# The interpretation of lm(y~x)?

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## The interpretation of lm(y~x)?

 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]] ______________________________________________ [hidden email] mailing list https://stat.ethz.ch/mailman/listinfo/r-helpPLEASE do read the posting guide http://www.R-project.org/posting-guide.htmland provide commented, minimal, self-contained, reproducible code.
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## Re: The interpretation of lm(y~x)?

 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 <[hidden email]> 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]] > > > ______________________________________________ > [hidden email] 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______________________________________________ [hidden email] mailing list https://stat.ethz.ch/mailman/listinfo/r-helpPLEASE do read the posting guide http://www.R-project.org/posting-guide.htmland provide commented, minimal, self-contained, reproducible code.