Psychology 202a Advanced Psychological Statistics October 27, 2015

The plan for today Continuing correlation and regression The decomposition of the sum of squares Regression inference Assumptions The problem of restriction of range Another way to understand correlation

Decomposing the sum of squares Recall that the model can be broken down into two components: –the part we do understand –the part we don’t understand The sum of squares can be broken down into corresponding components. These components have the same additive relationship as the model components.

Decomposition (cont.) This decomposition of variability is the basis for inference in regression. Mean squares The F ratio The ANOVA table

The ANOVA Table SourceSSdfMSF Model Error Total

The ANOVA Table SourceSSdfMSF Model Error Total

The ANOVA Table SourceSSdfMSF Model1 ErrorN - 2 TotalN - 1

The ANOVA Table SourceSSdfMSF Model1SS M / df M ErrorN – 2SS E / df E TotalN - 1

The ANOVA Table SourceSSdfMSF Model1 SS M / df M MS M / MS E ErrorN – 2 SS E / df E TotalN - 1

Assumptions for inference Linear relationship Independent errors Homoscedastic errors Normally distributed errors (digression in R)