I want to fit cubic spline functions with 5 B-spline basis functions to my data. In this case I have 9 knots as following : k1, k2, k3, k4, k5, k6, k7, k8, k9. k4 and k6 are boundary knots and k5 is interior knot. That is, the interval [k4,k6] is interesting interval and the data is in this interval. k3 is an exterior knot that I want to predict for it. How can I do this? Is there a way?

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