how do I find s subscript x and s subscript y for b1 = r(Sy/Sx)? Found in linear regression.
To find the values of s subscript x and s subscript y in the equation b1 = r(Sy/Sx), you need to compute the standard deviations of the x-values (s x) and the y-values (s y) in linear regression.
Here's the step-by-step process to find s subscript x and s subscript y:
1. Gather your data: Make sure you have a dataset that includes pairs of x and y values.
2. Calculate the mean of the x-values (x-bar): Add up all the x-values and divide by the number of data points. Let's call this value x-bar.
3. Calculate the mean of the y-values (y-bar): Add up all the y-values and divide by the number of data points. Let's call this value y-bar.
4. Calculate the sum of the squared differences of the x-values from the mean (Σ(x - x-bar)^2): For each x-value, subtract x-bar from it and square the result. Then sum up all these squared differences.
5. Calculate the sum of the squared differences of the y-values from the mean (Σ(y - y-bar)^2): For each y-value, subtract y-bar from it and square the result. Then sum up all these squared differences.
6. Calculate the product of the differences of each x-value and y-value from their respective means (Σ(x - x-bar)(y - y-bar)): For each pair of x and y values, subtract x-bar from x and y-bar from y. Multiply these differences for each pair and sum them up.
7. Calculate the standard deviation of the x-values (s x): Take the square root of the sum of the squared differences of the x-values from the mean divided by (n-1), where n is the number of data points.
s x = sqrt[Σ(x - x-bar)^2 / (n-1)]
8. Calculate the standard deviation of the y-values (s y): Take the square root of the sum of the squared differences of the y-values from the mean divided by (n-1), where n is the number of data points.
s y = sqrt[Σ(y - y-bar)^2 / (n-1)]
9. Calculate the correlation coefficient (r): Divide the sum of the product of the differences of each x-value and y-value from their respective means by the product of sx and sy.
r = Σ(x - x-bar)(y - y-bar) / (s x * s y)
10. Finally, substitute the values of r, s x, and s y in the equation b1 = r(Sy/Sx):
b1 = r(s y / s x)
By following these steps, you will be able to find the values of s subscript x and s subscript y in the equation b1 = r(Sy/Sx) for linear regression.