2. Consider a natural cubic spline model with two knots at ci and c2 given by y = Bo + B1r+ B2(r - c1) + Ba(r - ce2) +, where B2 + Ba = 0 and Bac1 + B3c2 = 0. Let f(r) = Bo + Bir + B2(r - c1) + Ba(r - c2) Assume that ci C2.

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.2: Determinants
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2. Consider a natural cubic spline model with two knots at ci and c2 given by
y = Bo + Bir+ B2(r – c1) + Ba(r - c2) +€,
where B2 + Ba = 0 and Bzci + Bzc2 = 0. Let f(r) = Bo + B1r + B2(r – cı) + Ba(r - c2). Assume that
ci < c2. Show that f(x) is a linear function whenever r < c2 or r> c2.
%3D
Transcribed Image Text:2. Consider a natural cubic spline model with two knots at ci and c2 given by y = Bo + Bir+ B2(r – c1) + Ba(r - c2) +€, where B2 + Ba = 0 and Bzci + Bzc2 = 0. Let f(r) = Bo + B1r + B2(r – cı) + Ba(r - c2). Assume that ci < c2. Show that f(x) is a linear function whenever r < c2 or r> c2. %3D
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