Correlation, simple formula, meaning

In summary, the conversation is about a math concept called correlation formula. The formula involves finding the mean of two sets of data, subtracting the mean from each value, and then calculating various sums and products. The purpose of this formula is to find the linear correlation between the two data sets. While the person asking the questions may not fully understand the logic behind the multiplication and division in the formula, they are aware that it involves statistical terms like covariance and standard deviations. They are seeking to gain a better understanding of the math behind the formula.
  • #1
ducmod
86
0

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

 
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  • #2
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.
 
  • #3
Svein said:
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!
 
  • #5

FAQ: Correlation, simple formula, meaning

What is correlation?

Correlation is a statistical measure that describes the relationship between two variables. It can range from -1 to 1, with 0 indicating no correlation and values closer to -1 or 1 indicating a strong negative or positive correlation, respectively.

What is the simple formula for calculating correlation?

The simple formula for correlation is r = (nΣXY - ΣXΣY) / √[(nΣX^2 - (ΣX)^2)(nΣY^2 - (ΣY)^2)], where n is the number of pairs of data, X and Y are the two variables, Σ represents the sum, and X^2 and Y^2 represent the squared values of X and Y, respectively.

What does a correlation coefficient of 0 mean?

A correlation coefficient of 0 means that there is no linear relationship between the two variables being analyzed. This does not necessarily mean that there is no relationship at all, as there could be a nonlinear relationship or a relationship that is not captured by the correlation coefficient.

Can correlation imply causation?

No, correlation does not imply causation. Just because two variables are strongly correlated does not mean that one causes the other. There could be other factors at play that are causing the relationship between the two variables.

What is the meaning of a negative correlation?

A negative correlation means that as one variable increases, the other variable decreases. In other words, there is an inverse relationship between the two variables. For example, as the temperature decreases, the number of ice cream sales may decrease.

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