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. The following table shows data for the 2011 season for the top 35 drivers (NASCAR website). These data are contained in the file NASCAR. Please see the data file NASCAR.

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 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 finishes (Top 10). Test for individual significance and discuss your findings and conclusions.

Create two new independent variables: Top 2–5 and Top 6–10. Top 2–5 represents the number of times the driver finished between second and fifth place and Top 6–10 represents the number of times the driver finished between sixth and tenth place. Develop an estimated regression equation that can be used to predict Winnings ($) using Poles, Wins, Top 2–5, and Top 6–10. Test for individual significance and discuss your findings and conclusions.

Based upon the results of your analysis, what estimated regression equation would you recommend using to predict Winnings ($)? Provide an interpretation of the estimated regression coefficients for this equation.

Transcribed Image Text:A B D F G H Driver Points Poles Top 10 Winnings (S) 6,529,870 8,485,990 6,197,140 Wins Тop 5 Tony Stewart Carl Edwards Kevin Harvick 2403 1 5 9. 19 2403 3 1 19 26 2345 4 9. 19 Matt Kenseth 2330 3 3 12 20 6,183,580 5,087,740 6,296,360 4,163,690 Brad Keselowski 2319 1 3 10 14 Jimmie Johnson 2304 2 14 21 Dale Earnhardt Jr. 2290 1 12 Jeff Gordon O Denny Hamlin Ryan Newman 2 Kurt Busch s Kyle Busch - Clint Bowyer 5 Kasey Kahne 5A.J. Allmendinger Greg Biffle B Paul Menard e Martin Truex Jr. O Marcos Ambrose 1 Jeff Burton e Juan Montoya 5 Mark Martin David Ragan 5 Joey Logano 5 Brian Vickers 7 Regan Smith 3 Jamie McMurray e David Reutimann O Bobby Labonte 2287 1 3 13 18 5,912,830 5,401,190 5,303,020 5,936,470 2284 1 5 14 2284 3 1 9. 17 2262 3 2 8 16 2246 1 4 14 18 6,161,020 1047 1 16 5,633,950 1041 1 8 15 4,775,160 1013 1 10 4,825,560 997 3 3 10 4,318,050 947 1 8. 3,853,690 937 1 3 12 3,955,560 936 1 5 12 4,750,390 935 2 5 3,807,780 932 2 2 8 5,020,780 930 2 2 10 3,830,910 906 2 1 8 4,203,660 902 2 4 6. 3,856,010 846 3 4,301,880 820 1 2 5 4,579,860 795 1 2 4 4,794,770 757 1 1 3 4,374,770 4,505,650 3,878,390 670 1 2 David Gilliland 572 1 2 e Casey Mears s Dave Blaney - Andy Lally* 5 Robby Gordon 5 J.J. Yeley 2,838,320 3,229,210 541 508 1 1 398 2,868,220 268 2,271,890 192 2,559,500

Question

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. The following table shows data for the 2011 season for the top 35 drivers (NASCAR website). These data are contained in the file NASCAR. Please see the data file NASCAR.

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 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 finishes (Top 10). Test for individual significance and discuss your findings and conclusions.

Create two new independent variables: Top 2–5 and Top 6–10. Top 2–5 represents the number of times the driver finished between second and fifth place and Top 6–10 represents the number of times the driver finished between sixth and tenth place. Develop an estimated regression equation that can be used to predict Winnings ($) using Poles, Wins, Top 2–5, and Top 6–10. Test for individual significance and discuss your findings and conclusions.

Based upon the results of your analysis, what estimated regression equation would you recommend using to predict Winnings ($)? Provide an interpretation of the estimated regression coefficients for this equation.

A
B
D
F
G
H
Driver
Points
Poles
Top 10
Winnings (S)
6,529,870
8,485,990
6,197,140
Wins
Тop 5
Tony Stewart
Carl Edwards
Kevin Harvick
2403
1
5
9.
19
2403
3
1
19
26
2345
4
9.
19
Matt Kenseth
2330
3
3
12
20
6,183,580
5,087,740
6,296,360
4,163,690
Brad Keselowski
2319
1
3
10
14
Jimmie Johnson
2304
2
14
21
Dale Earnhardt Jr.
2290
1
12
Jeff Gordon
O Denny Hamlin
Ryan Newman
2 Kurt Busch
s Kyle Busch
- Clint Bowyer
5 Kasey Kahne
5A.J. Allmendinger
Greg Biffle
B Paul Menard
e Martin Truex Jr.
O Marcos Ambrose
1 Jeff Burton
e Juan Montoya
5 Mark Martin
David Ragan
5 Joey Logano
5 Brian Vickers
7 Regan Smith
3 Jamie McMurray
e David Reutimann
O Bobby Labonte
2287
1
3
13
18
5,912,830
5,401,190
5,303,020
5,936,470
2284
1
5
14
2284
3
1
9.
17
2262
3
2
8
16
2246
1
4
14
18
6,161,020
1047
1
16
5,633,950
1041
1
8
15
4,775,160
1013
1
10
4,825,560
997
3
3
10
4,318,050
947
1
8.
3,853,690
937
1
3
12
3,955,560
936
1
5
12
4,750,390
935
2
5
3,807,780
932
2
2
8
5,020,780
930
2
2
10
3,830,910
906
2
1
8
4,203,660
902
2
4
6.
3,856,010
846
3
4,301,880
820
1
2
5
4,579,860
795
1
2
4
4,794,770
757
1
1
3
4,374,770
4,505,650
3,878,390
670
1
2
David Gilliland
572
1
2
e Casey Mears
s Dave Blaney
- Andy Lally*
5 Robby Gordon
5 J.J. Yeley
2,838,320
3,229,210
541
508
1
1
398
2,868,220
268
2,271,890
192
2,559,500

Accepted Answer

*answer: