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Correlation, simple formula, meaning

  1. May 18, 2015 #1
    1. The problem statement, all variables and given/known data

    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!

    2. Relevant equations

    3. The attempt at a solution
  2. jcsd
  3. May 18, 2015 #2


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    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.
  4. May 20, 2015 #3
    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. May 20, 2015 #4


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  6. May 21, 2015 #5
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