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Moving Beyond Linearity The truth is never linear! 1 / 23 Moving - PowerPoint PPT Presentation

May 13, 2023 •40 likes •520 views

Moving Beyond Linearity The truth is never linear! 1 / 23 Moving Beyond Linearity The truth is never linear! Or almost never! 1 / 23 Moving Beyond Linearity The truth is never linear! Or almost never! But often the linearity assumption is

  1. Moving Beyond Linearity The truth is never linear! 1 / 23

  2. Moving Beyond Linearity The truth is never linear! Or almost never! 1 / 23

  3. Moving Beyond Linearity The truth is never linear! Or almost never! But often the linearity assumption is good enough. 1 / 23

  4. Moving Beyond Linearity The truth is never linear! Or almost never! But often the linearity assumption is good enough. When its not . . . • polynomials, • step functions, • splines, • local regression, and • generalized additive models offer a lot of flexibility, without losing the ease and interpretability of linear models. 1 / 23

  5. Polynomial Regression y i = β 0 + β 1 x i + β 2 x 2 i + β 3 x 3 i + . . . + β d x d i + ǫ i Degree−4 Polynomial 0.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 300 250 0.15 Pr ( Wage > 250 | Age ) 200 Wage 0.10 150 100 0.05 50 0.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | || | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 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  6. Details • Create new variables X 1 = X , X 2 = X 2 , etc and then treat as multiple linear regression. 3 / 23

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