Linear regression
•Describes asymetric dependence of two quantitative variables
•Response variable depends on predictor(s)
•General formula: Y = a + bX + ε
•Y = response
•X = predictor
•a = intercept
•b = slope
•ε = residuals (error)
•Decomposition of total Sum Sq. into Regression Sum Sq. and Error Sum. Sq. as in ANOVA
•Significance testing by F-test
•FDFregr,DFerror = MSregr/ MSerror
•DFregr = number of predictors (1 in simple regression)
•Dferror = number of observations – DFregr – 1
•Coefficient of determination R2 = SSregr/SStotal
•Adjusted R2 = 1 – MSerror/MStotal
•Accounts for the estimate nature of the R2
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Regression assumptions
•Normality of residuals
•Indepdendence between residuals and fitted values
•Linear relationship between X and Y
•Check by Regression diagnostics
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Correlation



Correlation and causality
•Causality = if X changes, Y also changes
•Correlation = association between two variables
•A change caused by a manipulation in one does not imply a necessary change in the other
•Associations are mostly analyzed by regression
•Numerical equivalence between correlation and regression
•Significant regression does not mean causality
•Causality can only be demonstrated by manipulative experiments!