what does sxy mean

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What is S x y?

Intuitively, S x y is the result when you replace one of the x 's with a y.

Why is it important to calculate S x y and S x y at the beginning?

The pragmatic importance of this is that if you are doing a long question about linear regression, calculating S x x, S y y and S x y at the beginning can save you a lot of work.

What is the sum of the squares of the difference between each x and the mean x value?

S x x is the sum of the squares of the difference between each x and the mean x value.