Hi,
I am reading the book "Mixed Effects Models in S and S-Plus" and come
across an example with the Rail data.
I tried to use lm(travel~Rail,data=Rail) and got the following result:
Call:
lm(formula = travel ~ Rail, data = Rail)
Residuals:
Min 1Q Median 3Q Max
-6.6667 -1.0000 0.1667 1.0000 6.3333
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 66.5000 0.9477 70.169 < 2e-16 ***
Rail.L 54.3032 2.3214 23.392 2.22e-11 ***
Rail.Q -4.6917 2.3214 -2.021 0.066161 .
Rail.C -2.6584 2.3214 -1.145 0.274458
Rail^4 -0.5669 2.3214 -0.244 0.811181
Rail^5 11.1919 2.3214 4.821 0.000418 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
I wonder how the model is represented. Is it correct to write: Travel beta1 +
beta2*Rail + error? Beta1 should be Intercept which is clear to me.
But how to link beta2 with the coefficients Rail.L, Rail.Q, Rail.C, Rail^4
and Rail^5 shown in the result?
Thanks for your comments,
Best,
Jing
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Have you read An Introduction to R or other R tutorial? DO you know about ordered factors and contrasts in linear models? -- Bert On Wed, Feb 6, 2013 at 5:00 AM, jing tang <gimmytang at gmail.com> wrote:> Hi, > I am reading the book "Mixed Effects Models in S and S-Plus" and come > across an example with the Rail data. > I tried to use lm(travel~Rail,data=Rail) and got the following result: > > Call: > lm(formula = travel ~ Rail, data = Rail) > > Residuals: > Min 1Q Median 3Q Max > -6.6667 -1.0000 0.1667 1.0000 6.3333 > > Coefficients: > Estimate Std. Error t value Pr(>|t|) > (Intercept) 66.5000 0.9477 70.169 < 2e-16 *** > Rail.L 54.3032 2.3214 23.392 2.22e-11 *** > Rail.Q -4.6917 2.3214 -2.021 0.066161 . > Rail.C -2.6584 2.3214 -1.145 0.274458 > Rail^4 -0.5669 2.3214 -0.244 0.811181 > Rail^5 11.1919 2.3214 4.821 0.000418 *** > --- > Signif. codes: 0 ?***? 0.001 ?**? 0.01 ?*? 0.05 ?.? 0.1 ? ? 1 > > > I wonder how the model is represented. Is it correct to write: Travel > beta1 + beta2*Rail + error? Beta1 should be Intercept which is clear to me. > But how to link beta2 with the coefficients Rail.L, Rail.Q, Rail.C, Rail^4 > and Rail^5 shown in the result? > > Thanks for your comments, > > Best, > Jing > > [[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. >-- Bert Gunter Genentech Nonclinical Biostatistics Internal Contact Info: Phone: 467-7374 Website: http://pharmadevelopment.roche.com/index/pdb/pdb-functional-groups/pdb-biostatistics/pdb-ncb-home.htm
to start with, you should now what kinds of independent variables in your data=Rail. it looks like you depend variable is "travel". is "Rail" the only IV in your model? it seems has been classifed to L, Q, C. from the output, it seems the final model should be: E(travel)=66.5+54*Rail.L-4.7 Rail.Q-2.6* Rail.C-0.57 *Rail^4+12*Rail^5 but, in order to get this output, your function should be lm(travel~Rail.L+ Rail.Q+ Rail.C+ Rail^4+Rail^5, data=Rail) ??? On Wed, Feb 6, 2013 at 7:00 AM, jing tang <gimmytang@gmail.com> wrote:> Hi, > I am reading the book "Mixed Effects Models in S and S-Plus" and come > across an example with the Rail data. > I tried to use lm(travel~Rail,data=Rail) and got the following result: > > Call: > lm(formula = travel ~ Rail, data = Rail) > > Residuals: > Min 1Q Median 3Q Max > -6.6667 -1.0000 0.1667 1.0000 6.3333 > > Coefficients: > Estimate Std. Error t value Pr(>|t|) > (Intercept) 66.5000 0.9477 70.169 < 2e-16 *** > Rail.L 54.3032 2.3214 23.392 2.22e-11 *** > Rail.Q -4.6917 2.3214 -2.021 0.066161 . > Rail.C -2.6584 2.3214 -1.145 0.274458 > Rail^4 -0.5669 2.3214 -0.244 0.811181 > Rail^5 11.1919 2.3214 4.821 0.000418 *** > --- > Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 > > > I wonder how the model is represented. Is it correct to write: Travel > beta1 + beta2*Rail + error? Beta1 should be Intercept which is clear to me. > But how to link beta2 with the coefficients Rail.L, Rail.Q, Rail.C, Rail^4 > and Rail^5 shown in the result? > > Thanks for your comments, > > Best, > Jing > > [[alternative HTML version deleted]] > > > ______________________________________________ > 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. > >[[alternative HTML version deleted]]