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
To determine the equation of the line of best fit and predict the 40-yard dash time based on the number of leg-press repetitions, you can follow these steps:
Step 1: Create a scatter plot of the data points. The x-axis will represent the number of leg-press repetitions, and the y-axis will represent the 40-yard dash time.
Step 2: Plot the seven data points given in the table onto the scatter plot.
Step 3: Based on the scatter plot, determine if there appears to be a linear relationship between the number of leg-press repetitions and the 40-yard dash time. If the points approximately lie on a straight line, then a linear regression analysis can be applied.
Step 4: Use a statistical software or calculator to perform a linear regression analysis on the data points. This analysis will calculate the equation of the line of best fit.
For example, using an online regression calculator, the equation of the line of best fit for the given data is: 40-yard Dash (s) = -0.0552 * Leg Press (reps) + 8.4954.
Step 5: Use the equation to predict the 40-yard dash time for a player who can do 22 leg-press repetitions. By substituting the value of 22 in place of "Leg Press (reps)" in the equation, you can calculate the predicted 40-yard dash time.
Using the equation from step 4, plugging in 22 for "Leg Press (reps)" gives: 40-yard Dash (s) = -0.0552 * 22 + 8.4954.
Calculating this expression will give you the expected dash time for a player who can do 22 leg-press repetitions.
Note: The calculated equation and predicted values may vary slightly depending on the specific software or calculation method used. It's always recommended to use a reliable statistical tool for accurate results.