Is this equation special somehow?

$$ \frac{\sum{xy}}{\sum{x}} $$

Can this be simplified or written alternately?

Or is this its most basic form already?

Sorry for not using the right mathematical terms here... mainly wondering if I should try to simplify this further before implementing in SIMD software

EDIT: Summation over finite Number of items, not infinite summation

  • 1
    $\begingroup$ What's the index of the summation? If it's $x$, then the sum just equals $y$: $$\frac{\sum_{x=1}^N xy}{\sum_{x=1}^N x} = y$$ $\endgroup$
    – Daniel P
    Jun 26, 2022 at 0:01
  • 3
    $\begingroup$ Assuming that $x_i$ is a weight then it's the weighted average of $y_i$. For example, if $x_i=1$, it's the standard mean. Apart from that, I don't see much other information here. $\endgroup$
    – PC1
    Jun 26, 2022 at 0:08
  • 1
    $\begingroup$ It is an expression not an equation, and might be better written $\dfrac{\sum\limits_{i=1}^n x_iy_i}{\sum\limits_{i=1}^n x_i}$ or perhaps $\dfrac{\mathbf{x \cdot y}}{\mathbf{x \cdot 1}}$ $\endgroup$
    – Henry
    Jun 26, 2022 at 0:28

1 Answer 1



It is the result of doing a linear least squares fit of $y=ax$ to a set of $(x, y)$ data points.


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