NASCAR driver Matt Kenseth won the 2012 Daytona 500. His win was no surprise bec

Question

NASCAR driver Matt Kenseth won the 2012 Daytona 500. His win was no surprise because for the 2011 season he finished fourth in the point standings with 2330 points. In 2011, he earned $6.184 million dollars 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, on down to 1 point for the driver who finished last. 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. The accompanying spreadsheet contains the 2011 data for the top 35 NASCAR drivers. The variables include the drivers points for the season (POINTS), the number of poles won (POLES), the number of races won (WINS), the number of top 5 finishes (TOP5), and the number of top 10 finishes (TOP10), along with each drivers winnings (in millions of $).

1. Suppose that a driver has 22 top 10 finishes, 13 top 5 finishes, 3 wins, and no poles with a total of 2345 points for the season. How much should he expect to win?

Driver Points Poles Wins Top5 Top10 Winnings (s) 1 Tony Stewart 2403 1 51 9 19 6.53 2403 3 1 19 26 8.49 2 Carl Edwards 3 Kevin Harvick 2345 4 9 19 62 2330 3 3 12 20 6.18 4 Matt Kenseth Brad Keselowski 2319 1 3 10 14 5.09 5 6 Jimmie Johnson 2304 0 2 14 21 63 7 Dale Earnhardt Jr. 2290 1 0 4 12 4.16 8 Jeff Gordon 2287 1 3 13 18 5.91 9 Denny Hamlin 2284 0 1 5 14 54 0 Ryan Newman 2284 3 1 9 17 5.3 11 Kurt Busch 2262 3 2 8 16 5.94 12 Kyle Busch 2246 1 4 14 18 6.16 13 Clint Bowyer 1047 0 1 4 16 5.63 4 Kasey Kahne 1041 2 1 8 15 4.78 15 AJ. Allmendinger 101 0 0 1 10 4.83 Greg Biffle 997 3 0 31 10 4.32 6 947 0 1 4 8 3.85 17 Paul Menard 18 Martin Truex Jr. 0 1 5 12 4.75 19 Marcos Ambrose 936 20 Jeff Burton 935 0 0 2 5 3.81 932 2 0 2 8 5.02 21 Juan Montoya 930 2 0 2 10 3.83 22 Mark Martin 906 2 1 4 8 42 23 David Ragan 902 2 0 4 6 3.86 24 Joey Logano 846 0 0 31 7 4.3 25 Brian Vickers 820 0 1 2 5 4.58 26 Regan Smith 795 1 0 2 4 4.79 27 Jamie McMurray 28 David Reutimann 757 1 0 1 3 4.37 670 0 0 1 2 4.51 29 Bobby Labonte 572 0 0 1 2 3.88 30 David Gilliland 31 Casey Mears 32 Dave Blaney 508 0 0 1 1 3.3 398 0 0 0 0 2.89 33 Andy Lally 34 Robby Gordon J J. Yeley 192 0 0 0 2.56 35

Explanation / Answer

Solution

To predict expected win for driver with given values for all variables, we will use multiple regression equation.

The multiple regression output obtained using Excel is given below.

SUMMARY OUTPUT

Regression Statistics

Multiple R

0.9064

R Square

0.8215

Adjusted R Square

0.7907

Standard Error

0.5892

Observations

35

ANOVA

df

SS

MS

F

Significance F

Regression

5

46.3318

9.2664

26.6897

0.0000

Residual

29

10.0685

0.3472

Total

34

56.4003

Coefficients

Standard Error

t Stat

P-value

Lower 95%

Upper 95%

Intercept

3.1097

0.2267

13.7143

0.0000

2.6459

3.5734

Points

0.0001

0.0003

0.2533

0.8018

-0.0006

0.0007

Poles

-0.0156

0.1089

-0.1435

0.8869

-0.2384

0.2071

Wins

0.0012

0.1207

0.0096

0.9924

-0.2457

0.2480

Top5

0.0698

0.0519

1.3445

0.1892

-0.0364

0.1759

Top10

0.1125

0.0386

2.9150

0.0068

0.0336

0.1915

Here regression analysis shows that the regression model is significant in prediction each drivers winnings (p < .05). Hence we can use regression equation to predict estimated winnings.

Regression equation is,

Winnings = 3.1097 + (0.0001 * Points) – (0.0156 * Poles) + (0.0012 * Wins) + (0.0698 * Top5) + (0.1125 * Top10)

Winnings = 3.1097 + (0.0001 * 2345) – (0.0156 * 0) + (0.0012 * 3) + (0.0698 * 13) + (0.1125 * 22)

Winnings = 6.6815

Hence the driver with 22 top 10 finishes, 13 top 5 finishes, 3 wins, and no poles with a total of 2345 points for the season is expected to win 6.68 million $.

Regression Statistics

Multiple R

0.9064

R Square

0.8215

Adjusted R Square

0.7907

Standard Error

0.5892

Observations

35

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