2.-Statistics/R-squared.md

@@ -14,20 +14,20 @@ R² is a useful metric for assessing how well a model explains the relationship
 R² is calculated by comparing the total variation in the response variable to the variation explained by the model. The formula is:
 
 $$
-R^2 = 1 - \frac{SS_{\text{residual}}}{SS_{\text{total}}}
+R^2 = 1 - \frac{SSE}{SST}
 $$
 
 Where:
-- **SS_residual** is the sum of squared differences between the observed values $y_i$ and the values predicted by the model $\hat{y}_i$ (i.e., the residuals).
+- **SSE** (Residual Sum of Squares) is the sum of squared differences between the observed values $y_i$ and the predicted values $\hat{y}_i$:
 
 $$
-SS_{\text{residual}} = \sum_{i=1}^{n} (y_i - \hat{y}_i)^2
+SSE = \sum_{i=1}^{n} (y_i - \hat{y}_i)^2
 $$
 
-- **SS_total** is the total sum of squared differences between the observed values $y_i$ and the mean of the response variable $\bar{y}$.
+- **SST** (Total Sum of Squares) is the total sum of squared differences between the observed values $y_i$ and the mean of the response variable $\bar{y}$:
 
 $$
-SS_{\text{total}} = \sum_{i=1}^{n} (y_i - \bar{y})^2
+SST = \sum_{i=1}^{n} (y_i - \bar{y})^2
 $$
 
 In short, $R^2$ tells you how much of the variability in the response variable is captured by the model.
@@ -110,8 +110,8 @@ R^2_{\text{McFadden}} = 1 - \frac{\ln(L_{\text{full model}})}{\ln(L_{\text{null
 $$
 
 Where:
-- \(L_{\text{full model}}\) is the likelihood of the fitted model.
-- \(L_{\text{null model}}\) is the likelihood of the null model (a model with only an intercept).
+- $L_{\text{full model}}$ is the likelihood of the fitted model.
+- $L_{\text{null model}}$ is the likelihood of the null model (a model with only an intercept).
 
 #### Cox & Snell's Pseudo-R²
 
@@ -121,7 +121,7 @@ $$
 R^2_{\text{Cox-Snell}} = 1 - \left( \frac{L_{\text{null model}}}{L_{\text{full model}}} \right)^{2/n}
 $$
 
-Where \(n\) is the number of observations.
+Where $n$ is the number of observations.
 
 #### Nagelkerke's Pseudo-R²