regression analysis showed an F of 39. 3 and a p-value of 5. 75. With the p-value ≠¥ .01, the null hypothesis should be accepted. The hypothesis shows statistical significance between scoring averages and greens in regulation. Appendix D shows the results of the relationship between scoring average and greens in regulation. Appendix F shows that with driving distance used as the independent variable and driving accuracy as the dependent variable the resulting p-value is 1. 72. The null hypothesis should be accepted in this case with the p-value ≠¥ .01. The data shows that with a p-value of . 16 the driving accuracy appears to be the least significant factor in terms of average score. With a p-value of 5. 75 greens in regulation appears to be the most significant factor in terms of average score. Interpretation of Statistics PGA golfers have increased their driving distance due to new advanced technology of golf balls and golf clubs. In the past, the average driving distance has ranged from 260-286 yards. The goal of this study is to see the relationship between driving distance and player performance in terms of their accuracy with long range shots. This information is taken from the 008 PGA Tour and covers 125 players. The study’s null hypothesis deals with the link between variables of interest, driving distance, driving accuracy and greens in regulation, and states that increased driving distance has no effect on players’ accuracy and performance. The alternative hypothesis has a relationship between the golfers’ accuracy and driving distance. Our team used a scatter diagram to show the relationship between the two variables. We used a straight line model which has a linear regression. Our two variables on our scatter plot are scoring average and driving distance. There is no functional relation between the variables because there cannot be a straight line that passes through every point, however there is a statistical relation because all the points on the plot are scattered randomly around the line. We are using a simple linear regression model due to the one independent variable. Response is another name for the dependent variable, y. The slope is rise over run or the change in x to y. In Appendix F, the ANOVA shows the scoring average and driving distance. The coefficient gives us the information for the simple regression model. The constant is 70. 4 and gives us the y intercept and the slope coefficient is 0. 00342356. The null proves that there is not a relationship between the players’ average and performance. According to the 95% confidence interval demonstrates that the intercept is within the range of 67. 53551 and 73. 35093 and the slope coefficient is within the range of -0. 00527 and . 014914. The summary in the Appendix re gression gives us data about the analysis. Column one tells us that there is only a single independent variable. The following column states the relationship between the observed dependent variable and the predicted dependent variable. The simple Pearson’s correlation is the same thing as the one independent variable and has a correlation between the two variables. The coefficient of determination tells us proportions and how they can be credited to the x variable. The variation in scoring average is 0. 005% and is caused by the variation in driving distance. Lastly, the standard error of estimate tells us that it is not the same as our original prediction and is off by a score of 0. 42. The Appendix gives us the analysis of variance related to regression analysis. The mean square is represented by the degrees of freedom and the residual degrees of regression. The F-statistic shows a ratio of explained variance to not explained variance. If the regression sum of square is zero then that would mean the independent variable is not associated with the dependent variable’s variation. The larger the sum of squares the more the variation can be viewed by looking at the dependent variable. The F value is . 60774 with a p value of 0. 43714. Therefore, we can accept the null hypothesis because there is no relationship between the scoring average and driving distance. This is exemplified in Appendix E(1), where total driving distance was divided by total score. The higher the %, the lower the score. In this case, there is no trend in the chart because there is no correlation to driving distance and scores. Appendix E(2) shows the relationship between driving accuracy and scores, with the same inverse relationship. The higher the driving accuracy percentage, the lower the score. The graph shows a slight downward trend, meaning there is a slight correlation between accurate drives and better scores. Appendix E(3) shows that, by the same standard as E(1) and (2), there is a more noticeable downward trend. This goes to show that a green in regulation (GIR), although not always, will generally mean lower scores. Accuracy is more important than driving distance. Formulation of Analysis We now can determine if there is a relationship with players’ scoring average and driving distance, because of the statistical information associated with the PGA players. The biggest factor used to prove this relationship is the regression analysis. This lets us look at two variables and figure out if they are linked. The scoring average is the independent variable and the other three are the dependent variables. We used an excel spreadsheet to examine our values. Applying these numbers we are able to find the relationship between our variables. The observed variables are smaller and have a positive relationship between them. We used a 99% confidence level to show the link in scoring average and our variables. Players who have a higher than 99% level tend to drive the ball farther and typically have lower scores. Those players have an intercept of 73. 3509, compared to those that are lower than 99% who have an intercept of 66. 2953. Next, the only positive relationship we can see between the variables is the fact that players that are more accurate tend to have lower scores. Therefore we can reach the conclusion that accuracy improves scores. Conclusion and Recommendations The data shows that a correlation exists between scoring average, driving distance, and hitting greens in regulation. The regr ession analysis showed a p-value of . 02 showing that while a relationship exists between accuracy and scoring average it is relatively small. The relationship between driving distance and accuracy are dependent. With a p-value of 1. 72 the analysis shows that the more accurate the player is the further they are able to drive the ball. By making driving accuracy the dependent variable and driving distance the independent variable, the analysis showed that accuracy is dependent on the driving distance. The data for the analysis was collected for players on the PGA Tour for 2008. The data does not contain historical information on previous years. Without looking at data from previous years it cannot be determined if improvements in technology have resulted in the improvements for players. The data does show that it is important for the player to be able to drive the ball further in order to be more accurate. It also shows that player’s scores are improved with accuracy. With technology that produces clubs that are able to drive further the result is more accurate shots and therefore, better scores. By continuing to make improvement with clubs that are lighter and allow the players to swing harder and faster, players will continue to become more accurate in their shots. The more accurate the shots the better the scores of the players.