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--- chain_rules [2025/08/22 12:56] – [E.g] hkimscil
+++ chain_rules [2025/08/22 13:19] (current) – [e.g.] hkimscil
@@ Line 30: / Line 30: @@
 ====== e.g. ======
 see [[:gradient descent]]
+\begin{eqnarray*}
+\because{ \;\; } \text{predicted value } \; \hat{y} & = & a + b x \\
+\text{and }\;\;  \text{residual} & = & y - \hat{y} \\
+\therefore{} \;\; \text{residual}^2 & = & (y - (a + b x)) \\
+\therefore{} \sum{\text{residual}^2} & = & \sum{(y - (a + b x))^2} \\
+& = & \text{SSE,  sum of square residuals} \\
+\\
+\dfrac{\text{dSSE}}{\text{da}} & = &  \\
+\end{eqnarray*}
 y.hat = a + b * x