Find the meaning of 'Sxx' and 'Sxy' in simple linear regression

Bailee Richards

Bailee Richards

Answered question


Find the meaning of 'Sxx' and 'Sxy' in simple linear regression

Answer & Explanation



Beginner2022-11-27Added 6 answers

S x x is the sum of the squares of the difference between each x and the mean x value.
S x y is sum of the product of the difference between x its means and the difference between y and its mean.
So S x x = Σ ( x x ¯ ) ( x x ¯ ) and S x y = Σ ( x x ¯ ) ( y y ¯ ). Both of these are often rearranged into equivalent (different) forms when shown in textbooks.
Reece Black

Reece Black

Beginner2022-11-28Added 2 answers

S x x = x 2 ( x ) 2 n = x 2 n x ¯ 2
Intuitively, S x y is the result when you replace one of the x's with a y.
S x y = x y x y n = x y n x ¯ y ¯
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 = x y n x ¯ y ¯ ( x 2 n x ¯ 2 ) ( y 2 n y ¯ 2 ) = S x y S x x S y y
or to find the gradient of the best-fit line y=a+bx:
y y ¯ = b ( x x ¯ ) ,  where  b = S x y S x x

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