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ax³ + bx² + cx + d is just the general form of any cubic equation. If the software you downloaded can do regression then it should be able to tell you what those values are.
Excel can do regression too, and it says that the formula should be
y = 0.1481x³ - 0.5873x² - 0.2751x + 20.667.Those are all rounded to 5 figures, so they're not exact. Fractional form would be a lot more useful, but Excel doesn't do that.
As for making x the subject, it's considerably harder to do that for cubics than it is for quadratics. It's possible, but usually left to a computer.
Ok it was a step too far and reading further I would need those abcd numbers which would be a pain to use.
The software doesn't tell me what those numbers are although it looks as if it should.
Thanks anyway.
some follow up. It seems the curve is mostlikely a "cubic spline". There's some really nice free software for doing regression on curves
http://www.ebicom.net/~dhyams/cmain.htm
so I downloaded it and applied the cubic spline and it gives formula:
y = ax³ + bx² + cx + d
but that raises the question for me of: where or what are a b c and d and how do I rearrange the formula so that I have x = f(y)
thanks again.
ps, The software allows generating a lookup table but the formula of x = f(y) would be useful.
thanks very much. That has saved me a lot of head scratching.
Maybe one day I'll understand this maths stuff.
Thanks guys,
so if I understand this correctly, to calculate the difference on the x axis (which is what I need to do) between any two readings I would have to solve:
reading1 = 20 + x1^2 +(x1-2)^2
reading2 = 20 + x2^2 +(x2-2)^2
I would have to calculate x1 and x2. then find the square root of each and then subtract root of x1 from root of x2 to give me the dfference along the x axis.
so I think I know what to do, but the problem for me is that I haven't solved any equations like this for 35 years and I've completely forgotten how to do it.
any clues gratefully received,
thanks
Hi,
I have taken some measurements which are:
21,24,29,38,53,72
the unit of difference between each measurement is 1 (actually 1 stop of light less for each measurement. i.e. half the brightness each time).
the measuring device is obviously not linear in its response. Is there a way to calculate a formula to apply to reulting measuremnts so that when graphed the line is linear? The curve currently produced seems quite smooth so I thought it may be possible to do this.
thank you.
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