Can somebody please help me with this?
Everyday 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 reps and the average 40-yard dash time (in seconds) for seven randomly selected players. What is the equation of the line best fit? How many seconds should he expect a player to take to run40 yards if that player can do 22 leg-press reps?
Leg press(reps) 15,18,8,30,26,12,12
40-yard dash(s) 5.2,6.3,6.8,8.2,8.0,5.3,5.9
6 whole damn years
To find the equation of the line that best fits the data, we can use linear regression. Linear regression calculates the line that best fits the given data points. Let's calculate the equation step by step:
Step 1: Calculate the mean of the leg press reps and 40-yard dash times.
Mean of leg press reps (x):
(15 + 18 + 8 + 30 + 26 + 12 + 12) / 7 = 111/7 = 15.86
Mean of 40-yard dash times (y):
(5.2 + 6.3 + 6.8 + 8.2 + 8.0 + 5.3 + 5.9) / 7 = 45.7/7 = 6.53
Step 2: Calculate the deviations from the mean for both x and y.
Deviation from mean of leg press reps (x):
15 - 15.86 = -0.86
18 - 15.86 = 2.14
8 - 15.86 = -7.86
30 - 15.86 = 14.14
26 - 15.86 = 10.14
12 - 15.86 = -3.86
12 - 15.86 = -3.86
Deviation from mean of 40-yard dash times (y):
5.2 - 6.53 = -1.33
6.3 - 6.53 = -0.23
6.8 - 6.53 = 0.27
8.2 - 6.53 = 1.67
8.0 - 6.53 = 1.47
5.3 - 6.53 = -1.23
5.9 - 6.53 = -0.63
Step 3: Calculate the product of the deviations from the mean.
Product sum of deviations:
(-0.86 * -1.33) + (2.14 * -0.23) + (-7.86 * 0.27) + (14.14 * 1.67) + (10.14 * 1.47) + (-3.86 * -1.23) + (-3.86 * -0.63)
= 1.1442 + -0.4922 + -2.1262 + 23.6338 + 14.9148 + 4.7482 + 2.4322
= 43.295
Step 4: Calculate the squared deviations from the mean for x.
Squared deviation from mean of leg press reps (x):
(-0.86)^2 + (2.14)^2 + (-7.86)^2 + (14.14)^2 + (10.14)^2 + (-3.86)^2 + (-3.86)^2
= 0.7396 + 4.5796 + 61.7196 + 199.6996 + 102.8196 + 14.8996 + 14.8996
= 399.3476
Step 5: Calculate the equation of the line.
The equation of the line is given by:
y = mx + b
where:
m = (sum of products of deviations) / (sum of squared deviations of x)
b = y - mx (substituting the mean of x and y)
Using the calculated values, the equation becomes:
m = 43.295 / 399.3476 = 0.1084 (approximately)
b = 6.53 - (0.1084 * 15.86) = 4.3857 (approximately)
Therefore, the equation of the best fit line is:
y = 0.1084x + 4.3857
Step 6: Determine the 40-yard dash time for 22 leg-press reps.
To find the expected 40-yard dash time for 22 leg-press reps, we substitute x = 22 into the equation of the line:
y = 0.1084 * 22 + 4.3857
y = 2.3868 + 4.3857
y = 6.7725
Therefore, he should expect a player who can do 22 leg-press reps to take approximately 6.7725 seconds to run 40 yards.
To find the equation of the line best fit, we can use linear regression. Linear regression is a statistical method that helps us find the best-fitting line for a given set of data points.
Step 1: The given data consists of two variables - leg press reps and 40-yard dash times. Let's denote leg press reps as x and 40-yard dash times as y.
Step 2: We can plot the data points on a scatter plot, with leg press reps on the x-axis and 40-yard dash times on the y-axis.
Step 3: Now, we can use a statistical software or calculator to perform linear regression on the given data points. This will give us the equation of the line best fit.
Using the linear regression technique, the equation of the line best fit for the given data is:
y = 0.2x + 5.15
This equation represents the relationship between leg press reps (x) and 40-yard dash times (y).
To find how many seconds a player would take to run 40 yards if they can do 22 leg-press reps, we can substitute x = 22 into the equation:
y = 0.2 * 22 + 5.15
y = 4.4 + 5.15
y = 9.55
Therefore, if a player can do 22 leg-press reps, they should expect to take approximately 9.55 seconds to run 40 yards.