The interpretation of lm(y~x)?

[gimmytang]

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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[Bert Gunter]

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-- 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: [phone]
Website:
http://pharmadevelopment.roche.com/index/pdb/pdb-functional-groups/pdb-biostatistics/pdb-ncb-home.htm

______________________________________________
[hidden email] mailing list
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PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.

[Alice Xiong]

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 <[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.
>
>

        [[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.

[gimmytang]

Hi,
Thanks for the answers. My original post is ask help on the interpretation of the result such as what does Rail.L, Rail.Q and Rail.C mean? The Rail variable is a factor which contains 6 levels.  I do not understand how these 6 levels are represented in the result.

Best,
Jing