# STAT 371 F19 Lec 6 (24-09-2019) ANOVA and r-squared.pdf -...

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Lecture 624thSept 2019
2.7 Analysis of Variance (ANOVA)We want to develop an approach for assessing the strength of thelinear regression relationship.Going back to the R output you will notice that there is an F statisticprinted out. This F Statistic comes from an ANOVA table and looks torelate the known and unknown variability in our regression model.In general we have 3 components of variability:Total variability = Known variability + Unknown variabilityVariability present inoriginal datavariability explained bythe regression modelvariability that remainsunexplained
How do we measure these?
To find the rest wepartitionthe Total Sum of Squares where:?𝑖− ത? = ?𝑖− ത? + ො?𝑖− ො?𝑖
Result:Total Sum of Squares = Regression SS+ Error SSSST= SSR + SSEEach of these sums of squares is associated withdegrees of freedomand the decomposition is typically displayed in the so-calledAnalysisof Variance (ANOVA) table.Measures the variability inthe response variable that isexplained by the modelMeasures the variability inthe response variable thatisunexplained by themodel
Recall: Degrees of Freedom represent the number of independentcomponents that are needed to calculate the respective sum ofsquares.???=σ𝑖=1𝑛(?𝑖− ത?)2is the sum of n squared components with therestriction thatσ𝑖=1𝑛(?𝑖− ത?) = 0

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