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Default Trendline equation calculation

Equations generated by Excel for trendlines do not seem to match those
derived from the coeffiecients of a regression analysis.
And, when re-plotting data recalculated from the trendline equation for
original data, it is not the same - however when fitting a trendline to this
re-plotted data the same equation as the oringinal data is displayed!
Am I not writing the equation correctly, is this a genuine discrepency? Am
especially interested in polynomial fitted trendlines.
Many Thanks
 
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