fix cyfi445 labs 0-3

CYFI445/lectures/01_linear_regression_concept/1_plot_linear_regression.ipynb

@@ -10,7 +10,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 6,
+   "execution_count": 1,
    "id": "08a3e0d1",
    "metadata": {},
    "outputs": [
@@ -65,7 +65,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 8,
+   "execution_count": 2,
    "id": "76e04a69",
    "metadata": {},
    "outputs": [
@@ -90,12 +90,32 @@
    "metadata": {},
    "source": [
     "#### Calcuate Mean Squared Error when slope range between [-5, 9.05] with 0.05 inteval\n",
-    "- w to reprsent the slope"
+    "- w to reprsent the slope\n",
+    "\n",
+    "\n",
+    "$$\n",
+    "\\begin{bmatrix}-5 & -5 & -5 & -5 \\\\\n",
+    "-4.95 & -4.95 & -4.95 & -4.95 \\\\\n",
+    "-4.9 & -4.9 & -4.9 & -4.9 \n",
+    "\\end{bmatrix}\n",
+    "\\times\n",
+    "\\begin{bmatrix}\n",
+    "1 & 2 & 3 & 4 \\\\\n",
+    "1 & 2 & 3 & 4\\\\\n",
+    "1 & 2 & 3 & 4\n",
+    "\\end{bmatrix}\n",
+    "=\n",
+    "\\begin{bmatrix}\n",
+    "1 \\cdot -5 & 2 \\cdot -5 & 3 \\cdot -5 & 4 \\cdot -5\\\\\n",
+    "1 \\cdot -4.95 & 2 \\cdot -4.95 & 3 \\cdot -4.95 & 4 \\cdot -4.95\\\\\n",
+    "1 \\cdot -4.9 & 2 \\cdot -4.9 & 3 \\cdot -4.9 & 4 \\cdot -4.9\n",
+    "\\end{bmatrix}\n",
+    "$$"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 3,
+   "execution_count": null,
    "id": "34821a6b",
    "metadata": {},
    "outputs": [
@@ -119,12 +139,12 @@
     "Y = np.array([2.3, 3.4, 6.5, 6.8], dtype=np.float32)\n",
     "\n",
     "# Generate weights from -5 to 5\n",
-    "w_values = np.arange(-5, 9.05, 0.05)\n",
+    "w_values = np.arange(-5, 9.05, 0.05) # 281 values (281,)\n",
     "\n",
     "# Calculate MSE for each weight\n",
-    "y_preds = w_values[:, np.newaxis] * X\n",
-    "errors = Y - y_preds\n",
-    "mse_values = np.mean(errors**2, axis=1)\n",
+    "y_preds = w_values[:, np.newaxis] * X # (281,1) *(4) = (281,1) * (1,4) = (281,4)\n",
+    "errors = Y - y_preds # (281,4) = (4) - (281,4) = (1,4) - (281,4) \n",
+    "mse_values = np.mean(errors**2, axis=1) # (281,) mean over columns\n",
     "\n",
     "# Find optimal weight\n",
     "min_idx = np.argmin(mse_values)\n",
@@ -144,6 +164,27 @@
     "plt.show()\n"
    ]
   },
+  {
+   "cell_type": "code",
+   "execution_count": 8,
+   "id": "1870d1e3",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "(281, 4)"
+      ]
+     },
+     "execution_count": 8,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "y_preds.shape"
+   ]
+  },
   {
    "cell_type": "markdown",
    "id": "4c4f352e",
@@ -154,7 +195,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 2,
+   "execution_count": 4,
    "id": "39d1d373",
    "metadata": {},
    "outputs": [