Piecewise linear model: Let xÌƒ be a knownconstant, and suppose that a dependent variable y is related to an independent variable x_{1}as follows:

In other words, y and x_{1} are linearly related, but different lines are appropriate depending on whether x_{1} ‰¤ xÌƒ or x_{1} > xÌƒ. Define a new independent variable x_{2} by

Also define Î²_{2} = Î²^{ˆ—}_{0}ˆ’ Î²_{0} and Î²_{3} = Î²^{ˆ—}_{1}ˆ’ Î²_{1}. Find a multiple regression model involving y, x_{1}, x_{2}, Î²_{0}, Î²_{1}, Î²_{2}, and Î²_{3} that expresses the relationship described here.

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