6. 6 How Good is the Fitted Regression Line the Coefficient of Determination, r2 -An overall measure of goodness of fit that will tell us how well the estimated regression line fits the actual y values : e (Y1-Y)=(￥1-Y)+(Y1-￥1) yi- yi fei 6.34) ∑y+∑ (6.36) 2y. the total sum of squares(TSS) 2y. the explained sum of squares(ESS) e. the residual sum of squares(RSS) TSS=ESS+RS (638) (6.39) TSS ESS TSS (640) rt the(sample)coefficient of determination r2 measures the proportion or percentage of the total variation in Y explained by the regression model6.6 How Good is the Fitted Regression Line: the Coefficient of Determination, r2 ——An overall measure of “goodness of fit” that will tell us how well the estimated regression line fits the actual Y values. (5.5) (6.34) (6.36) . the totalsum of squares (TSS). .the explained sum of squares(ESS). .the residual sum ofsquares (RSS) TSS=ESS+RSS (6.38) (6.39) (6.40) r 2 the (sample) coefficient of determination. r 2 measures the proportion or percentage of the total variation in Y explained by the regression model. Yi = Yi +ei ˆ (Y Y) (Y Y) (Y Y ) i i i i − = ˆ − + − ˆ i i i y = ˆ y + e  = + 2 i 2 i 2 i y y e  2 i y  2 i ˆ y  2 i e TSS RSS TSS ESS 1 = + TSS ESS r 2 =