{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

# DMtutorial5s - Tutorial 6 suggested solutions 1 Suppose...

This preview shows pages 1–2. Sign up to view the full content.

Tutorial 6: suggested solutions 1. Suppose m ( x 1 , ..., x p ) = φ ( α 1 x 1 + ... + α p x p ). Prove that ∂m ( x 1 ,...,xp ) ∂x 1 ∂m ( x 1 ,...,xp ) ∂x 2 ... ∂m ( x 1 ,...,xp ) ∂xp = φ ( α 1 x 1 + ... + α p x p ) α 1 α 2 ... α p proof: Because ∂m ( x 1 , ..., x p ) ∂x k = φ ( α 1 x 1 + ... + α p x p ) α k 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 , predict the expectation of response using local linear kernel smoothing. the prediction value is ˆ g α X ) = n i =1 { s n, 2 α X ) K h α ( X i - X )) - s n, 1 α X ) K h α ( X i - X ))ˆ α ( X i - X ) /h } Y i s n, 2 α X ) s n, 0 α X ) - s 2 n, 1 α X ) where s n,k α X ) n i =1 K h α ( X i - X )) { ˆ α ( X i - X ) /h } k , k = 0 , 1 , 2 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 * W ind + g ( Radiation ) + ε. predict the ozone level when radiation=184.8, temperature=77.8, wind =9.9. (c) fit a single-index model and predict the ozone level when radiation=184.8, temperature=77.8, wind =9.9. and what is the prediction confidence interval for the expectation of Y . (a) The fitted regression model is

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 2

DMtutorial5s - Tutorial 6 suggested solutions 1 Suppose...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online