minor edits

Author: florian-huber

notebooks/17_machine_learning_algorithms_2.ipynb

@@ -3,7 +3,13 @@
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    "source": [
     "(ch_linear_models)=\n",
     "# Common Algorithms II - Linear Models\n",
@@ -521,7 +527,13 @@
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     "## Logistic Regression\n",
     "Logistic regression, despite its name, is not used for regression tasks. Instead, it is a classification algorithm, primarily used when the dependent variable is binary or categorical. It is a powerful statistical method used to model the probability of a certain class or event existing. Like linear regression, logistic regression models the relationship between a set of independent variables and a dependent variable. However, instead of fitting a line to the data, it uses a logistic function to output a probability value that is used for classification.\n",
@@ -545,13 +557,19 @@
     "\n",
     "$$\n",
     "P(y=1 ∣ x) = \\sigma(z) = \\frac{1}{1+e^{−(\\beta_0 + \\beta_1 x_1 + \\beta_2 x_2 + ... + \\beta_n x_n)}}\n",
-    "$$​"
+    "$$​\n"
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    "source": [
     "### Decision Boundary\n",
     "\n",
@@ -573,7 +591,13 @@
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    "source": [
     "### Simple Example: Student Exam Results\n",
     "\n",
@@ -792,17 +816,23 @@
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    "source": [
     "### Pros, Cons, Caveats\n",
     "\n",
-    "#### Pros:\n",
+    "**Pros:**\n",
     "\n",
     "- **Interpretability:** Logistic regression provides clear and interpretable coefficients that indicate the strength and direction of the relationship between independent variables and the dependent variable.\n",
     "- **Efficiency:** It is computationally efficient and scales well with large datasets.\n",
     "- **Probabilistic Outputs:** Provides probabilistic predictions, which can be useful for decision-making processes that incorporate uncertainty.\n",
     "\n",
-    "#### Cons:\n",
+    "**Cons:**\n",
     "\n",
     "- **Linearity Assumption:** Assumes a linear relationship between the independent variables and the log-odds of the dependent variable, which may not hold in all cases.\n",
     "- **Not Suitable for Complex Relationships:** Logistic regression may not perform well when the relationship between the independent and dependent variables is highly complex and non-linear.\n",
@@ -812,7 +842,13 @@
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    "source": [
     "## Hands-on Example: Logistic Regression\n",
     "\n",