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mlr-further issues

# mlr-further issues - MLR Further Issues MLR 1 2 3...

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MLR : Further Issues MLR : Further Issues 1. Functional Forms 1. Functional Forms 2. Adjusted R 2. Adjusted R - - squared squared 3. 3. Heteroskedasticity Heteroskedasticity

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A. Functional Forms A. Functional Forms capture non-linearities 1. Log 1. Log - functional forms functional forms more possibilities in interpretation y : level, x : level marginal effect y : log, x : level semi – elasticity x = 1 100( β ) % y : log, x : log elasticity x = 1% β % 2. Quadratics 2. Quadratics decreasing/increasing marginal effects l l l l 2 0 1 2 y x x β β β = + + l l 1 2 2 ~ marginal effect of x on y x x β β = + l l l 1 2 : 0 2 y inflection point x x β β = =
3. Models with interaction terms. 3. Models with interaction terms. marginal effect of a x depends on the magnitude on another x. e.g. if ( sqrtft ) = 0 not interesting interpretation reparameterization e.g. l l l l l 0 1 1 2 2 3 1 2 ( ) y x x x x β β β β = + + + n l l l l 0 1 2 3 ( ) ( ) ( )( ) hprice sqrtft rooms sqrtft rooms β β β β = + + + n l l 2 3 ( ) ( )

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