R help - Oct 2008 - Statistically significant in linear and non-linear model

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, 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

 

 

 


	[[alternative HTML version deleted]]

Well here is one example where x is not significant in a linear regression:
> x <- seq( -1,1, 0.1 )
> y <- x^2 + rnorm(21,0,.1)
> summary(lm(y~x))
Would you really want to dismiss any relationship (non-linear) between x and y
based on the above p-value?

--
Gregory (Greg) L. Snow Ph.D.
Statistical Data Center
Intermountain Healthcare
greg.snow at imail.org
801.408.8111

> -----Original Message-----
> From: r-help-bounces at r-project.org [mailto:r-help-bounces at r-
> project.org] On Behalf Of Hsiao-nan Cheung
> Sent: Tuesday, October 07, 2008 11:47 AM
> To: R-help
> Subject: [R] Statistically significant in linear and non-linear model
>
> 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, 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
>
>
>
>
>
>
>
>
>         [[alternative HTML version deleted]]
>
> ______________________________________________
> R-help at 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.

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.

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E-Mail: (Ted Harding) <Ted.Harding at manchester.ac.uk>
Fax-to-email: +44 (0)870 094 0861
Date: 07-Oct-08                                       Time: 19:16:04
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