3. 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 ($) using Poles, Wins, Top 2–5, and Top 6–10. Test for individual significance and discuss your findings and conclusions. Driver Points Poles Wins Top 5 Top 10 Winnings ($) Tony Stewart 2403 1 5 9 19 6,529,870 Carl Edwards 2403 3 1 19 26 8,485,990 Kevin Harvick 2345 0 4 9 19 6,197,140 Matt Kenseth 2330 3 3 12 20 6,183,580 Brad Keselowski 2319 1 3 10 14 5,087,740 Jimmie Johnson 2304 0 2 14 21 6,296,360 Dale Earnhardt Jr. 2290 1 0 4 12 4,163,690 Jeff Gordon 2287 1 3 13 18 5,912,830 Denny Hamlin 2284 0 1 5 14 5,401,190 Ryan Newman 2284 3 1 9 17 5,303,020 Kurt Busch 2262 3 2 8 16 5,936,470 Kyle Busch 2246 1 4 14 18 6,161,020 Clint Bowyer 1047 0 1 4 16 5,633,950 Kasey Kahne 1041 2 1 8 15 4,775,160 A.J. Allmendinger 1013 0 0 1 10 4,825,560 Greg Biffle 997 3 0 3 10 4,318,050 Paul Menard 947 0 1 4 8 3,853,690 Martin Truex Jr. 937 1 0 3 12 3,955,560 Marcos Ambrose 936 0 1 5 12 4,750,390 Jeff Burton 935 0 0 2 5 3,807,780 Juan Montoya 932 2 0 2 8 5,020,780 Mark Martin 930 2 0 2 10 3,830,910 David Ragan 906 2 1 4 8 4,203,660 Joey Logano 902 2 0 4 6 3,856,010 Brian Vickers 846 0 0 3 7 4,301,880 Regan Smith 820 0 1 2 5 4,579,860 Jamie McMurray 795 1 0 2 4 4,794,770 David Reutimann 757 1 0 1 3 4,374,770 Bobby Labonte 670 0 0 1 2 4,505,650 David Gilliland 572 0 0 1 2 3,878,390 Casey Mears 541 0 0 0 0 2,838,320 Dave Blaney 508 0 0 1 1 3,229,210 Andy Lally* 398 0 0 0 0 2,868,220 Robby Gordon 268 0 0 0 0 2,271,890 J.J. Yeley 192 0 0 0 0 2,559,500
Compound Probability
Compound probability can be defined as the probability of the two events which are independent. It can be defined as the multiplication of the probability of two events that are not dependent.
Tree diagram
Probability theory is a branch of mathematics that deals with the subject of probability. Although there are many different concepts of probability, probability theory expresses the definition mathematically through a series of axioms. Usually, these axioms express probability in terms of a probability space, which assigns a measure with values ranging from 0 to 1 to a set of outcomes known as the sample space. An event is a subset of these outcomes that is described.
Conditional Probability
By definition, the term probability is expressed as a part of mathematics where the chance of an event that may either occur or not is evaluated and expressed in numerical terms. The range of the value within which probability can be expressed is between 0 and 1. The higher the chance of an event occurring, the closer is its value to be 1. If the probability of an event is 1, it means that the event will happen under all considered circumstances. Similarly, if the probability is exactly 0, then no matter the situation, the event will never occur.
3. 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 ($) using Poles, Wins, Top 2–5, and Top 6–10. Test for individual significance and discuss your findings and conclusions.
| Driver | Points | Poles | Wins | Top 5 | Top 10 | Winnings ($) |
| Tony Stewart | 2403 | 1 | 5 | 9 | 19 | 6,529,870 |
| Carl Edwards | 2403 | 3 | 1 | 19 | 26 | 8,485,990 |
| Kevin Harvick | 2345 | 0 | 4 | 9 | 19 | 6,197,140 |
| Matt Kenseth | 2330 | 3 | 3 | 12 | 20 | 6,183,580 |
| Brad Keselowski | 2319 | 1 | 3 | 10 | 14 | 5,087,740 |
| Jimmie Johnson | 2304 | 0 | 2 | 14 | 21 | 6,296,360 |
| Dale Earnhardt Jr. | 2290 | 1 | 0 | 4 | 12 | 4,163,690 |
| Jeff Gordon | 2287 | 1 | 3 | 13 | 18 | 5,912,830 |
| Denny Hamlin | 2284 | 0 | 1 | 5 | 14 | 5,401,190 |
| Ryan Newman | 2284 | 3 | 1 | 9 | 17 | 5,303,020 |
| Kurt Busch | 2262 | 3 | 2 | 8 | 16 | 5,936,470 |
| Kyle Busch | 2246 | 1 | 4 | 14 | 18 | 6,161,020 |
| Clint Bowyer | 1047 | 0 | 1 | 4 | 16 | 5,633,950 |
| Kasey Kahne | 1041 | 2 | 1 | 8 | 15 | 4,775,160 |
| A.J. Allmendinger | 1013 | 0 | 0 | 1 | 10 | 4,825,560 |
| Greg Biffle | 997 | 3 | 0 | 3 | 10 | 4,318,050 |
| Paul Menard | 947 | 0 | 1 | 4 | 8 | 3,853,690 |
| Martin Truex Jr. | 937 | 1 | 0 | 3 | 12 | 3,955,560 |
| Marcos Ambrose | 936 | 0 | 1 | 5 | 12 | 4,750,390 |
| Jeff Burton | 935 | 0 | 0 | 2 | 5 | 3,807,780 |
| Juan Montoya | 932 | 2 | 0 | 2 | 8 | 5,020,780 |
| Mark Martin | 930 | 2 | 0 | 2 | 10 | 3,830,910 |
| David Ragan | 906 | 2 | 1 | 4 | 8 | 4,203,660 |
| Joey Logano | 902 | 2 | 0 | 4 | 6 | 3,856,010 |
| Brian Vickers | 846 | 0 | 0 | 3 | 7 | 4,301,880 |
| Regan Smith | 820 | 0 | 1 | 2 | 5 | 4,579,860 |
| Jamie McMurray | 795 | 1 | 0 | 2 | 4 | 4,794,770 |
| David Reutimann | 757 | 1 | 0 | 1 | 3 | 4,374,770 |
| Bobby Labonte | 670 | 0 | 0 | 1 | 2 | 4,505,650 |
| David Gilliland | 572 | 0 | 0 | 1 | 2 | 3,878,390 |
| Casey Mears | 541 | 0 | 0 | 0 | 0 | 2,838,320 |
| Dave Blaney | 508 | 0 | 0 | 1 | 1 | 3,229,210 |
| Andy Lally* | 398 | 0 | 0 | 0 | 0 | 2,868,220 |
| Robby Gordon | 268 | 0 | 0 | 0 | 0 | 2,271,890 |
| J.J. Yeley | 192 | 0 | 0 | 0 | 0 | 2,559,500 |
Trending now
This is a popular solution!
Step by step
Solved in 4 steps with 2 images
