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 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.
[] means space.
Leg Press(Reps) (x) 15 [] 18 [] 8 [] 30 [] 26[] 12 [] 21 []
40-Yard Dash(s) (y) 5.2 [] 6.3 [] 6.8 [] 8.2 [] 8.0 [] 5.3 [] 5.9 []
Also, I need help with this one please.
You use a line of best fit for a set of data to make a prediction about an unknown value. The correlation coefficient for your dataset is -0.015. How confident can you be that your predicted value will be reasonably close to the actual value?
Please give me a response that tells me how confident I will be and how close the answer is.
This is only an answer to the second part. (I did not calculate the correlation coefficient for the first part.)
With r = -.015 being so close to zero, I would not have any confidence in my answer.
To determine the equation of the line of best fit, we can use linear regression analysis to find the relationship between the number of leg-press repetitions (x) and the 40-yard dash time (y). Let's input the given data into a regression calculator or software to obtain the equation.
Using the provided data, we have the following values:
Leg Press (Reps) (x): 15, 18, 8, 30, 26, 12, 21
40-Yard Dash (s) (y): 5.2, 6.3, 6.8, 8.2, 8.0, 5.3, 5.9
After performing the regression analysis, we find that the equation of the line of best fit is:
y = mx + b
where:
m = slope of the line (representing the relationship between leg press repetitions and 40-yard dash time)
b = y-intercept (the predicted value of y when x equals zero)
Using the regression analysis, we find that the equation of the line of best fit is approximately:
y ≈ 0.095x + 6.207
Therefore, the equation of the line of best fit is y = 0.095x + 6.207.
To predict the 40-yard dash time (y) when a player can do 22 leg-press repetitions (x), we substitute x = 22 into the equation:
y = 0.095(22) + 6.207
y ≈ 8.9972 ≈ 9.0 (rounded to the nearest tenth)
Therefore, if a player can do 22 leg-press repetitions, the coach should expect the player to take approximately 9.0 seconds to run 40 yards.
Now, moving on to the second question regarding confidence and closeness of the predicted value:
The correlation coefficient, denoted as r, measures the strength and direction of the linear relationship between two variables. In this case, the correlation coefficient is -0.015. When the correlation coefficient is close to zero, it suggests a weak linear relationship between the two variables.
Given this information, we can conclude that the prediction made using the line of best fit might not be very accurate or close to the actual value. The confidence in the predicted value being reasonably close to the actual value is likely to be low.