Continuation of Problem 8.7 . Show how indicator variables can be used to develop a piecewise linear regression model with a discontinuity at the join point $t$.

Problem 8.7

Piecewise Linear Regression. In Example 7.3 

we showed how a linear regression model with a change in slope at some point $t\left(x_{\min }

Example 7.3

An important special case of practical interest involves fitting piecewise linear regression models. This can be treated easily using linear splines. For example, suppose that there is a single knot at t and that there could be both a slope change and a discontinuity at the knot. The resulting linear spline model is E(y)=S(x)= Boo+Box+10(x-1) + B(x-1) Now if x t, the model is = E(y) Boo+Box+10 (1)+ B11(x-1) =(Boo+Bio-Bit)+(Boi + B11)