Matt Kenseth won the 2012 Daytona 500, the most important race of the NASCAR season. His win was no surprise because for the 2011 season he finished fourth in the point standings with 2330 points, behind Tony Stewart (2403 points), Carl Edwards (2403 points), and Kevin Harvick (2345 points). In 2011 he earned $6,183,580 by winning three Poles (fastest driver in qualifying), winning three races, finishing in the top five 12 times, and finishing in the top ten 20 times. NASCAR’s point system in 2011 allocated 43 points to the driver who finished first, 42 points to the driver who finished second, and so on down to 1 point for the driver who finished in the 43rd position. In addition any driver who led a lap received 1 bonus point, the driver who led the most laps received an additional bonus point, and the race winner was awarded 3 bonus points. But the maximum number of points a driver could earn in any race was 48. Table 15.8 shows data for the 2011 season for the top 35 drivers (NASCAR website).
Step 2: Do
In a managerial report,
- Suppose you wanted to predict Winnings ($) using only the number of poles won (Poles), the number of wins (Wins), the number of top five finishes (Top 5), or the number of top ten finishes (Top 10). Which of these four variables provides the best single predictor of winnings?
- Develop an estimated regression equation (look at Equation 15.6 in our textbook as an example) that can be used to predict Winnings ($) given the number of poles won (Poles), the number of wins (Wins), the number of top five finishes (Top 5), and the number of top ten (Top 10) finishes. Test for individual significance, and then discuss your findings and conclusions.
Step 3: Discuss:
- What did you find in your analysis of the data? Were there any surprising results? What recommendations would you make based on your findings? Include details from your managerial report to support your recommendations.
Guided Response: Review several of your peer’s posts. In a minimum of 100 words each, respond to at least two of your fellow students’ posts in a substantive manner, and provide information that they may have missed or may not have considered regarding the application of Multiple Regression in business and economics. Do you agree with their conclusions? Why or why not?
Post by classmate 1
- Suppose you wanted to predict Winnings ($) using only the number of poles won (Poles), the number of wins (Wins), the number of top five finishes (Top 5), or the number of top ten finishes (Top 10). Which of these four variables provides the best single predictor of winnings?
Poles equals 0.406087
Wins equals 0.661562
Top 5 equals 0.861168
Top 10 equals 0.897756
The variable with the most highly correlation with winning dollars is the number of top 10 finishes, which is 0.897756
- Develop an estimated regression equation (look at Equation 15.6 in our textbook as an example) that can be used to predict Winnings ($) given the number of poles won (Poles), the number of wins (Wins), the number of top five finishes (Top 5), and the number of top ten (Top 10) finishes. Test for individual significance, and then discuss your findings and conclusions.
Looking at the P values comparing them with the T values, the only significant variable is top 10 which is .00147 compared to the t value of 3.50166
t Stat
P-value
Poles
-0.12069
0.904739
Wins
0.121777
0.903888
Top 5
1.413732
0.167734
Top 10
3.50166
0.00147
Adding poles, wins, and the top 5 variables added little to the model’s explanation of the variation of winnings. More data needs to be captured to understand the variation.
Post by classmate 2
Attached is the Regression for the Data File NASCAR. The data reflects that the number of top 10 finishes serves as the best predictor of winnings. A correlation coefficient near zero indicates no correlation; the sample data shows that the variable most highly correlated with winnings is the number of top ten finishes per the given coefficient (University of Arizona Global Campus, 2020).
The top ten finishes would be the best to utilize to predict winnings. The top ten finishes reflect a coefficient value of 117070.57, significantly higher than the other variables.
The regression equation is as follows: Y refers to the winnings predicted, X1 refers to the number of poles won, X2 refers to the number of wins, X3 refers to the number of top five finishes, and X4 refers to the number of top ten finishes; Y = 3140367.087, −12938.9208 (X1) + 13544.81269 (X2) + 71629.39328 (X3) + 117070.5768 (X4) (Anderson et al., 2021; University of Arizona Global Campus, 2020). The associated p-values are as follows: poles 0.9047, wins 0.9039, top five 0.1677, and top ten 0.0014. The p-values of poles, wins, and top five finishes all reflect greater than 0.05, thus supporting that these variables are not statistically significant. However, the top ten finishes’ p-value is less than 0.05, supporting that this variable’s value is statistically significant.
In my analysis of the data, I found it interesting that the model used had an R squared of 0.8205, whereas the model that included only the top ten as an independent variable had an R squared of 0.8060 (University of Arizona Global Campus, 2020). I noticed in the data the Multiplier R is reflected as 0.9058, which is the square root of R2, but of greater significance is the R squared number (Cameron, n.d.). Based on my review of the data, I would suggest further data be reviewed, including the points system and how these are allotted. To be honest, I have no idea how points are earned in NASCAR, but I would be interested to see if the points system itself affects the overall data and predictions of winnings.
References
Anderson, D. R., Sweeney, D. J., Williams, T. A., Camm, J. D., Cochran, J. J., Fry, M. J., & Ohlmann. J. W. (2021). Essentials of modern business statistics with Microsoft® Excel® (8th ed.). Cengage Learning
Cameron, A. (n.d.). Excel Multiple Regression. http://cameron.econ.ucdavis.edu/excel/ex61multipleregression.html (Links to an external site.)
University of Arizona Global Campus. (2020, September 11). Week 5 introduction. (Links to an external site.) [Video]. Kaltura. https://ashford.mediaspace.kaltura.com/media/BUS308+%7C+Week+5+Introduction/1_4c9qlzbm
