I am trying to understand the intuition behind using multiplication, especially for the context of calculating things like the covariance, correlation, R-squared, etc.
for example, I know that, in general, multiplication is a form of fast summation (2+2+2 or 2*3), also it is form of representing scaling when you multiply a constant to a variable/vector (3x) or a way to extract the proportion of a value, like in the case of probabilities or percentages. But for the following formula I don't understand what the multiplication here is trying to do, because it is neither scaling or fast summation (although it is rigorously) (I apologise for pasting an image with the formula, but I am not very good with LaTex)
Covariance formula: $S_{xy}=\frac{\sum_i(x_i-\overline{x})(y_i-\overline{y})}{n-1}$
