Download the data file 14_cr_10.txt at www.pearsonhighered.com/sullivanstats. The data represent a variety of variables measured on players in the 2015 National Football League (NFL) combine. Suppose you want to build a model to predict a player's weight. The following variables were measured:
y: Weight-weight of the player in pounds
x1: 40 YD-time (in seconds) to complete the 40-yard dash
x2: Vertical-standing vertical jump (in inches)
x3: Bench-number of times player can bench press 225 pounds
x4: Shuttle-time (in seconds) of the shuttle run
x5: Cone-time (in seconds) of the 3-cone run
x6: 20 YD-time (in seconds) of the 20-yard shuttle drill
(a) Find the least-squares regression equation
y̅ = b0 + b1x1 + b2x2 + b3x3 + b4x4 + b5x5 + b6x6.
(b) Use a partial F test to test whether 3-cone run and 20-yard shuttle drill do not significantly help to explain variability in weight.
(c) Use forward selection, backward elimination, or stepwise regression to identify the best model in predicting weight.