every day for a week he counts how many times each player can leg press 350 pounds. the following week, he has a each player sprint 40 yards every day. the table shows the average number of leg press reptitions 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 reptitions? round any values to the nearest tenth, if neccessary
To find the equation of the line of best fit, we need to find the equation of a linear regression line that represents the relationship between the average number of leg press repetitions and the average 40-yard dash time.
Let's denote the average number of leg press repetitions as x and the average 40-yard dash time as y.
The table is not provided, so we cannot find the exact equation of the line of best fit. However, we can provide the general formula for the equation.
The equation of a line in slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.
In this case, we need to find the slope and y-intercept of the line of best fit.
To find the slope, we can use the formula:
m = (Σ(x*y) - n*x̄*ȳ) / (Σx^2 - n*x̄^2)
Where:
Σ(x*y) represents the sum of the product of each pair of x and y values,
n represents the number of data points,
x̄ represents the mean of x values,
ȳ represents the mean of y values,
Σx^2 represents the sum of the squares of x values,
and n̄ represents the mean of n values.
To find the y-intercept, we can use the formula:
b = ȳ - m*x̄
Given the table of data, we can calculate the mean (x̄) of leg press repetitions and the mean (ȳ) of 40-yard dash times. However, without the specific values from the table, we cannot provide the exact equation of the line of best fit.
To estimate the expected 40-yard dash time for a player who can do 22 leg press repetitions, we would need to substitute x = 22 into the equation and calculate the corresponding y value. However, since we don't know the specific equation, we cannot provide an estimated time.