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24. A sports medicine major wanted to conduct an experiment to determine if there is a correlation (2 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. 12 32 7 26 28 15 Leg Press (reps) 1 40-yard Dash (s) 8.6 14.6 7.1 8.3 11.9 19.4 9.5​

Answer :

fichoh

Answer:

ŷ = 0.1197X + 9.2741

11.9 seconds

Step-by-step explanation:

Given the data:

Average number of leg press Repetition and average 40 yard dash line

Leg press rep (x) : 12 32 7 26 28 15 1

40 yard dash (y) : 8.6 14.6 7.1 8.3 11.9 19.4 9.5

Using the linear regression calculator :

The equation of the line of best fit obtained is :

y = 0.1197X + 9.2741

Where;

x = leg press (predictor variable)

y = 40 yard dash (predicted variable)

Slope = 0.1197

Intercept = 9.2741

How many seconds should he expect a player to take to run 40 yards if that player can do 22 leg-press repetitions?

22 leg press Repetitions = x

From the line of best fit equation :

y = 0.1197(22) + 9.2741

y = 11.9075

y = 11.9 seconds

MrRoyal

The lines of best fit is the trend line of the dataset.

  • The equation of line of best fit is [tex]\mathbf{y =0.120x + 9.274}[/tex]
  • The time for 22 leg-press reps is 11.9 seconds

(a) The equation of the line of best fit

The table is given as:

(x) : 12 32 7 26 28 15 1

(y) : 8.6 14.6 7.1 8.3 11.9 19.4 9.5

To determine the equation of line of best fit, we make use of a regression calculator.

Enter the above dataset in a regression calculator, the equation is:

[tex]\mathbf{y =0.120x + 9.274}[/tex] -- approximated to three decimal places

(b) The number of seconds for 22 leg-press reps

This means that x = 22.

So, we have:

[tex]\mathbf{y =0.120 \times 22 + 9.274}[/tex]

[tex]\mathbf{y =2.64 + 9.274}[/tex]

[tex]\mathbf{y =11.914}[/tex]

Approximate to the nearest tenth

[tex]\mathbf{y =11.9}[/tex]

Hence, the time for 22 leg-press reps is 11.9 seconds

Read more about linear regressions at:

https://brainly.com/question/18405415

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