# [R] newbie problem using Design.rcs

David Winsemius dwinsemius at comcast.net
Tue Dec 23 14:20:35 CET 2008

```On Dec 22, 2008, at 11:38 PM, sp wrote:

> Hi,
>
> I read data from a file. I'm trying to understand how to use
> Design.rcs by using simple test data first. I use 1000 integer
> values (1,...,1000) for x (the predictor) with some noise (x+.02*x)
> and I set the response variable y=x. Then, I try rcs and ols as
> follows:
>
Not sure what sort of noise that is.

> m = ( sqrt(y1) ~ ( rcs(x1,3) ) ); #I tried without sqrt also
> f = ols(m, data=data_train.df);
> print(f);
>
> [I plot original x1,y1 vectors and the regression as in
> y <- coef2 + coef2*x1 + coef2*x1*x1]

That does not look as though it would capture the structure of a
restricted **cubic** spline. The usual method in Design for plotting a
model prediction would be:

plot(f, x1 = NA)

>
>
> But this gives me a VERY bad fit:
> "

Can you give some hint why you consider this to be a "VERY bad fit"?
It appears a rather good fit to me, despite the test case apparently
not being construct with any curvature which is what the rcs modeling
strategy should be detecting.

--
David Winsemius

> Linear Regression Model
>
> ols(formula = m, data = data_train.df)
>
>         n Model L.R.       d.f.         R2      Sigma
>      1000       4573          2     0.9897       0.76
>
> Residuals:
>      Min        1Q    Median        3Q       Max
> -4.850930 -0.414008 -0.009648  0.418537  3.212079
>
> Coefficients:
>             Value Std. Error      t Pr(>|t|)
> Intercept  5.90958  0.0672612  87.86        0
> x1         0.03679  0.0002259 162.88        0
> x1'       -0.01529  0.0002800 -54.60        0
>
> Residual standard error: 0.76 on 997 degrees of freedom
> "
>
> I appreciate any and all help!
>
> Sincerely,
> sp
>
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