Create an image that portrays a sports medicine study relating to a correlation between the strength of soccer players' legs and their 40-yard sprint times. In the image, an African-American female researcher is seen overseeing the testing process where athletes, of diverse descents including Caucasian, Hispanic, Asian, and Middle-Eastern, perform leg press tasks with a 350-pound weight. In another part of the image, these same soccer players, from a birds-eye-view, are shown sprinting a distance of 40 yards in an athletic field. There should be no text within the image.

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

I'm honestly so confused

Using linear interpolation on the interval [15,23] that would be

9.5 + (22-15)/(23-15) * (11.9-9.5) = 11.6

That is, since 22 is 7/8 of the way from 15 to 23, he should produce a value 7/8 of the way from 9.5 to 11.9

i got 11.6 instead??

haha im so lost and this is due in 3 days ughhhhhhh

how do we know this is correct tho? can someone who gets feedback come backkk n say what the score was for them plz?? that would be lots of help.. not only that but if it was wrong maybe put that was would help us to put a better answer or sumthing idk this is kinda making me second guess if its even right ngl..

for those of u who still need the answer ;

the reason Ms. Sue got 11.9 and ale got 11.6 is because they both have different data.

ale's 11.6 :
leg press (reps): 12, 32, 7, 11, 23, 28, 15
40-yard dash(s): 8.6, 14.6, 7.1, 8.3, 11.9, 9.5

The equation from the calculator is y = 0.3 + 5
y = 0.3 x 22 + 5
y = 6.6 + 5
y = 11.6

Ms. Sue's 11.9 :
the data entered above
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

just use Ms. Sue's answer.

so really, it depends on what ur data for the question is. read the numbers carefully !!!
u can use the desmos calc to help u as well :]

- good soup

Thank You!!

ms sue is right but the way she presents the data is really confusing and disorganized, it would be better if she split the questions into A and B and then answered them accordingly.

To find the equation of the line of best fit and predict the time it takes for a player to run 40 yards given their leg press repetitions, we can use linear regression analysis. Here are the steps to find the equation and make the prediction:

Step 1: Organize the given data into two lists: leg press repetitions (x-values) and 40-yard dash times (y-values).

Leg Press (Reps): 12, 32, 7, 11, 23, 28, 15
40-Yard Dash (Seconds): 8.6, 14.6, 7.1, 8.3, 11.9, 13.4, 9.5

Step 2: Calculate the average of the x-values and y-values.

Average leg press repetitions (x̄) = (12 + 32 + 7 + 11 + 23 + 28 + 15) / 7 = 18.6
Average 40-yard dash times (ȳ) = (8.6 + 14.6 + 7.1 + 8.3 + 11.9 + 13.4 + 9.5) / 7 = 10.6

Step 3: Calculate the deviation of each x-value and y-value from their respective averages.

Deviation of leg press repetitions (x - x̄):
-6.6, 13.4, -11.6, -7.6, 4.4, 9.4, -3.6

Deviation of 40-yard dash times (y - ȳ):
-2, 4, -3.5, -2.3, 1.3, 2.8, -1.1

Step 4: Calculate the product of the deviations (x - x̄)(y - ȳ) for each data point.

Product of deviations:
-6.6 * -2 = 13.2
13.4 * 4 = 53.6
-11.6 * -3.5 = 40.6
-7.6 * -2.3 = 17.5
4.4 * 1.3 = 5.7
9.4 * 2.8 = 26.3
-3.6 * -1.1 = 3.96

Step 5: Calculate the squared deviation of x-values from the average (x - x̄)^2 for each data point.

Squared deviation of leg press repetitions:
(-6.6)^2 = 43.56
13.4^2 = 179.56
(-11.6)^2 = 134.56
(-7.6)^2 = 57.76
4.4^2 = 19.36
9.4^2 = 88.36
(-3.6)^2 = 12.96

Step 6: Calculate the sum of the squared deviations of x-values.

Sum of squared deviations of leg press repetitions = 545.12

Step 7: Calculate the slope (m) of the regression line.

m = Σ[(x - x̄)(y - ȳ)] / Σ(x - x̄)^2

m = (13.2 + 53.6 + 40.6 + 17.5 + 5.7 + 26.3 + 3.96) / 545.12
m = 5.096 / 545.12
m ≈ 0.009348

Step 8: Calculate the y-intercept (b) of the regression line.

b = ȳ - m * x̄
b = 10.6 - 0.009348 * 18.6
b ≈ 10.4164

Step 9: Write the equation of the line of best fit as y = mx + b.

Equation of the line of best fit: y = 0.009348x + 10.4164

To predict the time it takes for a player to run 40 yards if that player can do 22 leg press repetitions, substitute x = 22 into the equation and solve for y.

y = (0.009348 * 22) + 10.4164
y ≈ 10.6057

Therefore, if a player can do 22 leg press repetitions, we would expect them to take approximately 10.6 seconds to run 40 yards.

So does anyone have the answer for the data of 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
?