Polynomial regression: Difference between revisions

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=={{header|R}}==

The easiest (and most robust) approach to solve this in R is to use the base package's ''lm'' function which will find the least squares solution via a QR decomposition:

R has several tools for fitting. Here we use a generalized nonlinear least squares method with the polynomial as model:

<lang R>~~library(nlme)~~

x <- c(0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10)

x <- c(0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10)i

y <- c(1, 6, 17, 34, 57, 86, 121, 162, 209, 262, 321)

coef(lm(y ~ x + I(x^2)))</lang>

fitted <- gnls(y ~ c0*x^2 + c1*x + c2, start=list(c0=1, c1=1, c2=0))

print(paste(fitted$coeff[[1]], "*x^2 + ",

fitted$coeff[[2]], "*x + ",

fitted$coeff[[3]]))

'''Output'''

# get several info about the fitting process

print(summary(fitted))</lang>

(Intercept) x I(x^2)

1 2 3

</lang>

The "base" <tt>nls</tt> could be used with algorithm "port", since the default Gauss-Newton has problems recognizing the convergence:

<lang R>nls(y ~ c0*x^2 + c1*x + c2, start=list(c0=1, c1=1, c2=0), trace=TRUE)</lang>

gives

5.364254e-29 : 3 2 1

Error in nls(y ~ c0 * x^2 + c1 * x + c2, start = list(c0 = 1, c1 = 1, :

number of iterations exceeded maximum of 50

And even increasing the maximum possible iterations, it does not finish properly (even if the result, as we can see with the trace option, is reached!). Instead, the

<lang R>nls(y ~ c0*x^2 + c1*x + c2, start=list(c0=1, c1=1, c2=0), algorithm="port")</lang>

works fine.

=={{header|Ruby}}==