STAT 541: Regression intro

# Statistics 541: Regression introduction

## Admistrivia

• Return notes to student
• Anyone figure out how to get JMP to do a trimmed mean?
• Read chapter 1 of Myers Read sections 2.1-3, 2.9

## Regression introduction

Basic structure and goals (chapter 1)
• Y = beta0 + beta1 X1 + ... + betap Xp + epsilon
• Goals
• prediction
• Causation (see talk this afternoon: 4:30 Paul Holland 111 Annenburg. A "big gun.")
• The betas might actually be interesting themselves
• We will focus on how to tell if your regression is statistically legitimate
• Leave you to decide if it makes any sceintific sense

## Simple linear regression (Chapter 2 from Myers)

Basic structure

• Simple means only 1 x variable (called independent variables, but I rarely use that termonology.)
• slope and intercept/centercept
Least squares
• minimize sum (y - y-hat)2

minimize sum (y - b0 + b1 X)2

Now define c = b0 + Y-bar - b1 X-bar is the deviation from the centercept.

• b1 = Sxy/Sxx
• c = 0
• b0 = Y-bar - b1 X-bar
Don't leave anything on the table approach:
• residuals = (y - y-hat) shouldn't be predicatable from X
• Residuals should have zero mean
• So residuals should be uncorrelated with X
• E(Y - b0 - b1) = 0
• Cov(Y - b0 - b1 X,X) = 0
See book for how to derive standard errors
• E(estimate) = true paramenter (unbiased)
• Var(slope) = sigma2/Sxx
• Var(centercept) = sigma2/n
• Var(intercept) = sigma2(1/n + x-bar2//Sxx)
Estimate the error by MSE

## Using JMP and bluging rule

• Display (A lage chain of liquor stores would like to konw how much display space in its stores to devote to a new wine. Management believes that most products generate about \$50 in sales per linear shelf-foot per month.)
• Tukey's bulging rule by hand and by picture

Last modified: Thu Jan 25 08:31:40 2001