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I used my TI-83 to find the quadratic regression of two data columns. The accuracy wasn't close at all. So I tried cubic and then finally quartic regression. The accuracy still isn't close enough. Is there any way I can improve the accuracy? I can't add any more data, unfortunetly.

Edit 1:

To address Henry's comment, my plotted data looks similar to y=x^(1/3)

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    If i$t$ is in fact a cube root, that explains why polynomials don't fit well. The cube root gets too flat for a polynomial. As I suggested below, taking the logarithm of all the data will check this. y=x^($1$/3) implies log(y)=(log(x))/3 and you should get a good linear fit.2011-05-20

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This may mean your data is poorly fit by a polynomial. Three ways it can fail is either to be exponential, to have poles, or be like a sine wave. Plotting the data with the fits you have overlayed may give you some ideas. If it is exponential, taking the logarithm of one will render it linear (or close to polynomial). If it has poles, using a rational function will help. Procedures are given in chapter 3.2 of Numerical Recipes. The obsolete versions are free. If it is a sine wave, an FFT can help-chapter 12 of NR.

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    Normally when you do a regression you get an equation that looks like y=f(x) where$x$is a polynomial. Your tool is probably giving you that, but you need to remember that you took the log of all your y values. So the output of the equation is the log of the y you should predict. Just exponentiate that y.2011-05-23
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If, as you say, it looks like $y=x^\frac{1}{3}$, then you might try a power regression, which will give you a formula of the form $y=ax^b$.