A sports medicine major wanted to conduct an experiment to determine if there is a correlation between the members of the soccer team's leg strength and the time it takes for them to sprint 40 yards. He sets up the following test and records the data: Every day for a week, he counts how many times each player can leg press 350 pounds. The following week, he has each player sprint 40 yards every day. The table shows the average number of leg-press repetitions and the average 40-yard dash time (in seconds) for seven randomly selected players. What is the equation of the line of best fit? How many seconds should he expect a player to take to run 40 yards if that player can do 22 leg-press repetitions? Round any values to the nearest tenth, if necessary. Leg Press (reps) 12 32 7 11 23 28 15 40-yard Dash (s) 8.6 14.6 7.1 8.3 11.9 13.4 9.5
To find the equation of the line of best fit, we can use linear regression analysis.
Using a calculator or statistical software, we find that the equation of the line of best fit is:
40-yard Dash (s) = 0.2517 * Leg Press (reps) + 7.8224
Therefore, if a player can do 22 leg-press repetitions, we can substitute this value into the equation to find the expected time for the 40-yard dash:
40-yard Dash (s) = 0.2517 * 22 + 7.8224
40-yard Dash (s) ≈ 13.77
Therefore, we can expect a player who can do 22 leg-press repetitions to take approximately 13.8 seconds to run 40 yards.