Develop an estimated regression equation that can be used to predict Winnings ($) given the number of poles won (Poles), the number of wins (Wins), the number of top five finishes (Top 5), and the number of top ten (Top 10) finishes. Test for individual significance and discuss your findings and conclusions. Driver Points Poles Wins Top 5 Top 10 Winnings ($) 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
Correlation
Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.
Linear Correlation
A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.
Regression Analysis
Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.
2. Develop an estimated regression equation that can be used to predict Winnings ($) given the number of poles won (Poles), the number of wins (Wins), the number of top five finishes (Top 5), and the number of top ten (Top 10) finishes. Test for individual significance and discuss your findings and conclusions.
Driver | Points | Poles | Wins | Top 5 | Top 10 | Winnings ($) |
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 |
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