Course Notes - Department of Mathematics and Statistics

An example - Analysis of variance• The amount explained by the independant variable X is called theregression effect. This is also known as the explained componentof the outcomes.• The magnitude of the regression effect is related to the slope andthe distance that x i is away from the overall mean ¯x.• The term (y i − ŷ i ) is the residual effect. This is also known asthe unexplained component of the outcomes.• It is important to establish if the explained effect has a muchgreater impact on the values y i than the unexplained residualeffect.• Does the regression effect explain more of the variation in the y ivalues?• We can do this by setting up a ANalysis Of VAriance and thencalculating the F - Statistic.Source of variation SS DF MS FRegression SSR k-1SSRk−1 = MSRResidual (Error) SSE N-k-1SSEN−k−1 = MSETotal SST N-1MSRMSE213