Piecewise linear model: Let xÌ be a knownconstant, and suppose that a dependent variable y is related to an independent variable x 1 as follows:

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

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

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

so if x1 < X2 if x1 >