Piecewise linear model Let x Igrave 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 curren x Igrave or x 1 x Igrave Define a ...

Piecewise linear model: Let xÌ be a knownconstant, and suppose that a dependent variable y is related

Question:

Piecewise linear model: Let xÌƒ 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

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 ‰¤ xÌƒ or x₁ > xÌƒ. Define a new independent variable x₂ by

so if x1 < ĩ X2 if x1 > ĩ

Also define Î²₂ = Î²^ˆ—₀ˆ’ Î²₀ and Î²₃ = Î²^ˆ—₁ˆ’ Î²₁. Find a multiple regression model involving y, x₁, x₂, Î²₀, Î²₁, Î²₂, and Î²₃ that expresses the relationship described here.