Piecewise Linear Regression. Suppose that y is piecewise
Chapter 12, Problem 126MEE(choose chapter or problem)
Piecewise Linear Regression. Suppose that \(y\) is piecewise linearly related to \(x\). That is, different linear relationships are appropriate over the intervals \(-\infty<x \leq x^{*}\) and \(x^{*}<x<\infty\).
(a) Show how indicator variables can be used to fit such a piecewise linear regression model, assuming that the point \(x^{*}\) is known.
(b) Suppose that at the point \(x^{*}\) a discontinuity occurs in the regression function. Show how indicator variables can be used to incorporate the discontinuity into the model.
(c) Suppose that the point \(x^{*}\) is not known with certainty and must be estimated. Suggest an approach that could be used to fit the piecewise linear regression model.
Equation Transcription:
Text Transcription:
y
x
-\infty<x \leq x^*
x^*<x<\infty
x^*
x^*
x^*
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