What is the meaning of 'Sxx' and 'Sxy' in simple

Margie Marx 2021-12-14 Answered
What is the meaning of Sxx and Sxy in simple linear regression? I know the formula but what is the meaning of those formulas?
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Expert Answer

Cheryl King
Answered 2021-12-15 Author has 36 answers

Sxx is the sum of the squares of the difference between each x and the mean x value.
Sxy is sum of the product of the difference between x its means and the difference between y and its mean.
So Sxx=(xx)(xx) and Sxy=(xx)(yy). Both of these are often rearranged into equivalent (different) forms when shown in textbooks.

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psor32
Answered 2021-12-16 Author has 33 answers

To add to the answer from above,
Sxx=x2(x)2n=x2nx2
Intuitively, Sxy is the result when you replace one of the x's with a y.
Sxy=xyxyn=xynxy
Also, just for your information, the good thing about this notation is that it simplifies other parts of linear regression.
For example, the product-moment correlation coefficient:
r=xynxy(x2nx2)(y2ny2)=SxySxxSyy
or to find the gradient of the best-fit line y=a+bx:
yy=b(xx),where b=SxyS×
The pragmatic importance of this is that if you are doing a long question about linear regression, calculating Sxx,Syy and Sxy at the beginning can save you a lot of work.

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