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I just have a quick question on quadratic equations, if we are given a whole bunch of data when plotted, it gives us some quadratic relationship. But I tried to use the old fashioned way to find this approximate equation by finding $c$ at $x =0,$ and: $$y_1=ax_1^2+bx_1+c$$ $$y_2=ax_2^2+bx_2+c$$ I come to find that the area of the curve in the excel from say $x_1$ to $x_{10}$ is significantly different to what I found using the curve that I have found using simultaneous equations integrating from $x_1$ to $x_{10}.$

So my question is how do we find a good approximate for a quadratic equation when we are given some set of data which exhibits a quadratic relationship?

Aurora Borealis
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  • If your are sure it is quadratic equation then we have three unknowns a, b and c. In your assumed equation substitute any three (x, y) and solve three equations for a, b and c – Fawad Oct 27 '18 at 04:06
  • When you say mention the curve in excel, are you using the quadratic regression curve fit that excel gives you? – D.B. Oct 27 '18 at 04:07
  • The a b c is indeed what I found, but as I have mentioned the area of the curve i found using these a b c via integration gives a wide error gap between the better equation given on excel via integration. – Aurora Borealis Oct 27 '18 at 05:21

1 Answers1

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You can try to do an OLS estimation. There's a function in Excel to do that, is called LINEAR.ESTIMATE or something similar. What this function does is finding the values for $a, b$ and $c$ that best fit your data. "Best fit" means, in this context, the values that make the $\sum_{i=1}^n (y_i - a x_{i}^2 - b x_i - c)^2$ as small as possible.

Patricio
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