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

Hello!

The Equation is:
y = 4.536 + 0.107
And the second question is:
y = 6.89

To find the equation of the line of best fit and predict the 40-yard dash time for a given number of leg-press repetitions, we can use linear regression analysis. This will help us determine the relationship between the two variables.

Step 1: Plot the data points on a scatter plot.
First, plot the leg press repetitions on the x-axis and the corresponding 40-yard dash times on the y-axis. Use seven randomly selected players' data from the table you provided.

Step 2: Calculate the correlation coefficient.
To determine if there is a correlation, calculate the correlation coefficient (r) between leg press repetitions and 40-yard dash times. You can use a statistical software or an Excel sheet to perform this calculation. If the value of r is between -1 and 1, the closer it is to -1/-0.9 or 1/0.9, the stronger the correlation. If it is closer to 0, there is a weak correlation.

Step 3: Determine the equation of the line of best fit.
To find the equation of the line of best fit, we use the equation: y = mx + b, where y represents the predicted 40-yard dash time, x represents the number of leg press repetitions, m represents the slope, and b represents the y-intercept.

Step 4: Plug in the given number of leg press repetitions.
Once you have the equation of the line, substitute the given number of leg-press repetitions into the equation to find the predicted 40-yard dash time for that player.

After performing these steps, you will have the equation of the line of best fit and the predicted 40-yard dash time for the given leg press repetitions.

I am not going to do this for you.

You can use :

http://www.wolframalpha.com/input/?i=linear+regression&a=*C.linear+regression-_*Calculator.dflt-&f2={104%2C+117%2C+131%2C+145%2C+160%2C+171}&f=LinearFitCalculator.data\u005f{104%2C+117%2C+131%2C+145%2C+160%2C+171}&a=*FVarOpt-_**LinearFitCalculator.data2--