I really need help with this question. I someone could help me out that would be great. Thanks in advance.

A college football coach wants to know if there 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 time each player can leg press 350 lbs. 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 for seven randomly selected players. What is the equation of the line of best fit? How many second should he expect a player to take a run 40 yards if that player can do 22 leg press repetitions. Round any values to the nearest tenth if necessary.

leg press 15 18 8 30 26 12 21

40 yard dash 5.2 6.3 6.8 8.2 8.2 5.3 5.9

plot leg presses on the x-axis , and the corresponding 40 yd dash times on the y-axis

then fit a line to the points (best fit)

If you look at the "Related Questions" below, you will see that this question has been asked repeatedly since 2015 and no real answer has been given, and the first post consists of about 20 replies in almost panic note, with many students replying in total chaos.

It appears to me that the results of the experiment are all over the place. The two slowest times were recorded when the athlete's leg strength was the greatest and the fastest times when the number of leg presses were the least. Looks like an inverse relation: the weaker the legs, the faster the times? This does not seem logical.
Plotting the points does not help much, it shows no nice pattern.
Good luck getting any valid statistical results from this.

To find the equation of the line of best fit, we can use linear regression analysis. Linear regression helps us determine the relationship between two variables and create a line that represents the best fit for the data points.

Step 1: Calculate the mean of the leg press repetitions and the mean of the 40-yard dash times.

Mean of leg press repetitions:
(15 + 18 + 8 + 30 + 26 + 12 + 21) / 7 = 20.7

Mean of 40-yard dash times:
(5.2 + 6.3 + 6.8 + 8.2 + 8.2 + 5.3 + 5.9) / 7 = 6.6714 (rounded to four decimal places)

Step 2: Calculate the sum of the products of each leg press repetition and its corresponding 40-yard dash time, as well as the sum of the squares of the leg press repetitions.

Sum of the products:
(15 * 5.2) + (18 * 6.3) + (8 * 6.8) + (30 * 8.2) + (26 * 8.2) + (12 * 5.3) + (21 * 5.9) = 1936.5

Sum of the squares of the leg press repetitions:
(15^2) + (18^2) + (8^2) + (30^2) + (26^2) + (12^2) + (21^2) = 3030

Step 3: Calculate the slope (m) of the line of best fit using the formula:

m = (n * ∑(x*y) - ∑(x) * ∑(y)) / (n * ∑(x^2) - (∑(x))^2)

where n is the number of data points, x is the leg press repetitions, y is the 40-yard dash times, ∑ represents the sum, and ∑(x*y) represents the sum of the products of x and y.

n = 7
∑(x*y) = 1936.5
∑(x) = 20.7 * 7 = 144.9
∑(x^2) = 3030

Substituting the values into the formula:

m = (7 * 1936.5 - 144.9 * 6.6714) / (7 * 3030 - 144.9^2)

m = 0.053

Step 4: Calculate the y-intercept (b) of the line of best fit using the formula:

b = (∑(y) - m * ∑(x)) / n

∑(y) = 6.6714 * 7 = 46.7

Substituting the values into the formula:

b = (46.7 - 0.053 * 144.9) / 7

b = -1.920

The equation of the line of best fit is y = 0.053x - 1.920.

To calculate the expected time 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 = 0.053 * 22 - 1.920

y = 0.166

Therefore, the player should be expected to take approximately 0.2 seconds (rounded to the nearest tenth) to run 40 yards.

did not do the plot , just wanted to comment on the "inverse relation"

stronger (and larger) linemen are usually slower than the smaller backs and receivers