BENG449 Problem 6 2

# BENG449 Problem 6 2 - BENG449 Problem Set 6 Question 2 Alex...

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

BENG449 – Problem Set 6, Question 2 Alex Lemon March 11, 2008 1 Part A The plot of S ( b 1 , b 2 ) is a three-dimensional graph in which the height of the graph above the b 1 - b 2 plot gives the value of the residual sum of squares if the noisy data is estimated using the double-exponential model with the given parameter values. On the speciFed region, S ( b ) appears to be globally convex with a minimum corresponding to the OLS estimates for β 1 and β 2 . In the Frst trial, this optimization point was found to be at b 1 = 0 . 0490 and b 2 = 0 . 0200; in the second trial, the OLS estimates were b 1 = 0 . 0520 and b 2 = 0 . 0190. 2 Part B There are two ways to think about whether or not S ( b ) is a noisy function. On the one hand, S ( b ) is a smooth function of b 1 and b 2 , so the three-dimensional plot of the residual sum of squares versus the parameter values is a smooth function. When we generate noisy data, we usually expect to see random vari- ation around some underlying relationship with the result that a plot of the noisy data is not in general a smooth function. However, the plot of S ( b ) is a smooth function of the parameter values, b 1 and b 2 . On the other hand, S ( b ) is a function of the noisy data that was generated, and in this sense, the graph

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 07/19/2008 for the course BENG 449 taught by Professor Richardcarson during the Spring '08 term at Yale.

### Page1 / 7

BENG449 Problem 6 2 - BENG449 Problem Set 6 Question 2 Alex...

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

View Full Document
Ask a homework question - tutors are online