Good Example Of Race Results For 1975-2003 Report

Business Statistics: NASCAR Winston Cup

1. The data set obtained was gathered by Larry Winner for the Journal of Statistics Education. He observed that incorporating sports data into introductory lessons on statistics. The information on NASCAR Winston Cup contained data such as: (a) year of the race, (b) number of cars in the race, (c) total race payout, (d) monthly consumer price index for urban consumers, (e) Spearman’s rho, (f) Kendall’s tau, (g) track length, (h) laps completed by winner, (i) winning time, (j) track name, etc. The year when the race happened is given including the number if cars that participated in the race. The total amount paid to the winners and race participants is also given. For the research not to be biased by inflation, the consumer price index for that particular month was also stated. The Spearman’s rho is a nonparametric measure of statistical dependence between two variables. On the other hand, Kendall’s tau is also a statistics that also measure association between two variables using the tau test for hypothesis testing. Furthermore, the track length and the number of laps completed by the winners were also compiled, including the winning time, and the name of the track where the race was held.
2. Shown in Table 1 are the two research questions that this paper attempts to answer by statistical analysis of the data. In the second and third columns, the descriptive statistics and the variables to be used (in computing the statistics) are stated respectively.
Listed are the three peer-reviewed articles from journals, and two popular sources consulted by the author in explaining the results of the paper.

Peer-reviewed Sources:

1) Abere, A., Bronsteen, P., & Elzinga, K. G. (2012). The economics of NASCAR. The Oxford Handbook of Sports Economics Volume 1: The Economics of Sports, 1, 318.
2) Pruitt, S.W., Cornwell, T.B. & Clark, J.M. (2004). The NASCAR Phenomenon: Auto Racing Sponsorships and Shareholder Wealth. Journal of Advertising Research, 44, pp 281-296. doi:10.1017/S0021849904040279.
3) Winner, L. (2006). NASCAR Winston Cup Race Results for 1975-2003. Journal of Statistics Education, 14(1).

Popular Sources:

1) McCormick, S. (2015). What is NASCAR? Retrieved April 2, 2015 from http://nascar.about.com/od/nascar101/f/whatisnascar.htm
2) Pope, A. T., & Tollison, R. D. (2010). “Rubbin’is racin''': evidence of the Peltzman effect from NASCAR. Public Choice, 142(3-4), 507-513.

Introduction

Brief History of Car Racing
NASCAR Winston Cup
Funding the Race and Race Payout for the Winners
What is the average speed of the winning cars in NASCAR Winston Cup?
Does consumer price index for urban consumers directly affect the total race payout?
Conclusion
The average speed of the NASCAR Winston Cup is ________________.
The consumer price index directly affects the total race payout.
The Final Project
Racing has always fascinated humans whether it is by running, swimming, horse-back riding, or car racing. The latter is much more sophisticated nowadays due to the technological advances in engine design and overall car performance testing. In 1948, Bill France Sr. founded the National Association for Stock Car Auto Racing (more popularly known as NASCAR). It has been originally divided into three categories: modified, roadsters, and strictly stock (McCormick, 2015). The appeal to the fans is more on the story behind the race. There are unique characters, connections and, rivalries, involved. Furthermore, fans enjoy the full five-sense experience of watching a car race. Although, accidents do happen frequently during these type of races (Pope and Tollison, 2010).
This paper attempts to gather historical data from NASCAR Winston Cup (from 1975 to 2003) and examine them to answer two research questions. First is “What is the average speed of the winning cars in NASCAR Winston Cup?” Finding that number and comparing it to the normal car speeds at present evaluates how fast is fast in NASCAR standards. The second question pertains to the total race payout as NASCAR fans are keen how much money is involved. The prize could have been affected by the inflation rates from that time period. The second research question is: ”Does consumer price index (for urban consumers) directly affect the total race payout?”
For the first research question: “What is the average speed of the winning cars in NASCAR Winston Cup?”, the appropriate descriptive statistic to be used is the mean or the average. Although the researcher is tempted to use the median due to the variability in data, it was noted that there are 898 races corresponding to 898 data points as well. To compute for the speed, the track length (in miles) is multiplied by the number of laps to get the total distance covered by the car. The distance is then divided by the winning time (in minutes). The resulting speed is multiplied by 1.61 and 60 to convert it from miles per minute to kilometers per hour. The latter, being the more common unit used in car speed. The average or the mean is obtained by dividing the sum of the speeds of the winning cars divided by the number of races (898 all in all). The computed mean is 191.1 km/ hour. In normal highways, this speed is already over-speeding and is equivalent to a penalty due to traffic violation. The population standard deviation is 43.8. This value tells that there is inherent variability in the data set. This corresponds to a coefficient of variation of 22.9%.
The second research question involves consumer price index (CPI-U) and total race payout. Does consumer price index for urban consumers directly affect the total race payout? This is done by simple linear regression with CPI-U as the independent variable x and total race payout as the dependent variable y. The scatter plot and least squares line is obtained using MS Excel (See Figure 1). However, the r2 (coefficient of determination) is on 0.5455. This tells that only 54.55% of the variability in the data is captured by the model. The resulting least squares line is y = 23229 x -.000002.
Figure 1: Scatter Plot of Consumer Price Index versus Total Race Payout
Checking for other models with higher coefficient of determination (r2) values, exponential, logarithmic, power, and polynomial functions were superimposed on the model. Among these, the exponential model yields the highest r2 value at 0.8779 with the model y = 14955exp(0.0284x). The curve is shown in Figure 2. This model is better since 87.79% of the variability is captured by the model. This irregularity might be attributed to dynamics within individual race as affected by advertising and sponsorship (Pruitt, et. al. 2004). There are specifics details that affect total race payout aside from increase in prices of consumer goods (Abere, et. al. 2012). However, generally, as price of commodities increase, total race payout increase even though there is an indirect relationship.
Figure 2: Exponential Model on the Scatter Plot
Thus, the research has responded to the two research questions. The average speed of the NASCAR Winston Cup is 191.1 km/ hour which is above the normal speed limit in highways in the United States. The consumer price index also affects the total race payout though indirectly. Using the data set of consumer price indexes, the model with the highest r2 value at 0.8779 is the exponential model: y= 14955 exp(0.0284x). This suggests an indirect relationship which can be attributed to the economics and marketing dynamics of each race.

References:

Abere, A., Bronsteen, P., & Elzinga, K. G. (2012). The economics of NASCAR. The Oxford Handbook of Sports Economics Volume 1: The Economics of Sports, 1, 318.
McCormick, S. (2015). What is NASCAR? Retrieved April 2, 2015 from http://nascar.about.com/od/nascar101/f/whatisnascar.htm
Pope, A. T., & Tollison, R. D. (2010). “Rubbin’is racin''': evidence of the Peltzman effect from NASCAR. Public Choice, 142(3-4), 507-513.
Pruitt, S.W., Cornwell, T.B. & Clark, J.M. (2004). The NASCAR Phenomenon: Auto Racing Sponsorships and Shareholder Wealth. Journal of Advertising Research, 44, pp 281-296. doi:10.1017/S0021849904040279.
Winner, L. (2006). NASCAR Winston Cup Race Results for 1975-2003. Journal of Statistics Education, 14(1).