I have been working on a single dimensional data and trying to fit a linear model. The constraints i have is i cannot use the built in polynomial fitting functions. Thus i need to find how well my data fits using residuals and residual plots. I know polynomial regression is a linear model in terms of coefficients hence i thought analyzing residual plot would be a good idea. Also i know the rule of thumb: if residual plot shows no particular pattern then you are good. But what i am confused about is : Does this property or rule of thumb applies in all cases? In both linear and polynomial regression? Do i have any similar measures to measure the goodness of the fit?

Some further notes about my model :

$ y = \beta_{0} + \beta_{1} x + \beta_{2}x^2 ........+\beta_{k}x^k$

i want to figure the best degree of polynomial which fits my model. At each iteration i need to figure out the goodness of my model hence the correct interpretation of residuals is important.

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    $\begingroup$ Is this a school assignment? If not, why can't you use built-in functions? If it is a school assignment, please add the self-study tag and see meta.stackoverflow.com/questions/334822/… $\endgroup$ – Peter Flom - Reinstate Monica Aug 20 '17 at 11:32
  • $\begingroup$ I would really appreciate if i could instead get some resource to study about error measures for polynomial regression. I am willing to complete my assignment on my own didnt ask anyone to write my code. Redirecting to some long meta post which would hurt my deadlines is so not a considerable thought for me at the moment @Peter Flom $\endgroup$ – Shubham Singh rawat Aug 23 '17 at 15:59

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