Transcription of Lecture Notes #7: Residual Analysis and Multiple ...
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Lecture Notes #7: Residual Analysis and Multiple ...
Lecture Notes #7: Residual Analysis and Multiple Regression7-1 Richard GonzalezPsych 613 Version (Nov 2021) Lecture Notes #7: Residual Analysis and Multiple RegressionReading AssignmentKNNL chapter 6 and chapter 10; CCWA chapters 4, 8, and 101. Statistical assumptionsThe standard regression model assumes that the residuals, or s, are independently, identi-cally distributed (usually called iid for short) as normal with = 0and variance 2.(a) IndependenceA Residual should not be related to another Residual . Situations where independencecould be violated include repeated measures and time series because two or more resid-uals come from the same subject and hence may be correlated. Another violation ofindependence comes from nested designs where subjects are clustered (such as in thesame school, same family, same neighborhood). There are regression techniques thatrelax the independence assumption, as we saw in the repeated measures section of thecourse.(b) Identically distributedAs stated above, we assume that the residuals are distributed N(0, 2 ).
relax the independence assumption, as we saw in the repeated measures section of the course. (b)Identically distributed As stated above, we assume that the residuals are distributed N(0, σ2 ϵ). That is, we assume that each residual is sampled from the same normal distribution with a mean of zero and the same variance throughout.
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