4-3 1 Goodness of fit statistics We would like some measure of how well our regression model actually fits the data. We have goodness of fit statistics to test this: i.e. how well the sample regression function(srf) fits the data. The most common goodness of fit statistic is known as R2.One way to define rl is to say that it is the square of the correlation coefficient between y and y For another explanation, recall that what we are interested in doing is explaining the variability of y about its mean value, y i,, the total sum of squares,TSS总变差: 7SS=∑(01-y) We can split the Tss into two parts, the part which we have explained (known as the explained sum of squares, ESS)and the part which we did not explain using the model (the rss)".4-3 1 Goodness of Fit Statistics • We would like some measure of how well our regression model actually fits the data. * • We have goodness of fit statistics to test this: i.e. how well the sample regression function (srf) fitsthe data. • The most common goodness of fit statistic is known as R2 . One way to define R2 is to say that it is the square of the correlation coefficient between y and . • For another explanation, recall that what we are interested in doing is explaining the variability of y about its mean value, , i.e. the total sum of squares, TSS总变差: • We can split the TSS into two parts, the part which we have explained (known as the explained sum of squares, ESS) and the part which we did not explain using the model (the RSS)*. y $ = ( − ) t t TSS y y 2 y