Goodness-of-Fit We can think of each observation as being made up of an explained part,and an unexplained part, y=+We then define the following >(y-is the total sum of squares(SST) ∑(，-)}is the explained sum of squares(SSE) is the residual sum of squares(SSR) Then SST =SSE +SSR Econometrics 15-Zhuxi @SJTU 16
Econometrics 15 - Zhuxi @SJTU 16 Goodness-of-Fit Then SST SSE SSR ˆ is the residualsum of squares(SSR) ˆ is the explained sum of squares(SSE) is the totalsum of squares(SST) ˆ ˆ We then define the following : up of an explained part, and an unexplained part, We can think of each observation as being made 2 2 2 i i i i i i u y y y y y y u
Goodness-of-Fit (continued) How do we think about how well our sample regression line fits our sample data? Can compute the fraction of the total sum of squares(SST)that is explained by the model,call this the R-squared of regression R2=SSE/SST=1-SSR/SST Econometrics 15-Zhuxi @SJTU 17
Econometrics 15 - Zhuxi @SJTU 17 Goodness-of-Fit (continued) How do we think about how well our sample regression line fits our sample data? Can compute the fraction of the total sum of squares (SST) that is explained by the model, call this the R-squared of regression R2 = SSE/SST = 1 – SSR/SST