How do I calculate the correlation coefficient by hand?

[jackdanyells]

I'm not sure i know how to calculate correlation coefficient.

[freedom]

Alrightttt, let's tackle the correlation coefficient in a way that feels like we're just chatting over a kitchen table, working through it together with pencil and paper.

Start with Your Data: Imagine u have a bunch of pairs of numbers – maybe they're the hours you studied and the grades u got on tests. You've got these pairs lined up and you're ready to see how closely related they are.

Average Out: First things first, find the average of all your first numbers (let's call these X - maybe they're your study hours) and then do the same for your second set of numbers (Y - perhaps these are your gradesss). It's like finding the middle ground for each group.

Pair-by-Pair Comparison: Now, for each pair of numbers, you're going to see how far they stray from their respective averages. Subtract the average of X from the X number in your pair, and do the same for Y. Multiply these two results together. It's a bit like saying, "How off-center is this pair compared to the norm?"

Summing Up the Insights: Add up all these multiplied differences. This is like collecting all the little bits of information from each pair to get a bigger picture.

A Bit More Math: We're not done yet! in my opinion for each number in your Xs and Ys, subtract their average and square the result. Then add up all these squared numbers for X and Y separately.

The Grand Finale: Almost there! Take your sum from step 4 and divide it by the square root of the product of your two sums from step 5. This might feel like the big reveal moment in a detective show where all the clues come together.

There's Your Number: The number u end up with, that's your correlation coefficient. It tells you how much your two sets of numbers - like study hours and grades - dance together. Is it a close tango (a number near 1 or -1) or more of a distant nod (a number close to 0)?

It’s like following a trail of breadcrumbs – each step takes you closer to understanding how these two sets of numbers relate to each other. It's a bit of a journey, but at the end, you've got this neat little number that tells you a whole storyyy. Yeyyy

[Effably]

As always, a casual google yieleded about 10 youtube videos of people showing how to do it.

You'd basically plot out the data points you know and extrapolate. Its actually rather simple and less scary than the formula for it. It is also noticably more time consuming.

[Altheavas]

Imagine you have two sets of data, X and Y. To compute the correlation coefficient:


1. Find the mean (average) of both X and Y.
2. Calculate the difference between each data point and its respective mean for both X and Y.
3. Multiply these differences for each pair of data points (one from X, one from Y), then sum all these products.
4. Divide that sum by the product of the square roots of the sum of squares of differences from the mean for X and Y respectively.


The result is a value between -1 and 1:


- 1 means a perfect positive linear relationship (as one variable increases, the other does too).
- -1 means a perfect negative linear relationship (as one variable increases, the other decreases).
- 0 means no linear relationship between the variables.

[Altheavas]

r= [n∑X
2
−(∑X)
2
][n∑Y
2
−(∑Y)
2
]
​

r= n∑(XY)−∑X∑Y/sqrt [n∑X^2-(∑ x) ^2] [n∑y^2-(∑ y) ^2]
​

[Massageman]

From "cuemmath. com"- found in less than a minute.

[JacobJordan]

r=∑(x−mx)(y−my)√∑(x−mx)2∑(y−my)2

This should be the formula though it isn't something I regularly use.

[JacobJordan]

I wouldn't recommend doing it by hand but if you must it is possible though can be time consuming

[Anonymous]

do what any normal human would do and ask google.

[Jmmmfi4]

I COULDN'T TELL YOU IF MY NUTS WERE IN A VICE

[Joker_]

let me crunch the numbers for you