# Calculate Line Of Best Fit Using Exponential Weighting?

I know how to calculate a line of best fit with a set of data.
I want to be able to exponentially weight the data that is more recent so that the more recent data has a greater effect on the line.

How can I do this?

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Now, if only you could be more precise on how you expect "exponential weighing" to be done to your data... – J. M. Jul 30 '11 at 2:53

Hmm, you make it much general, by just saying "exponential". So just a general answer:

Define $d_i=now-time_i$ the time-difference of the i'th data-point to "now". If $d_i$ can be zero, add one: $d_i=1 + now - time_i$

Then use the concept of "weighting" for each datapoint: assume a weight $w_i = \exp(1/d_i)$ which is handled as $w_i$'th multiplicity of that datapoint. Unweighted, each datapoint occurs in the correlation/regression formula with multiplicity $1$ and, for instance the number of cases N is just the sum $N = \sum_{i=1}^n 1$ . Weighting means here to replace N by W: , $W = \sum_{i=1}^n w_i$ and analoguously in the computation of mean, variance and covariance include the weight instead of "1" in the formulae.

(While I'm writing this I just see, that the was an answer of Ross crossing, so this may be redundant meanwhile...)

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Most linear least squares algorithms let you set the measurement error of each point. Errors in point $i$ are then weighted by $\frac{1}{\sigma_i}$. So assign a smaller measurement error to more recent points. One algorithm is available for free in the obsolete version of Numerical Recipes, chapter 15.

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