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I face a strange problem.

I have data $[X,Y]$ with no noise. If I plot $Y$ as a function of $X$, it looks like a straight line and the regression coefficient is quite good.

For the simplest model $$Y = 1 + aX\\ a = 0.328841508328634 ± 2.36619297413024\cdot 10^{-5}\\ \chi^2/doF = 0.00149066816255509\\ R^2 = 0.999325489519206$$

The problem is that, if I continue adding powers of X, the fit is better and better, all parameters stay highly significant.

However, whatever can be the degree of the polynomial, the residuals keep a sinusoidal shape. This probably reveals that I am using a wrong function. Can this symptom on residuals give an idea of a better function?

Thomas Andrews
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Claude Leibovici
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    It sounds like linear is actually the best model in this case. The sinusoidal appearance is normal when increasing the degree of the polynomial fit, and definitely suggests that increasing the degree is the wrong approach. – abiessu Sep 01 '13 at 05:03
  • @abiessu. I totally agree with all your statements but the sinusoidal appearance of the results happens for any degree (sure, smaller amplitudes). But does the trend of residuals indicate something to be done ? – Claude Leibovici Sep 01 '13 at 06:07
  • The best suggestion I have is to then go back to the source of the data and ask questions like "Does a linear model make sense for this data?" "What does a linear model imply about the data?" – abiessu Sep 01 '13 at 14:48

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