Monday, April 28, 2003

Linear and Other Models

• different forms of models
• general linear model

Reading

Chapter 11 and class notes.

Homework

Problem: Let $x_1,\dots,x_n$ be constants, and suppose

$$Y_i = \beta_1(1-e^{-\beta_2 x_i}) + \varepsilon_i$$

with the $\varepsilon_i$ independent $N(0.\sigma^2)$ ramdom variables.

a.

Find the normal equations for the least squares estimators of $\beta_1$ and $\beta_2$.

b.

Suppose $\beta_2$ is known. Find the least squares estimator for $\beta_1$ as a function of the data and $\beta_2$.

Due Friday, May 2, 2003.