# [R] The explanation of ns() with df =2

Michael Friendly friendly at yorku.ca
Tue Apr 15 14:18:40 CEST 2014

```No, the curves on each side of the know are cubics, joined
so they are continuous.  Se the discussion in \S 17.2 in
Fox's Applied Regression Analysis.

On 4/15/2014 4:14 AM, Xing Zhao wrote:
> Dear all
>
> I understand the definition of Natural Cubic Splines are those with
> linear constraints on the end points. However, it is hard to think
> about how this can be implement when df=2. df=2 implies there is just
> one knot, which, according the the definition, the curves on its left
> and its right should be both be lines. This means the whole line
> should be a line. But when making some fits. the result still looks
> like 2nd order polynomial.
>
>
> Thanks
> Xing
>
> ns(1:15,df =2)
>                1           2
>   [1,] 0.0000000  0.00000000
>   [2,] 0.1084782 -0.07183290
>   [3,] 0.2135085 -0.13845171
>   [4,] 0.3116429 -0.19464237
>   [5,] 0.3994334 -0.23519080
>   [6,] 0.4734322 -0.25488292
>   [7,] 0.5301914 -0.24850464
>   [8,] 0.5662628 -0.21084190
>   [9,] 0.5793481 -0.13841863
> [10,] 0.5717456 -0.03471090
> [11,] 0.5469035  0.09506722
> [12,] 0.5082697  0.24570166
> [13,] 0.4592920  0.41197833
> [14,] 0.4034184  0.58868315
> [15,] 0.3440969  0.77060206
> attr(,"degree")
> [1] 3
> attr(,"knots")
> 50%
>    8
> attr(,"Boundary.knots")
> [1]  1 15
> attr(,"intercept")
> [1] FALSE
> attr(,"class")
> [1] "ns"     "basis"  "matrix"
>

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Michael Friendly     Email: friendly AT yorku DOT ca
Professor, Psychology Dept. & Chair, Quantitative Methods
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