On 07-Oct-08 17:46:52, Hsiao-nan Cheung wrote: > Hi, > I have a question to ask. if in a linear regression model, the > independent variables are not statistically significant, is it > necessary to test these variables in a non-linear model? > Since most of non-linear form of a variable can be represented > to a linear combination using Taylor's theorem,
That depends on the coefficients in the Taylor's series expansion. It is quite possible to have the linear coefficient zero, and the quadratic coefficient non-zero. > so I wonder whether the non-linear form is also not statistically > significant in such a situation. > > Best Regards > Hsiao-nan Cheung > 2008/10/08 Example: X <- 0.2*((-10):10) Y <- 0.5*(X^2) + 0.2*rnorm(21) X2 <- X^2 [A] Linear regression, Y on X: summary(lm(Y ~ X))$coef # Estimate Std. Error t value Pr(>|t|) # (Intercept) 0.72840442 0.1554215 4.6866382 0.0001606966 # X 0.06570652 0.1283351 0.5119919 0.6145564688 So the coefficient of X is not significant. [B] Quadratic regression, Y on X and X^2: summary(lm(Y ~ X + X2))$coef # Estimate Std. Error t value Pr(>|t|) # (Intercept) 0.003425041 0.07203265 0.04754846 9.625997e-01 # X 0.065706524 0.03957727 1.66020864 1.141924e-01 # X2 0.494304121 0.03666239 13.48259513 7.570563e-11 So the coefficient of X is still not significant (P = 0.14), but the coefficient of X^2 is *highly* significant! So it all depends ... of course the original coefficients (Taylor) could be anything. Ted. -------------------------------------------------------------------- E-Mail: (Ted Harding) <[EMAIL PROTECTED]> Fax-to-email: +44 (0)870 094 0861 Date: 07-Oct-08 Time: 19:16:04 ------------------------------ XFMail ------------------------------ ______________________________________________ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
