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A college football coach wants to know if the is a correlation between his players' 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 tables 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?

Leg Press (reps)|40-yard Dash (s)
15 |5.2
18 |6.3
8 |6.8
30 |8.2
26 |8.0
12 |5.3
21 |5.9

Answer :

The correct answer is the equation of the line of best fit is y=0.11x+4.54, and it would take the player 6.96 seconds to run.

Explanation:
Using technology, we calculate the line of best fit; we first enter the data points as a scatter plot, then run the regression tool, which gives us y=ax+b, where a=0.11 and b=4.54.

We now use this equation, y=0.11x+4.54, to calculate the amount of time it would take a player to run 40 yards if the player can do 22 leg-press reps:

y=0.11(22)+4.54=6.96.

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