incorporating TR comments into Ch 15

DS-100 · May 9, 2023 · e7e5d0d · e7e5d0d
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diff --git a/content/ch/15/figures/scatterplotSLR.png b/content/ch/15/figures/scatterplotSLR.png
diff --git a/content/ch/15/linear_case.ipynb b/content/ch/15/linear_case.ipynb
diff --git a/content/ch/15/linear_categorical.ipynb b/content/ch/15/linear_categorical.ipynb
diff --git a/content/ch/15/linear_feature_eng.ipynb b/content/ch/15/linear_feature_eng.ipynb
diff --git a/content/ch/15/linear_multi.ipynb b/content/ch/15/linear_multi.ipynb
diff --git a/content/ch/15/linear_multi_fit.ipynb b/content/ch/15/linear_multi_fit.ipynb
@@ -68,7 +68,7 @@
     "\n",
     "$$\n",
     "\\begin{aligned}\n",
-    "y_2 \\approx  \\theta_0 + \\theta_1 x_{2,1} + \\ldots + \\theta_p x_{2,p} \n",
+    "y_2 \\approx  \\theta_0 + \\theta_1 x_{2,1} + \\ldots + \\theta_p x_{2,p}. \n",
     "\\end{aligned}\n",
     "$$\n",
     "\n",
@@ -88,7 +88,7 @@
     "Putting these notational definitions together, we can write the vector of predictions for the entire dataset using matrix multiplication:\n",
     "\n",
     "$$\n",
-    "{\\textbf{X}} {\\boldsymbol{\\theta}}\n",
+    "{\\textbf{X}} {\\boldsymbol{\\theta}.}\n",
     "$$\n",
     "\n",
     "If we check the dimensions of $\\textbf{X}$ and $\\boldsymbol{\\theta}$, we can confirm that ${\\textbf{X}} {\\boldsymbol{\\theta}}$ is an $n$-dimensional column vector.\n",
@@ -122,7 +122,7 @@
    "source": [
     "$$\n",
     "\\frac{1}{n} \\sum_i [y_i - (\\theta_0 + \\theta_1 x_{i,1} + \\cdots + \\theta_p x_{i,p})]^2 \n",
-    "= \\frac{1}{n}  \\lVert \\mathbf{y} - {\\textbf{X}} {\\boldsymbol{\\theta}} \\rVert^2\n",
+    "= \\frac{1}{n}  \\lVert \\mathbf{y} - {\\textbf{X}} {\\boldsymbol{\\theta}} \\rVert^2.\n",
     "$$"
    ]
   },

diff --git a/content/ch/15/linear_pa.ipynb b/content/ch/15/linear_pa.ipynb
diff --git a/content/ch/15/linear_simple_fit.ipynb b/content/ch/15/linear_simple_fit.ipynb
@@ -112,7 +112,7 @@
    "metadata": {},
    "source": [
     "These equations are called the *normal equations*. \n",
-    "In the first equation, we see that $\\hat{\\theta}_0$ can be represented as a function of $\\hat{\\theta}_1$.\n",
+    "In the first equation, we see that $\\hat{\\theta}_0$ can be represented as a function of $\\hat{\\theta}_1$,\n",
     "\n",
     "$$\n",
     "\\hat{\\theta}_0 = \\bar{y} - \\hat{\\theta}_1 \\bar{x}.\n",
@@ -154,7 +154,7 @@
     "We have derived the equation  for the least squares line that we used in the previous section. There, we used the `pandas` built-in methods to compute\n",
     "$SD(\\mathbf{x})$, $SD(\\mathbf{y})$, and $r(\\mathbf{x}, \\mathbf{y})$,\n",
     "to easily calculate the equation for this line.\n",
-    "However, in practice we recommend using the functionality provided in `scikit-learn` to do the model fitting."
+    "However, in practice we recommend using the functionality provided in `scikit-learn` to do the model fitting:"
    ]
   },
   {

diff --git a/content/ch/15/linear_summary.ipynb b/content/ch/15/linear_summary.ipynb
@@ -59,11 +59,18 @@
     "+ Several models can be equally effective in predicting/explaining the response variable\n",
     "\n",
     "If we are concerned with making inferences, where we want to interpret/understand the model, then we should err on the side of simpler models. \n",
-    "On the other hand, if our primary concern is the predictive ability of a model, then we tend not to concern ourselves with the number of coefficients and their interpretation.  \n",
+    "On the other hand, if our primary concern is the predictive ability of a model, then we tend not to concern ourselves with the number of coefficients and their interpretation. But, this \"black box\" approach can lead to models that, say, overly depend on anomalous values in the data or models that are inadequate in other ways. So be careful with the black box approach, especially when the predictions may be harmful to people.  \n",
     "\n",
     "In this chapter, we have used linear models in a descriptive way. We introduced a few notions for deciding when to include a feature in a model by examining residuals for patterns, comparing the size of standard errors and the change in the multiple $R^2$. Often times we settled for a \n",
     "simpler model that was easier to interpret. In the next chapter, we look at other more formal tools for choosing the features to include in a model. "
    ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": []
   }
  ],
  "metadata": {