Lab 3 Slides

# Lab 3 Slides - Moving to multiple dimensions So far only...

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Moving to multiple dimensions So far, only worked with one covariate and one response variable Obviously not enough for most real-life situations Will often return to the simple linear model for insight into difficulties interpreting the higher dimensional problem Lecture 6 – p. 1/ ? ?

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Moving to multiple dimensions Old issues in multiple linear regression: Parameter estimation Hypothesis testing Confidence regions Diagnosis of residuals Lecture 6 – p. 2/ ? ?
Moving to multiple dimensions New issues in multiple linear regression: Model selection (which covariates) Simultaneous hypotheses Multi-collinearity (relationship of covariates to each other) Categorical covariates Interactions (effects of one variable depends on the values of another) Lecture 6 – p. 3/ ? ?

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Moving to multiple dimensions Still will work within a linear frame work Assume P covariates of interest and 1 response variable (conditional on covariates): y i = β 0 + β 1 x i 1 + ... + β P x iP + ǫ i E ( ǫ i ) = 0 and V ar ( ǫ i ) = σ 2 , ǫ i assumed to be uncorrelated Lecture 6 – p. 4/ ? ?
What is linear? Defined as a model that is linear in the parameters, not

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## This note was uploaded on 01/15/2010 for the course MATH 423 taught by Professor Steele during the Spring '06 term at McGill.

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Lab 3 Slides - Moving to multiple dimensions So far only...

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