find the value for the correlation coefficient r.
x 5 1 4 2 3
y 5 10 12 4 8
We do not do your work for you. Here is a source with a (relatively) simple formula for calculating r.
http://davidmlane.com/hyperstat/A51911.html
In the future, you can find the information you desire more quickly, if you use appropriate key words to do your own search. Also see http://hanlib.sou.edu/searchtools/.
I hope this helps. Thanks for asking.
I DID NOT ASK YOU TO DO MY HOMEWORK, I JUST WANTED THE FORMULA.....
the formula is pie r squared times -12
To find the correlation coefficient (r) between two sets of data, you need to follow a few steps:
Step 1: Calculate the mean (average) for both sets of data. Let's call the mean for x as x̄ and the mean for y as ȳ.
For x:
x̄ = (5 + 1 + 4 + 2 + 3) / 5 = 15 / 5 = 3
For y:
ȳ = (5 + 10 + 12 + 4 + 8) / 5 = 39 / 5 = 7.8
Step 2: Subtract the mean from each corresponding value to get the deviation for both x and y. Let's call the deviation for x as dx and for y as dy.
For x:
dx = (5 - 3), (1 - 3), (4 - 3), (2 - 3), (3 - 3) = 2, -2, 1, -1, 0
For y:
dy = (5 - 7.8), (10 - 7.8), (12 - 7.8), (4 - 7.8), (8 - 7.8) = -2.8, 2.2, 4.2, -3.8, 0.2
Step 3: Calculate the sum of products of the deviations by multiplying dx and dy for each corresponding pair.
dx * dy = 2 * (-2.8) + (-2) * 2.2 + 1 * 4.2 + (-1) * (-3.8) + 0 * 0.2
= -5.6 - 4.4 + 4.2 + 3.8 + 0
= -2
Step 4: Calculate the sum of the squares of deviations for both x and y.
For x:
(dx)^2 = 2^2 + (-2)^2 + 1^2 + (-1)^2 + 0^2
= 4 + 4 + 1 + 1 + 0
= 10
For y:
(dy)^2 = (-2.8)^2 + 2.2^2 + 4.2^2 + (-3.8)^2 + 0.2^2
= 7.84 + 4.84 + 17.64 + 14.44 + 0.04
= 44.8
Step 5: Calculate the correlation coefficient (r) using the formula:
r = (Σ(dx * dy)) / sqrt(Σ(dx^2) * Σ(dy^2))
r = -2 / sqrt(10 * 44.8) ≈ -0.195
So, the correlation coefficient (r) for the given data sets is approximately -0.195.