Assessing-Model-Goodness-of-Fit-to-the-Data.md

@@ -10,3 +10,8 @@ This is a measure to compare observed values of the response variable with fitte
 
 <img src="https://latex.codecogs.com/svg.latex?Dev&space;=&space;-2(ln(L(M_1))-ln(L(M_y)))" title="Dev = -2(ln(L(M_1))-ln(L(M_y)))" />
 
+If the model fits the data perfectly, <img src="https://latex.codecogs.com/svg.latex?Dev&space;=&space;0" title="Dev = 0" />. In practice, <img src="https://latex.codecogs.com/svg.latex?L(M_1)&space;<&space;L(M_y)" title="L(M_1) < L(M_y)" /> and therefore, <img src="https://latex.codecogs.com/svg.latex?Dev&space;>&space;0" title="Dev > 0" />. Another common global measure of fit is a generalized Pearson's <img src="https://latex.codecogs.com/svg.latex?\chi^2" title="\chi^2" /> statistic: 
+
+<img src="https://latex.codecogs.com/svg.latex?\chi^2&space;=&space;\sum_i{\frac{(\mu_i-\hat{\mu}_i)^2}{\sqrt{var(\hat{\mu}_i)}}}" title="\chi^2 = \sum_i{\frac{(\mu_i-\hat{\mu}_i)^2}{\sqrt{var(\hat{\mu}_i)}}}" />
+
+### 3. Comparing Models 
\ No newline at end of file