Solution to Tutorial 6

# Solution to Tutorial 6 - Solution to Tutorial 6 1. For each...

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

Solution to Tutorial 6 1. For each of the following regression models, indicate whether it is a general linear regression model. If not, state whether it can be expressed in the form of a linear regression model after some suitable transformation a. Y i = β 0 + β 1 X i 1 + β 2 log X i 2 + β 3 X 2 i 1 + ε i b. Y i = ε i exp( β 0 + β 1 X i 1 + β 2 X 2 i 2 ) ,w i t h ε i > 0 c. Y i = β 0 log( β 1 X i 1 )+ ε i d. Y i =log( β 1 X i 1 β 2 log X i 2 + ε i e. Y i =[1+exp( β 0 + β 1 X i 1 + ε i ] - 1 No of these are linear models, but a, b, d e can be transformed to linear regression models 2. Consider the multiple linear regression models Y i = β 1 X i 1 + β 2 X i 2 + ε i ,i =1 , ..., n where ε i are uncorrelated with i =0and 2 i = σ 2 state the least square criterion and derive the least squares estimators for β 1 and β 2 . Let Q ( b 1 ,b 2 )= n X i =1 { Y i - b 1 X i 1 - b 2 X i 2 } 2 by calculus, we have dQ ( b 1 2 ) db 1 = - 2 n X i =1 { Y i - b 1 X i 1 - b 2 X i 2 } X i 1 dQ ( b 1 2 ) db 2 = - 2 n X i =1 { Y i - b 1 X i 1 - b 2 X i 2 } X i 2 The normal equations are n X i =1 X 2 i 1 b 1 + n X i

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.

## This note was uploaded on 10/04/2010 for the course STAT ST3131 taught by Professor Xiayingcun during the Fall '09 term at National University of Singapore.

### Page1 / 2

Solution to Tutorial 6 - Solution to Tutorial 6 1. For each...

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

View Full Document
Ask a homework question - tutors are online