1 files changed, 280 insertions, 0 deletions
diff --git a/sem6/prob/stat6/Opgaver.ipynb b/sem6/prob/stat6/Opgaver.ipynb
new file mode 100644
index 0000000..81a2213
--- /dev/null
+++ b/sem6/prob/stat6/Opgaver.ipynb
@@ -0,0 +1,280 @@
+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": 53,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import numpy as np\n",
+    "import matplotlib.pyplot as plt\n",
+    "from IPython.display import display, Math\n",
+    "from scipy import stats"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Problem 1\n",
+    "\n",
+    "> The following data indicate the relationship between x, the speciﬁc gravity of\n",
+    "a wood sample, and Y , its maximum crushing strength in compression parallel to\n",
+    "the grain.\n",
+    "> 1. Plot a scatter diagram. Does the linear relationship seem reasonable\n",
+    "> 2. Estimate the regression coefficients\n",
+    "> 3. Predict the maximum crushing strength of a wood sample whose specific gravity is $0.43$\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 25,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "x_i = np.array([0.41,  0.46,  0.44,  0.47,  0.42,  0.39,  0.41,  0.44,  0.43,  0.44])\n",
+    "y_i = np.array([1.850, 2.620, 2.340, 2.690, 2.160, 1.760, 2.500, 2.750, 2.730, 3.120])\n",
+    "x_mean = np.mean(x_i)\n",
+    "y_mean = np.mean(y_i)\n",
+    "\n",
+    "t = np.linspace(np.min(x_i), np.max(x_i))\n",
+    "\n",
+    "n = len(x_i)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 7,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "<matplotlib.collections.PathCollection at 0x7fa6ad4ab2e0>"
+      ]
+     },
+     "execution_count": 7,
+     "metadata": {},
+     "output_type": "execute_result"
+    },
+    {
+     "data": {
+      "image/png": "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\n",
+      "text/plain": [
+       "<Figure size 432x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "# Part A\n",
+    "plt.scatter(x_i, y_i)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 28,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "A: -2.8259168241966486, B: 12.245746691871574\n"
+     ]
+    },
+    {
+     "data": {
+      "text/plain": [
+       "[<matplotlib.lines.Line2D at 0x7fa6ad289250>]"
+      ]
+     },
+     "execution_count": 28,
+     "metadata": {},
+     "output_type": "execute_result"
+    },
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 432x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "# Part B\n",
+    "\n",
+    "S_xY = sum((x * y for (x, y) in zip(x_i, y_i))) - n * x_mean * y_mean\n",
+    "S_xx = sum((x * x for x in x_i)) - n * x_mean * x_mean\n",
+    "\n",
+    "B = S_xY / S_xx\n",
+    "A = y_mean - B * x_mean\n",
+    "print(f\"A: {A}, B: {B}\")\n",
+    "\n",
+    "plt.scatter(x_i, y_i)\n",
+    "plt.plot(t, B * t + A)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 33,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "No 'a' percentage is given, so we just fint the regression value at 0.43\n",
+      "The predicted maximum strength is 2.4397542533081285\n",
+      "Wait this makes no sense, 0.43 is in the sample set.b\n"
+     ]
+    }
+   ],
+   "source": [
+    "# Part C\n",
+    "where = 0.43\n",
+    "print(f\"No 'a' percentage is given, so we just fint the regression value at {where}\")\n",
+    "\n",
+    "print(f\"The predicted maximum strength is {B * where + A}\")\n",
+    "\n",
+    "# TODO TODO GET HELP\n",
+    "print(\"Wait this makes no sense, 0.43 is in the sample set.b\")"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Problem 2\n",
+    "\n",
+    "This seemes like a continuation.\n",
+    "\n",
+    "> In Problem 4.\n",
+    "> 1. Estimate the variance of an individual response.\n",
+    "\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 41,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "The estimated variance is 0.10566006616257498\n"
+     ]
+    }
+   ],
+   "source": [
+    "S_YY = sum((y*y for y in y_i)) - n * y_mean * y_mean\n",
+    "SS_R = (S_xx * S_YY - (S_xY)**2) / S_xx\n",
+    "sigma2 = SS_R / (n - 2)\n",
+    "print(f\"The estimated variance is {sigma2}\")"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Problem 3\n",
+    "\n",
+    "> The following data set presents the heights of 12 male law school classmates whose\n",
+    "law school examination scores were roughly equal. It also gives their annual salaries\n",
+    "5 years after graduation. Each of them went into corporate law. The height is in\n",
+    "inches and the salary in units of $1,000.\n",
+    "> 1. Do the above data establish the hypothesis that a lawyer’s salary is related to\n",
+    "his height? Use the 5 percent level of signiﬁcance.\n",
+    "> 2. What was the null hypothesis in part (a)?\n",
+    "\n",
+    "\n",
+    "## Part A\n",
+    "\n",
+    "We let the null hypothesis be that there is no relation between the salary and height, thus that $\\beta = 0$."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 45,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "x_i = np.array([64, 65, 66, 67, 69, 70, 72, 72, 74, 74, 75, 76])\n",
+    "y_i = np.array([91, 94, 88, 103, 77, 96, 105, 88, 122, 102, 90, 114])\n",
+    "\n",
+    "alpha = 0.05\n",
+    "\n",
+    "n = len(x_i)\n",
+    "\n",
+    "x_mean = np.mean(x_i)\n",
+    "y_mean = np.mean(y_i)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 56,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "B: 1.4571428571428193\n",
+      "TS: 1.7483281067751004\n",
+      "p_value: 0.11098065306186689\n",
+      "h_0 is accepted and thus there is no connection, which kind of makes sense.\n"
+     ]
+    }
+   ],
+   "source": [
+    "# Part A\n",
+    "S_xx = sum((x * x for x in x_i)) - n * x_mean**2\n",
+    "S_YY = sum((y * y for y in y_i)) - n * y_mean**2\n",
+    "S_xY = sum((x * y for (x, y) in zip(x_i, y_i))) - n * x_mean * y_mean\n",
+    "SS_R = (S_xx * S_YY - (S_xY)**2) / S_xx\n",
+    "\n",
+    "print(f\"B: {(B := S_xY / S_xx)}\")\n",
+    "TS = np.sqrt(((n - 2) * S_xx) / SS_R) * np.abs(B)\n",
+    "print(f\"TS: {TS}\")\n",
+    "\n",
+    "p_value = 2 * (1 - stats.t.cdf(TS, n-2))\n",
+    "print(f\"p_value: {p_value}\")\n",
+    "if p_value < alpha:\n",
+    "    print(\"h_0 is rejected and there is a connection between salary and height. Why tho\")\n",
+    "else:\n",
+    "    print(\"h_0 is accepted and thus there is no connection, which kind of makes sense.\") "
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.9.2"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 4
+}