# Updating formula for the sample covariance and correlation online dating sites in united state of america

Along with the running sum or average, keep a copy of the oldest datum used to calculate it.

As the new datum arrives, subtract off the oldest one, add the newest one, and divide by the window width $W$.

If stability does become an issue for you there are some other things that can be done.

Let's say that at time $t$ you have $\bar x$, $\text$ and $s^2$, and an observation, $x_$ and you want to have those three computed quantities at time $t 1$.

Here's how you can update them: $t=t 1\ e_t = x_t-\bar x\quad\text \bar x \text \ \bar x = \bar x e_t/t \ \text = \text e_t\cdot (x_t-\bar x)\quad\text e_t^2\ s^2 = SSE/(t-1) $ This calculation is much more stable than the raw calculation of $\sum_i^t x_i^2$ version (which you'll find in many old books, and which is not too bad when working by hand, where you can see when you're losing precision).

Note that while statistically independent variables are always uncorrelated, the converse is not necessarily true.

In the special case of , so the covariance reduces to the usual variance .

In the absence of information to the contrary I assume you want univariate calculations and you want the $n-1$-denominator version of variance.

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