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 $43$rd 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$).$

Tony Stewart $2403159196,529,87045$

Carl Edwards $24033119268,485,990186$

Kevin Harvick $2345049196,197,14056$

Matt Kenseth $23303312206,183,58095$

Brad Keselowski $23191310145,087,74071$

Jimmie Johnson $23040214216,296,360125$

Dale Earnhardt Jr$.2290104124,163,69048$

Jeff Gordon $22871313185,912,830102$

Denny Hamlin $2284015145,401,19048$

Ryan Newman $2284319175,303,02087$

Kurt Busch $2262328165,936,47066$

Kyle Busch $22461414186,161,020100$

Clint Bowyer $1047014165,633,950311$

Kasey Kahne $1041218154,775,16076$

A$.$J$.$ Allmendinger $1013001104,825,56019$

Greg Biffle $997303104,318,05037$

Paul Menard $94701483,853,69033$

Martin Truex Jr$.937103123,955,56039$

Marcos Ambrose $936015124,750,39046$

Jeff Burton $93500253,807,78023$

Juan Montoya $93220285,020,78026$

Mark Martin $930202103,830,91028$

David Ragan $90621484,203,66033$

Joey Logano $90220463,856,01042$

Brian Vickers $84600374,301,88034$

Regan Smith $82001254,579,86012$

Jamie McMurray $79510244,794,77022$

David Reutimann $75710134,374,77012$

Bobby Labonte $67000124,505,65011$

David Gilliland $57200123,878,39011$

Casey Mears $54100002,838,32000$

Dave Blaney $50800113,229,21010$

Andy Lally$*39800002,868,22000$

Robby Gordon $26800002,271,89000$

J$.$J$.$ Yeley $19200002,559,500001.$ Suppose you wanted to predict Winnings $($$$)$ using only the number of poles won $($Poles$),$ the numberof wins $($Wins$),$ the number of top five finishes $($Top $5),$ or the number of top ten finishes $($Top $10).$Which of these four variables provides the best single predictor of winnings? $2.$ Develop an estimated regression equation that can be used to predict Winnings $($$$)$ given the numberof poles won $($Poles$),$ the number of wins $($Wins$),$ the number of top five finishes $($Top $5),$ and thenumber of top ten finishes $($Top $10).$ Test for individual significance and discuss your findings andconclusions. $3.$ Create two new independent variables: Top $25$ and Top $610.$ Top $25$ represents the number oftimes the driver finished between second and fifth place and Top $610$ represents the number of timesthe driver finished between sixth and tenth place. Develop an estimated regression equation that canbe used to predict Winnings $($$$)$ using Poles, Wins, Top $25,$ and Top $610.$ Test for individualsignificance and discuss your findings and conclusions. $4.$ Based upon the results of your analysis, what estimated regression equation would you recommendusing to predict Winnings $($$$)?$ Provide an interpretation of the estimated regression coefficients forthis equation.