From bf73aff1f41a2451a7a4cb4e04e59e6f84930783 Mon Sep 17 00:00:00 2001
From: Tanish Yelgoe <143334319+tanishy7777@users.noreply.github.com>
Date: Fri, 29 Nov 2024 19:40:26 +0530
Subject: [PATCH] Updated notebooks/negative_binomial.html to correct the
 formula given, from log(Yi) = RHS to log(E(Yi) = RHS where RHS is a linear
 relationship of features. (#859)

---
 docs/notebooks/negative_binomial.ipynb | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

diff --git a/docs/notebooks/negative_binomial.ipynb b/docs/notebooks/negative_binomial.ipynb
index 5ba96bfb..a7e00b70 100644
--- a/docs/notebooks/negative_binomial.ipynb
+++ b/docs/notebooks/negative_binomial.ipynb
@@ -561,13 +561,13 @@
     "### Model 1 \n",
     "\n",
     "$$\n",
-    "\\log{Y_i} = \\beta_1 \\text{Academic}_i + \\beta_2 \\text{General}_i + \\beta_3 \\text{Vocational}_i + \\beta_4 \\text{Math\\_std}_i\n",
+    "\\log(\\mathbb{E}[Y_i]) = \\beta_1 \\text{Academic}_i + \\beta_2 \\text{General}_i + \\beta_3 \\text{Vocational}_i + \\beta_4 \\text{Math\\_std}_i\n",
     "$$\n",
     "\n",
     "### Model 2\n",
     "\n",
     "$$\n",
-    "\\log{Y_i} = \\beta_1 \\text{Academic}_i + \\beta_2 \\text{General}_i + \\beta_3 \\text{Vocational}_i + \\beta_4 \\text{Math\\_std}_i\n",
+    "\\log(\\mathbb{E}[Y_i]) = \\beta_1 \\text{Academic}_i + \\beta_2 \\text{General}_i + \\beta_3 \\text{Vocational}_i + \\beta_4 \\text{Math\\_std}_i\n",
     "            + \\beta_5 \\text{General}_i \\cdot \\text{Math\\_std}_i + \\beta_6 \\text{Vocational}_i \\cdot \\text{Math\\_std}_i\n",
     "$$\n",
     "\n",
@@ -605,7 +605,7 @@
     "\n",
     "So, for example, the first model for a student under the Vocational program reduces to\n",
     "$$\n",
-    "\\log{Y_i} = \\beta_3 + \\beta_4 \\text{Math\\_std}_i\n",
+    "\\log(\\mathbb{E}[Y_i]) = \\beta_3 + \\beta_4 \\text{Math\\_std}_i\n",
     "$$\n",
     "\n",
     "And one last thing to note is we've decided not to inclide an intercept term, that's why you don't see any $\\beta_0$ above. This choice allows us to represent the effect of each program directly with $\\beta_1$, $\\beta_2$, and $\\beta_3$."