Piecewise linear model: Let x̃ be a knownconstant, and suppose

Piecewise linear model: Let x̃ be a knownconstant, and suppose that a dependent variable y is related to an independent variable x1as follows:
Piecewise linear model: Let x̃ be a knownconstant, and suppose


In other words, y and x1 are linearly related, but different lines are appropriate depending on whether x1 ‰¤ x̃ or x1 > x̃. Define a new independent variable x2 by

so if x1 < ĩ X2 if x1 > ĩ


Also define β2 = βˆ—0ˆ’ β0 and β3 = βˆ—1ˆ’ β1. Find a multiple regression model involving y, x1, x2, β0, β1, β2, and β3 that expresses the relationship described here.