[R] Using R for Multiple Regression

[(Ted Harding)]

On 30-Jul-10 15:07:46, Ambikesh Jayal wrote:
> Hi,
> Subject: Using R for Multiple Regression
> 
> I am new to statistic but am interested in applying mathematical
> models to solve biological problems. I have used a linear model
> to generate the test data. When using this data I expect R to
> correctly identify the model but that does not seem to be the case.
> I am certain that I am doing something wrong but not able to figure
> it out.
> 
> Model:
> Y = m1x1 + m2x2+ m3X3 + c
> 

> 
> Model Identified by R using lm(formula = y ~ x1 + x2 + x3)
> (Intercept) 8.000e+01
> x1          1.100e+01
> x2                 NA
> x3                 NA
> 
> 
> The data I am using is as follows:
> 
> y x1 x2 x3
> 91 1 14 2
> 102 2 15 5
> 113 3 16 8
> 124 4 17 11
> 135 5 18 14
> 146 6 19 17
> 157 7 20 20
> 168 8 21 23
> 179 9 22 26
> 190 10 23 29
> 
> Kind regards
> Dr. Ambikesh Jayal,

You should look again at your data!

You have x2 = 13 + x1, x3 = 3*x1 - 1 in these data.
Hence your model

  Y = m1*x1 + m2*x2+ m3*X3 + c

with m1=5, m2=6, m3=0, c=2 is the same as

  Y = 5*x1 + 6*(x1+13) + 0*(3*x1 - 1) + 2
    = 11*x1 + 6*13 + 2
    = 11*x1 + 80

and R has found that the coefficient of x1 is 1.100e+01 = 11,
and that the intercept is 8.000e+01 = 80, and has also identified
that, after allowing for x1, x2 and x3 are irrelevant.

So, to try out how R behaves in linear regression, you should
use data which do not have this property that some of the independent
variables (x1,x2,x3) are linear functions of the others.

However, in trying it out as you have, you have already found out
something very important about linear regression! (And about R).

Hoping this helps,
Ted.

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Date: 30-Jul-10                                       Time: 17:59:51
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