DMtutorial5 - Tutorial 6 1 Suppose m(x1 xp =(1 x1 p xp...

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Tutorial 6 1. Suppose m ( x 1 , ..., x p ) = φ ( α 1 x 1 + ... + α p x p ). Prove that ∂m ( x 1 ,...,x p ) ∂x 1 ∂m ( x 1 ,...,x p ) ∂x 2 ... ∂m ( x 1 ,...,x p ) ∂x p = φ 0 ( α 1 x 1 + ... + α p x p ) α 1 α 2 ... α p 2. For a single-index model Y = φ ( α > X ) + ε . Suppose ( X i , y i ) are the observations and the estimator for α is ˆ α . For a new point X 0 , predict the expectation of response using local linear kernel smoothing. 3. For the ozone concentration data . (a) fit a linear regression model and predict the ozone level when radiation=184.8, temperature=77.8, wind =9.9. (b) fit a partially linear regression model ozone = β 1 * termperature + β 2 * Wind + g ( Radiation ) + ε. predict the ozone level when radiation=184.8, temperature=77.8, wind =9.9.
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