A sports medicine major wanted to conduct an experiment to determine if there is a correlation between the members of the soccer

Question

2 years ago

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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: 8.6, 14.6, 7.1, 8.3, 11.9, 13.4, 9.5

Mathematics

2 answers:

Viefleur [7K] · Answer 1 · 2022-10-08T05:33:42+03:00

Answer:

1) The equation of the line of best fit is y = 0.3·x + 5

2) The time it would take a player that can complete 22 leg press repetitions to run 40 yards is 11.6 seconds

Step-by-step explanation:

1) The given data are;

Leg press (Reps): ${}$ 40-yard Dash Time

12 ${}$ 8.6

32 ${}$ 14.6

7 ${}$ 7.1

11 ${}$ 8.3

23 ${}$ 11.9

28 ${}$ 13.4

15 ${}$ 9.5

From the attached graph we observe that with the data sorted in increasing order, there is a linear relation between the number of leg presses and the time to complete a 40 yard dash

The slope = (14.6 - 7.1)/(32 - 7) = 0.3

The equation of the line of best fit is the linear equation of the data given in point and slope form as follows;

y - 7.1 = 0.3×(x - 7)

y - 7.1 = 0.3·x - 2.1

The equation of the line of best fit is therefore;

y = 0.3·x + 5

Where;

y = The time to complete the 40-yard dash

x = The number of leg press completed

2) When x = 22, we have;

y = 0.3 × 22 + 5 = 11.6 seconds

If a player can do 22 leg-press repetitions, it would take the player 11.6 seconds to complete the 40 yard-dash.