spring2013stat202-lecture07

spring2013stat202-lecture07 - Lecture 7 Wed Jan 30 36-202...

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Lecture 7 36-202 Wed, Jan. 30 Spring 2013 This document is available on: (under ‘course content’) Multiple Linear Regression [Reserve Material References: Chapter 13 of Statistics By Agresti and Franklin; Chapter 11 of Introduction to the Practice of Statistics by Moore, McCabe] Chapter 30 of Stats: Data and Models by Deveaux et al] In the previous series of lectures (lecture 3 through 6), we investigated models for explaining variability of a response Y using a single explanatory (predictor) variable X: Models we’ve seen for the relationship between Y and a single X: Simple (one X) Linear Regression model: Y = β 0 + β 1 X + ε i Simple (one X) Linear Regression model with Transformation: Y = β 0 + β 1 X transformed + ε i Quadratic Regression model with one X: Y = β 0 + β 1 X + β 2 X 2 + ε i Cubic Regression model with one X: Y = β 0 + β 1 X + β 2 X 2 + β 3 X 3 + ε i But the world is (of course) complicated, and very often we are interested in explaining how some Y is predicted from multiple explanatory (predictor) variables, X 1 , X 2 , … . The least complicated kind of model is where the contribution is linear from each variable. This gives rise to multiple linear regression .

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Statistics Lecture 7 Page 2 of 10 This document is available on: (under ‘course content’) The Multiple Linear Regression Model A model of the relationship in the population between a response variable Y and p -many explanatory (‘predictor’) variables X 1 , X 2 , … , X p . The Multiple Linear Regression Model proposes that the observed response is given by: y i = β 0 + β 1 x 1 i + β 2 x 2 i + . . . + β p x pi + ε i where the errors ε i are (as in the simple linear regression model) assumed to be: independent, and:
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