Linear Regression Basics II Fin250f: Lecture 7.1 Spring 2010 Brooks, chapter ,3.7, 3.8

Outline  Matrix introduction  Multivariate linear model Standard errors Matlab OLS function  What’s a big sample?  Data mining  Goodness of fit

Matrices (Appendix A5)

Matrices

Even More Matrices: Transpose

Multivariate Linear Model

Least Square Solution

Matlab Code  OLS function (ols.m)  Setting up CRSP data (ccrspmat.m)  Example: Estimating CAPM beta rollingcapm.m  Example: Simple return forecast simpleretfcast.m  Example: Monday returns? monday.m

What’s a Large Sample?  Asymptotic results T goes to infinity  When are these results valid?  Depends Complexity/stationarity of data Complexity of model

Data Snooping (see 3.7)  For finite data can always find something positive Significant beta Accurate forecasts Profitable trades  “In sample bias”  “mclinearsnoop.m”  Snooping versus Mining

Goodness of Fit and other Objectives  How good is a “fit” or a forecast?  Basic objective function

Various Measures

Traditional: R-squared (R^2)

R^2  Good Easy and intuitive  Bad Not well defined statistically Always improves with more parameters  (See adjusted R^2) Can often be high when there are time trends Not well defined objective