Correlation, simple formula, meaning

[ducmod]

Homework Statement

Hello!

Here is the quote of mathisfun explanation of correlation formula and after $my understanding or questions: Let us call the two sets of data "x" and "y" (in our case Temperature is x and Ice Cream Sales is y): Step 1: Find the mean of x, and the mean of y Step 2: Subtract the mean of x from every x value (call them "a"), do the same for y (call them "b")$ with step 2 we compute how each variable differs from the mean

Step 3: Calculate: a × b, a2 and b2 for every value

$here I come to the point where I need help: I understand that we have to square each value from step 2 (a and b) to avoid negative numbers;$ but I don't understand the meaning (ligic; why) of multiplication of variables from step 2 a x b

Step 4: Sum up a × b, sum up a2 and sum up b2

Step 5: Divide the sum of a × b by the square root of [(sum of a2) × (sum of b2)]

$in step 5 again I don't understand the logic of multiplication, what does this multiplication mean; and then the division.$ usually, division shows how many parts of divisor are in divident, or percent.

Thank you!

Homework Equations

The Attempt at a Solution

 

[Svein]

What you are quoting is an algorithm, a recipe to find the linear correlation between two data sets. Why the algorithm is the way it is, and what the meaning of the numbers represent - wait until you have a basic knowledge of statistics.

 

[ducmod]

What you are quoting is an algorithm, a recipe to find the linear correlation between two data sets. Why the algorithm is the way it is, and what the meaning of the numbers represent - wait until you have a basic knowledge of statistics.

Thank you. You are right that I need statistics knowledge, and I am moving towards it.
I also understand that it's an algorithm. I even know that numerator reflect covariance, and in the denominator there is a multiplication of standard deviations.
But my question is not about statistical terms or there usage, but more about the meaning and logic of this multiplication, I assume that there is a simple math logic which I don't understand.
I am learning on my own.
Thank you!

 

[Svein]

As a start, check out this page: http://onlinestatbook.com/2/regression/intro.html.

 

[ducmod]

As a start, check out this page: http://onlinestatbook.com/2/regression/intro.html.

Thank you very much! :) This is such a golden mine! :)