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.
To find the equation of the line of best fit, we need to determine the relationship between leg-press repetitions and 40-yard dash time. We can use linear regression analysis to find this relationship.
First, let's label the average number of leg-press repetitions as x and the average 40-yard dash time as y. The table is as follows:
Leg-Press Repetitions (x): 12, 16, 18, 20, 22, 24, 26
40-Yard Dash Time (y): 5.1, 4.7, 4.4, 4.2, 4.0, 3.8, 3.6
Using a graphing calculator or spreadsheet software, we can input these data points and find the equation of the line of best fit. The equation is typically in the form y = mx + b, where m represents the slope and b represents the y-intercept.
Using linear regression analysis, we can find that the equation of the line of best fit is y = -0.15x + 7.58.
To find how many seconds a player would take to run 40 yards if they can do 22 leg-press repetitions, we substitute x = 22 into the equation:
y = -0.15(22) + 7.58
y = -3.30 + 7.58
y = 4.28
Therefore, we can expect a player who can do 22 leg-press repetitions to take approximately 4.3 seconds to run 40 yards.