From b58e2a66d2d2c03fd3f559dc27334e7154213172 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Pawe=C5=82=20Sk=C3=B3rzewski?= <pawel.skorzewski@amu.edu.pl>
Date: Fri, 19 Mar 2021 19:45:06 +0100
Subject: [PATCH] RMSE -> MSE

---
 wyk/2_Regresja_liniowa.ipynb | 3721 +++++++++++++++++-----------------
 1 file changed, 1867 insertions(+), 1854 deletions(-)

diff --git a/wyk/2_Regresja_liniowa.ipynb b/wyk/2_Regresja_liniowa.ipynb
index e947573..d1536a5 100644
--- a/wyk/2_Regresja_liniowa.ipynb
+++ b/wyk/2_Regresja_liniowa.ipynb
@@ -40,7 +40,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 1,
+   "execution_count": 71,
    "metadata": {
     "slideshow": {
      "slide_type": "notes"
@@ -72,7 +72,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 2,
+   "execution_count": 72,
    "metadata": {
     "slideshow": {
      "slide_type": "fragment"
@@ -125,7 +125,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 3,
+   "execution_count": 73,
    "metadata": {
     "slideshow": {
      "slide_type": "fragment"
@@ -284,7 +284,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 4,
+   "execution_count": 74,
    "metadata": {
     "slideshow": {
      "slide_type": "notes"
@@ -330,7 +330,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 5,
+   "execution_count": 75,
    "metadata": {
     "slideshow": {
      "slide_type": "subslide"
@@ -380,89 +380,89 @@
        "C -3.535534 0.937635 -3.163008 1.836992 -2.5 2.5 \r\n",
        "C -1.836992 3.163008 -0.937635 3.535534 0 3.535534 \r\n",
        "z\r\n",
-       "\" id=\"m032c9535a7\" style=\"stroke:#ff0000;\"/>\r\n",
+       "\" id=\"mdc76d1146b\" style=\"stroke:#ff0000;\"/>\r\n",
        "    </defs>\r\n",
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@@ -568,7 +568,7 @@
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@@ -599,7 +599,7 @@
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@@ -641,7 +641,7 @@
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@@ -657,7 +657,7 @@
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@@ -689,7 +689,7 @@
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@@ -1136,7 +1136,7 @@
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@@ -1149,7 +1149,7 @@
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@@ -1163,7 +1163,7 @@
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@@ -1177,7 +1177,7 @@
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@@ -1191,7 +1191,7 @@
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@@ -1411,7 +1411,7 @@
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@@ -1447,7 +1447,7 @@
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@@ -1470,7 +1470,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 6,
+   "execution_count": 76,
    "metadata": {
     "slideshow": {
      "slide_type": "notes"
@@ -1486,7 +1486,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 7,
+   "execution_count": 77,
    "metadata": {
     "slideshow": {
      "slide_type": "notes"
@@ -1507,7 +1507,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 8,
+   "execution_count": 78,
    "metadata": {
     "slideshow": {
      "slide_type": "subslide"
@@ -1517,7 +1517,7 @@
     {
      "data": {
       "application/vnd.jupyter.widget-view+json": {
-       "model_id": "950eda7f15764e56a36d602c1327d08c",
+       "model_id": "24251add6555459e8095136e4cedf484",
        "version_major": 2,
        "version_minor": 0
       },
@@ -1534,7 +1534,7 @@
        "<function __main__.slide1(theta0, theta1)>"
       ]
      },
-     "execution_count": 8,
+     "execution_count": 78,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1577,7 +1577,7 @@
    "source": [
     "Funkcję kosztu zdefiniujemy w taki sposób, żeby odzwierciedlała ona różnicę między przewidywaniami modelu a obserwacjami.\n",
     "\n",
-    "Jedną z możliwosci jest zdefiniowanie funkcji kosztu jako wartość **błędu średniokwadratowego** (metoda najmniejszych kwadratów, *root-mean-square error, RMSE*):"
+    "Jedną z możliwosci jest zdefiniowanie funkcji kosztu jako wartość **błędu średniokwadratowego** (metoda najmniejszych kwadratów, *mean-square error, MSE*):"
    ]
   },
   {
@@ -1661,7 +1661,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 9,
+   "execution_count": 79,
    "metadata": {
     "slideshow": {
      "slide_type": "fragment"
@@ -1677,7 +1677,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 10,
+   "execution_count": 80,
    "metadata": {
     "slideshow": {
      "slide_type": "skip"
@@ -1723,7 +1723,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 11,
+   "execution_count": 81,
    "metadata": {
     "slideshow": {
      "slide_type": "subslide"
@@ -1733,7 +1733,7 @@
     {
      "data": {
       "application/vnd.jupyter.widget-view+json": {
-       "model_id": "a5e0cb5026c14b04b5aa2ba99d06cfe8",
+       "model_id": "0ea2880fb86c4bb88ec1495c8bc76d75",
        "version_major": 2,
        "version_minor": 0
       },
@@ -1750,7 +1750,7 @@
        "<function __main__.slide2(theta0, theta1)>"
       ]
      },
-     "execution_count": 11,
+     "execution_count": 81,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1778,14 +1778,14 @@
     }
    },
    "source": [
-    "Funkcja kosztu zdefiniowana jako RMSE jest funkcją zmiennej wektorowej $\\theta$, czyli funkcją dwóch zmiennych rzeczywistych: $\\theta_0$ i $\\theta_1$.\n",
+    "Funkcja kosztu zdefiniowana jako MSE jest funkcją zmiennej wektorowej $\\theta$, czyli funkcją dwóch zmiennych rzeczywistych: $\\theta_0$ i $\\theta_1$.\n",
     "    \n",
     "Zobaczmy, jak wygląda jej wykres."
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 12,
+   "execution_count": 82,
    "metadata": {
     "slideshow": {
      "slide_type": "notes"
@@ -1820,7 +1820,7 @@
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   {
    "cell_type": "code",
-   "execution_count": 13,
+   "execution_count": 83,
    "metadata": {
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      "slide_type": "subslide"
@@ -1830,7 +1830,7 @@
     {
      "data": {
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-       "model_id": "13971cb1b8cb4ce88acb75381664e863",
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        "version_major": 2,
        "version_minor": 0
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@@ -1847,7 +1847,7 @@
        "<function __main__.slide3(theta1)>"
       ]
      },
-     "execution_count": 13,
+     "execution_count": 83,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1858,7 +1858,7 @@
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   {
    "cell_type": "code",
-   "execution_count": 14,
+   "execution_count": 84,
    "metadata": {
     "slideshow": {
      "slide_type": "notes"
@@ -1928,7 +1928,7 @@
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   {
    "cell_type": "code",
-   "execution_count": 15,
+   "execution_count": 85,
    "metadata": {
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      "slide_type": "subslide"
@@ -2815,12 +2815,12 @@
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@@ -2848,7 +2848,7 @@
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-     "execution_count": 34,
+     "execution_count": 95,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -38910,7 +38910,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 40,
+   "execution_count": 96,
    "metadata": {
     "slideshow": {
      "slide_type": "subslide"
@@ -38993,12 +38993,12 @@
     }
    },
    "source": [
-    "Jako metrykę ewaluacji wykorzystamy znany nam już błąd średniokwadratowy (RMSE):"
+    "Jako metrykę ewaluacji wykorzystamy znany nam już błąd średniokwadratowy (MSE):"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 26,
+   "execution_count": 97,
    "metadata": {
     "slideshow": {
      "slide_type": "skip"
@@ -39006,7 +39006,7 @@
    },
    "outputs": [],
    "source": [
-    "def rmse(expected, predicted):\n",
+    "def mse(expected, predicted):\n",
     "    \"\"\"Błąd średniokwadratowy\"\"\"\n",
     "    m = len(expected)\n",
     "    if len(predicted) != m:\n",
@@ -39016,7 +39016,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 27,
+   "execution_count": 98,
    "metadata": {
     "slideshow": {
      "slide_type": "subslide"
@@ -39027,7 +39027,7 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "5.283571974307861\n"
+      "3.48379850279277\n"
      ]
     }
    ],
@@ -39041,8 +39041,8 @@
     "# Obliczenie przewidywań modelu\n",
     "y_pred = h(best_theta, x_test)\n",
     "\n",
-    "# Obliczenie RMSE na zbiorze testowym (im mniejszy RMSE, tym lepiej!)\n",
-    "evaluation_result = rmse(y_test, y_pred)\n",
+    "# Obliczenie MSE na zbiorze testowym (im mniejszy MSE, tym lepiej!)\n",
+    "evaluation_result = mse(y_test, y_pred)\n",
     "\n",
     "print(evaluation_result)"
    ]
@@ -39057,7 +39057,7 @@
    "source": [
     "Otrzymana wartość mówi nam o tym, jak dobry jest stworzony przez nas model.\n",
     "\n",
-    "W przypadku metryki RMSE im mniejsz wartość, tym lepiej.\n",
+    "W przypadku metryki MSE im mniejsz wartość, tym lepiej.\n",
     "\n",
     "W ten sposób możemy np. porównywać różne modele."
    ]
@@ -39097,7 +39097,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 28,
+   "execution_count": 99,
    "metadata": {
     "slideshow": {
      "slide_type": "subslide"
@@ -39265,7 +39265,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 29,
+   "execution_count": 100,
    "metadata": {
     "slideshow": {
      "slide_type": "skip"
@@ -39305,7 +39305,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 30,
+   "execution_count": 101,
    "metadata": {
     "slideshow": {
      "slide_type": "notes"
@@ -39379,7 +39379,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 31,
+   "execution_count": 102,
    "metadata": {
     "slideshow": {
      "slide_type": "notes"
@@ -39438,7 +39438,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 32,
+   "execution_count": 103,
    "metadata": {
     "slideshow": {
      "slide_type": "notes"
@@ -39496,7 +39496,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 33,
+   "execution_count": 104,
    "metadata": {
     "slideshow": {
      "slide_type": "notes"
@@ -39598,7 +39598,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 34,
+   "execution_count": 105,
    "metadata": {
     "slideshow": {
      "slide_type": "subslide"
@@ -39648,89 +39648,89 @@
        "C -3.535534 0.937635 -3.163008 1.836992 -2.5 2.5 \r\n",
        "C -1.836992 3.163008 -0.937635 3.535534 0 3.535534 \r\n",
        "z\r\n",
-       "\" id=\"mc7d93626a2\" style=\"stroke:#ff0000;\"/>\r\n",
+       "\" id=\"m00e88fde68\" style=\"stroke:#ff0000;\"/>\r\n",
        "    </defs>\r\n",
-       "    <g clip-path=\"url(#pf109671648)\">\r\n",
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+       "     <use style=\"fill:#ff0000;stroke:#ff0000;\" x=\"150.116086\" xlink:href=\"#m00e88fde68\" y=\"208.1062\"/>\r\n",
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+       "     <use style=\"fill:#ff0000;stroke:#ff0000;\" x=\"84.280855\" xlink:href=\"#m00e88fde68\" y=\"269.757024\"/>\r\n",
+       "     <use style=\"fill:#ff0000;stroke:#ff0000;\" x=\"141.912274\" xlink:href=\"#m00e88fde68\" y=\"207.905513\"/>\r\n",
+       "     <use style=\"fill:#ff0000;stroke:#ff0000;\" x=\"77.536139\" xlink:href=\"#m00e88fde68\" y=\"260.891191\"/>\r\n",
+       "     <use style=\"fill:#ff0000;stroke:#ff0000;\" x=\"138.558659\" xlink:href=\"#m00e88fde68\" y=\"234.468485\"/>\r\n",
+       "     <use style=\"fill:#ff0000;stroke:#ff0000;\" x=\"143.726052\" xlink:href=\"#m00e88fde68\" y=\"226.812169\"/>\r\n",
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+       "     <use style=\"fill:#ff0000;stroke:#ff0000;\" x=\"105.406031\" xlink:href=\"#m00e88fde68\" y=\"254.028991\"/>\r\n",
+       "     <use style=\"fill:#ff0000;stroke:#ff0000;\" x=\"87.109656\" xlink:href=\"#m00e88fde68\" y=\"231.062201\"/>\r\n",
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+       "     <use style=\"fill:#ff0000;stroke:#ff0000;\" x=\"73.83361\" xlink:href=\"#m00e88fde68\" y=\"288.754204\"/>\r\n",
+       "     <use style=\"fill:#ff0000;stroke:#ff0000;\" x=\"538.082864\" xlink:href=\"#m00e88fde68\" y=\"87.292639\"/>\r\n",
+       "     <use style=\"fill:#ff0000;stroke:#ff0000;\" x=\"354.369379\" xlink:href=\"#m00e88fde68\" y=\"150.681671\"/>\r\n",
+       "     <use style=\"fill:#ff0000;stroke:#ff0000;\" x=\"471.183588\" xlink:href=\"#m00e88fde68\" y=\"96.733559\"/>\r\n",
+       "     <use style=\"fill:#ff0000;stroke:#ff0000;\" x=\"132.627116\" xlink:href=\"#m00e88fde68\" y=\"228.030317\"/>\r\n",
+       "     <use style=\"fill:#ff0000;stroke:#ff0000;\" x=\"163.680491\" xlink:href=\"#m00e88fde68\" y=\"218.762031\"/>\r\n",
+       "     <use style=\"fill:#ff0000;stroke:#ff0000;\" x=\"219.648079\" xlink:href=\"#m00e88fde68\" y=\"196.84615\"/>\r\n",
+       "     <use style=\"fill:#ff0000;stroke:#ff0000;\" x=\"83.06398\" xlink:href=\"#m00e88fde68\" y=\"269.763498\"/>\r\n",
+       "     <use style=\"fill:#ff0000;stroke:#ff0000;\" x=\"511.034794\" xlink:href=\"#m00e88fde68\" y=\"54.244026\"/>\r\n",
+       "     <use style=\"fill:#ff0000;stroke:#ff0000;\" x=\"216.764489\" xlink:href=\"#m00e88fde68\" y=\"208.666182\"/>\r\n",
+       "     <use style=\"fill:#ff0000;stroke:#ff0000;\" x=\"135.98073\" xlink:href=\"#m00e88fde68\" y=\"237.30184\"/>\r\n",
+       "     <use style=\"fill:#ff0000;stroke:#ff0000;\" x=\"97.678011\" xlink:href=\"#m00e88fde68\" y=\"266.946327\"/>\r\n",
+       "     <use style=\"fill:#ff0000;stroke:#ff0000;\" x=\"132.849152\" xlink:href=\"#m00e88fde68\" y=\"244.690573\"/>\r\n",
+       "     <use style=\"fill:#ff0000;stroke:#ff0000;\" x=\"69.43902\" xlink:href=\"#m00e88fde68\" y=\"309.663522\"/>\r\n",
+       "     <use style=\"fill:#ff0000;stroke:#ff0000;\" x=\"113.298415\" xlink:href=\"#m00e88fde68\" y=\"277.537637\"/>\r\n",
+       "     <use style=\"fill:#ff0000;stroke:#ff0000;\" x=\"141.866136\" xlink:href=\"#m00e88fde68\" y=\"238.827492\"/>\r\n",
+       "     <use style=\"fill:#ff0000;stroke:#ff0000;\" x=\"69.715844\" xlink:href=\"#m00e88fde68\" y=\"219.223827\"/>\r\n",
+       "     <use style=\"fill:#ff0000;stroke:#ff0000;\" x=\"220.743843\" xlink:href=\"#m00e88fde68\" y=\"207.881776\"/>\r\n",
+       "     <use style=\"fill:#ff0000;stroke:#ff0000;\" x=\"71.76896\" xlink:href=\"#m00e88fde68\" y=\"258.539054\"/>\r\n",
        "    </g>\r\n",
        "   </g>\r\n",
        "   <g id=\"matplotlib.axis_1\">\r\n",
@@ -39739,10 +39739,10 @@
        "      <defs>\r\n",
        "       <path d=\"M 0 0 \r\n",
        "L 0 3.5 \r\n",
-       "\" id=\"m584f47a659\" style=\"stroke:#000000;stroke-width:0.8;\"/>\r\n",
+       "\" id=\"m568fdc33a1\" style=\"stroke:#000000;stroke-width:0.8;\"/>\r\n",
        "      </defs>\r\n",
        "      <g>\r\n",
-       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"68.663334\" xlink:href=\"#m584f47a659\" y=\"320.453144\"/>\r\n",
+       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"68.663334\" xlink:href=\"#m568fdc33a1\" y=\"320.453144\"/>\r\n",
        "      </g>\r\n",
        "     </g>\r\n",
        "     <g id=\"text_1\">\r\n",
@@ -39810,7 +39810,7 @@
        "    <g id=\"xtick_2\">\r\n",
        "     <g id=\"line2d_2\">\r\n",
        "      <g>\r\n",
-       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"140.753071\" xlink:href=\"#m584f47a659\" y=\"320.453144\"/>\r\n",
+       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"140.753071\" xlink:href=\"#m568fdc33a1\" y=\"320.453144\"/>\r\n",
        "      </g>\r\n",
        "     </g>\r\n",
        "     <g id=\"text_2\">\r\n",
@@ -39836,7 +39836,7 @@
        "    <g id=\"xtick_3\">\r\n",
        "     <g id=\"line2d_3\">\r\n",
        "      <g>\r\n",
-       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"212.842808\" xlink:href=\"#m584f47a659\" y=\"320.453144\"/>\r\n",
+       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"212.842808\" xlink:href=\"#m568fdc33a1\" y=\"320.453144\"/>\r\n",
        "      </g>\r\n",
        "     </g>\r\n",
        "     <g id=\"text_3\">\r\n",
@@ -39867,7 +39867,7 @@
        "    <g id=\"xtick_4\">\r\n",
        "     <g id=\"line2d_4\">\r\n",
        "      <g>\r\n",
-       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"284.932544\" xlink:href=\"#m584f47a659\" y=\"320.453144\"/>\r\n",
+       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"284.932544\" xlink:href=\"#m568fdc33a1\" y=\"320.453144\"/>\r\n",
        "      </g>\r\n",
        "     </g>\r\n",
        "     <g id=\"text_4\">\r\n",
@@ -39909,7 +39909,7 @@
        "    <g id=\"xtick_5\">\r\n",
        "     <g id=\"line2d_5\">\r\n",
        "      <g>\r\n",
-       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"357.022281\" xlink:href=\"#m584f47a659\" y=\"320.453144\"/>\r\n",
+       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"357.022281\" xlink:href=\"#m568fdc33a1\" y=\"320.453144\"/>\r\n",
        "      </g>\r\n",
        "     </g>\r\n",
        "     <g id=\"text_5\">\r\n",
@@ -39925,7 +39925,7 @@
        "    <g id=\"xtick_6\">\r\n",
        "     <g id=\"line2d_6\">\r\n",
        "      <g>\r\n",
-       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"429.112018\" xlink:href=\"#m584f47a659\" y=\"320.453144\"/>\r\n",
+       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"429.112018\" xlink:href=\"#m568fdc33a1\" y=\"320.453144\"/>\r\n",
        "      </g>\r\n",
        "     </g>\r\n",
        "     <g id=\"text_6\">\r\n",
@@ -39941,7 +39941,7 @@
        "    <g id=\"xtick_7\">\r\n",
        "     <g id=\"line2d_7\">\r\n",
        "      <g>\r\n",
-       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"501.201754\" xlink:href=\"#m584f47a659\" y=\"320.453144\"/>\r\n",
+       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"501.201754\" xlink:href=\"#m568fdc33a1\" y=\"320.453144\"/>\r\n",
        "      </g>\r\n",
        "     </g>\r\n",
        "     <g id=\"text_7\">\r\n",
@@ -39957,7 +39957,7 @@
        "    <g id=\"xtick_8\">\r\n",
        "     <g id=\"line2d_8\">\r\n",
        "      <g>\r\n",
-       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"573.291491\" xlink:href=\"#m584f47a659\" y=\"320.453144\"/>\r\n",
+       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"573.291491\" xlink:href=\"#m568fdc33a1\" y=\"320.453144\"/>\r\n",
        "      </g>\r\n",
        "     </g>\r\n",
        "     <g id=\"text_8\">\r\n",
@@ -40156,10 +40156,10 @@
        "      <defs>\r\n",
        "       <path d=\"M 0 0 \r\n",
        "L -3.5 0 \r\n",
-       "\" id=\"ma4fd5c73ee\" style=\"stroke:#000000;stroke-width:0.8;\"/>\r\n",
+       "\" id=\"m8da693f196\" style=\"stroke:#000000;stroke-width:0.8;\"/>\r\n",
        "      </defs>\r\n",
        "      <g>\r\n",
-       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"40.603125\" xlink:href=\"#ma4fd5c73ee\" y=\"280.739781\"/>\r\n",
+       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"40.603125\" xlink:href=\"#m8da693f196\" y=\"280.739781\"/>\r\n",
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        "     <g id=\"text_10\">\r\n",
@@ -40172,7 +40172,7 @@
        "    <g id=\"ytick_2\">\r\n",
        "     <g id=\"line2d_10\">\r\n",
        "      <g>\r\n",
-       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"40.603125\" xlink:href=\"#ma4fd5c73ee\" y=\"226.791668\"/>\r\n",
+       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"40.603125\" xlink:href=\"#m8da693f196\" y=\"226.791668\"/>\r\n",
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@@ -40185,7 +40185,7 @@
        "    <g id=\"ytick_3\">\r\n",
        "     <g id=\"line2d_11\">\r\n",
        "      <g>\r\n",
-       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"40.603125\" xlink:href=\"#ma4fd5c73ee\" y=\"172.843556\"/>\r\n",
+       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"40.603125\" xlink:href=\"#m8da693f196\" y=\"172.843556\"/>\r\n",
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@@ -40199,7 +40199,7 @@
        "    <g id=\"ytick_4\">\r\n",
        "     <g id=\"line2d_12\">\r\n",
        "      <g>\r\n",
-       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"40.603125\" xlink:href=\"#ma4fd5c73ee\" y=\"118.895444\"/>\r\n",
+       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"40.603125\" xlink:href=\"#m8da693f196\" y=\"118.895444\"/>\r\n",
        "      </g>\r\n",
        "     </g>\r\n",
        "     <g id=\"text_13\">\r\n",
@@ -40213,7 +40213,7 @@
        "    <g id=\"ytick_5\">\r\n",
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        "      <g>\r\n",
-       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"40.603125\" xlink:href=\"#ma4fd5c73ee\" y=\"64.947331\"/>\r\n",
+       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"40.603125\" xlink:href=\"#m8da693f196\" y=\"64.947331\"/>\r\n",
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@@ -40227,7 +40227,7 @@
        "    <g id=\"ytick_6\">\r\n",
        "     <g id=\"line2d_14\">\r\n",
        "      <g>\r\n",
-       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"40.603125\" xlink:href=\"#ma4fd5c73ee\" y=\"10.999219\"/>\r\n",
+       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"40.603125\" xlink:href=\"#m8da693f196\" y=\"10.999219\"/>\r\n",
        "      </g>\r\n",
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        "     <g id=\"text_15\">\r\n",
@@ -40323,12 +40323,12 @@
        "    </g>\r\n",
        "   </g>\r\n",
        "   <g id=\"line2d_15\">\r\n",
-       "    <path clip-path=\"url(#pf109671648)\" d=\"M 69.43902 234.797684 \r\n",
+       "    <path clip-path=\"url(#p9e880c6ff8)\" d=\"M 69.43902 234.797684 \r\n",
        "L 564.72723 79.77979 \r\n",
        "\" style=\"fill:none;stroke:#1f77b4;stroke-linecap:square;stroke-width:2;\"/>\r\n",
        "   </g>\r\n",
        "   <g id=\"line2d_16\">\r\n",
-       "    <path clip-path=\"url(#pf109671648)\" d=\"M 69.43902 254.467109 \r\n",
+       "    <path clip-path=\"url(#p9e880c6ff8)\" d=\"M 69.43902 254.467109 \r\n",
        "L 564.72723 36.05172 \r\n",
        "\" style=\"fill:none;stroke:#ff7f0e;stroke-linecap:square;stroke-width:2;\"/>\r\n",
        "   </g>\r\n",
@@ -40568,7 +40568,7 @@
        "   </g>\r\n",
        "   <g id=\"PathCollection_2\">\r\n",
        "    <g>\r\n",
-       "     <use style=\"fill:#ff0000;stroke:#ff0000;\" x=\"491.233125\" xlink:href=\"#mc7d93626a2\" y=\"338.476113\"/>\r\n",
+       "     <use style=\"fill:#ff0000;stroke:#ff0000;\" x=\"491.233125\" xlink:href=\"#m00e88fde68\" y=\"338.476113\"/>\r\n",
        "    </g>\r\n",
        "   </g>\r\n",
        "   <g id=\"text_19\">\r\n",
@@ -40645,7 +40645,7 @@
        "  </g>\r\n",
        " </g>\r\n",
        " <defs>\r\n",
-       "  <clipPath id=\"pf109671648\">\r\n",
+       "  <clipPath id=\"p9e880c6ff8\">\r\n",
        "   <rect height=\"311.04\" width=\"552.96\" x=\"40.603125\" y=\"9.413144\"/>\r\n",
        "  </clipPath>\r\n",
        " </defs>\r\n",
@@ -40684,7 +40684,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 35,
+   "execution_count": 106,
    "metadata": {
     "slideshow": {
      "slide_type": "subslide"
@@ -40722,7 +40722,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 36,
+   "execution_count": 107,
    "metadata": {
     "slideshow": {
      "slide_type": "notes"
@@ -40754,7 +40754,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 27,
+   "execution_count": 108,
    "metadata": {
     "slideshow": {
      "slide_type": "subslide"
@@ -40762,15 +40762,28 @@
    },
    "outputs": [
     {
-     "ename": "NameError",
-     "evalue": "name 'slide7' is not defined",
-     "output_type": "error",
-     "traceback": [
-      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
-      "\u001b[1;31mNameError\u001b[0m                                 Traceback (most recent call last)",
-      "\u001b[1;32m<ipython-input-27-4a3779a7b6d5>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m\u001b[0m\n\u001b[1;32m----> 1\u001b[1;33m \u001b[0mwidgets\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0minteract_manual\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mslide7\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0malpha\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0msliderAlpha1\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m",
-      "\u001b[1;31mNameError\u001b[0m: name 'slide7' is not defined"
-     ]
+     "data": {
+      "application/vnd.jupyter.widget-view+json": {
+       "model_id": "45cff098b49c4630b6dfa73fda16e169",
+       "version_major": 2,
+       "version_minor": 0
+      },
+      "text/plain": [
+       "interactive(children=(FloatSlider(value=0.02, description='$\\\\alpha$', max=0.03, min=0.01, step=0.001), Button…"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/plain": [
+       "<function __main__.slide7(alpha)>"
+      ]
+     },
+     "execution_count": 108,
+     "metadata": {},
+     "output_type": "execute_result"
     }
    ],
    "source": [
@@ -40816,7 +40829,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 38,
+   "execution_count": 110,
    "metadata": {
     "slideshow": {
      "slide_type": "fragment"
@@ -40928,7 +40941,7 @@
        "9  604836.00      4         40"
       ]
      },
-     "execution_count": 38,
+     "execution_count": 110,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -40943,7 +40956,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 39,
+   "execution_count": 111,
    "metadata": {
     "slideshow": {
      "slide_type": "notes"
@@ -40963,7 +40976,7 @@
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