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Determine slope intercept y=mx+b from 2 arrays

Posted on 2013-01-16
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Last Modified: 2013-01-18
Hi All -

Ironically, I'm quite handy with data, but pretty bad at Math.  I'm in the process of building a revenue forecasting tool and have a good way to forecast calls.  What I want to do now is apply a slope intercept formula to forecasted calls to guess how many orders those calls will yield.  

See the attached spreadsheet for an example of what I'm talking about.  You can ignore the formulas as i just used them to generate some example data.  What I really want to understand is how Excel comes up with the y=mx+b formula that it shows on the graph.  

Please explain the math to me as if I were in 6th grade (like i said... not my strong point).  

Also - please don't offer any suggestions on spreadsheet formulas I could use to apply the slope intercept as the tool isn't Excel based.  I just need to understand the "paper and pencil math" so i can re-produce it in-memory
Slope-for-EE.xlsx
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Question by:ducky801
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by:ozo
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PCableGuy earned 500 total points
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by:ozo
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Minimizing the sum of the squares of the differences between mx+b and y
gives the maximum likelyhood estimator under the assumption that the y values were produced from mx+b  +  independent Gaussian errors.

Taking the derivatives of the sum of the squares of the differences with respect to m and b
and setting them to 0 finds the minimum.
Each constraint is a linear equation on m and b, and solving them simultaneously gives
the standard formula.
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