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 (2 points)
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The equation of the line of best fit can be determined by performing linear regression analysis on the given data points. Using a statistical software or calculator, one can calculate the equation of the line of best fit, which represents the relationship between leg press repetitions and 40-yard dash time.
To find the equation of the line of best fit using the given data:
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
The equation of the line of best fit is:
40-yard Dash Time (s) = a * leg press repetitions + b
Using the least squares method, the equation of the line of best fit can be approximated as:
40-yard Dash Time (s) ≈ -0.082 * leg press repetitions + 12.629
Therefore, the equation of the line of best fit is approximately y = -0.082x + 12.629.
To determine how many seconds a player should take to run 40 yards if they can do 22 leg press repetitions, substitute the value of x as 22 into the equation and solve for y:
y = -0.082 * 22 + 12.629
y ≈ -1.804 + 12.629
y ≈ 10.825
Therefore, a player who can do 22 leg press repetitions is expected to take approximately 10.8 seconds to run 40 yards.