01-corr-analysis-stadnikov-aleksander_v2.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np \n",
    "from scipy.stats import pearsonr\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.stats import ttest_ind"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Входные данные: n объектов, каждый из которых характеризуется\n",
    "двумя числовыми признаками:\n",
    "Требуется исследовать степень взаимосвязи между двумя\n",
    "признаками некоторых объектов. Для каждого набора данных\n",
    "необходимо выполнить следующие задания.\n",
    "1. Визуализировать данные на плоскости в виде точек\n",
    "2. Статистически оценить коэффициент корреляции Пирсона\n",
    "между признаками x и y.\n",
    "3. Проверить статистическую гипотезу о некоррелированности\n",
    "признаков x и y на уровне значимости 0,05.\n",
    "Все описанные выше задания требуется выполнить для двух\n",
    "наборов данных.\n",
    "1. Смоделированные независимые случайные вектора\n",
    "имеющие гауссовское распределение с заданным математическим\n",
    "ожиданием 'a' и корреляционной матрицей 'R'.\n",
    "2. Реальные статистические данные из заданного набора\n",
    "(выдаются преподавателем).\n",
    "Отчёт кроме прочих обязательных элементов должен включать:\n",
    "1) изображения данных в виде точек на плоскости;\n",
    "2) статистические оценки коэффициентов корреляции Пирсона для\n",
    "каждого набора данных, сравнение статистической оценки\n",
    "коэффициента корреляции Пирсона с реальным коэффициентом\n",
    "корреляции Пирсона для смоделированных данных;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1000,\n",
       " array([-1,  0]),\n",
       " array([[1. , 0.9],\n",
       "        [0.9, 2. ]]))"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "n = 1000\n",
    "a = np.array([-1, 0])\n",
    "r = np.array([[1, 0.9], [0.9, 2]])\n",
    "n, a, r"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-0.9337133 ,  0.66722389],\n",
       "       [-0.90023737, -1.22071056],\n",
       "       [-1.62094102, -1.10811572],\n",
       "       ...,\n",
       "       [-1.06579866,  0.3543697 ],\n",
       "       [-1.95614851, -1.61685092],\n",
       "       [-1.91279199, -1.44318618]])"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gendata = np.random.multivariate_normal(mean=a, cov=r, size=n)\n",
    "gendata"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "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": [
    "plt.scatter(x=gendata[:,0], y=gendata[:,1], c='black', edgecolors='white')\n",
    "plt.xlabel('X')\n",
    "plt.ylabel('Y')\n",
    "plt.savefig('data/multinoraml-dist-scatterplot.jpeg', dpi=500)\n",
    "plt.savefig('data/multinoraml-dist-scatterplot.svg')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "corr coeff: 0.6317817518124901\n",
      "real correlation: 0.6363961030678927\n",
      "diff: -0.00461435125540266\n",
      "p-value: 1.6068303505446378e-112\n"
     ]
    }
   ],
   "source": [
    "corrpearson, p = pearsonr(x=gendata[:,0],y=gendata[:,1])\n",
    "print(f'corr coeff: {corrpearson}\\\n",
    "\\nreal correlation: {r[0, 1] / np.sqrt(r[0, 0] * r[1, 1])}\\\n",
    "\\ndiff: {corrpearson - r[0, 1] / np.sqrt(r[0, 0] * r[1, 1])}\\\n",
    "\\np-value: {p}')\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Ttest_indResult(statistic=-19.74727168097967, pvalue=1.953493250259269e-79)"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ttest_ind(gendata[:,0],gendata[:,1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Sex</th>\n",
       "      <th>Gestation</th>\n",
       "      <th>Weight</th>\n",
       "      <th>Length</th>\n",
       "      <th>Head</th>\n",
       "      <th>Chest</th>\n",
       "      <th>Mother.s.age</th>\n",
       "      <th>type</th>\n",
       "      <th>region</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>female</td>\n",
       "      <td>40</td>\n",
       "      <td>2800</td>\n",
       "      <td>50.0</td>\n",
       "      <td>31.0</td>\n",
       "      <td>30.0</td>\n",
       "      <td>25</td>\n",
       "      <td>r</td>\n",
       "      <td>bz</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>female</td>\n",
       "      <td>38</td>\n",
       "      <td>3250</td>\n",
       "      <td>50.0</td>\n",
       "      <td>36.0</td>\n",
       "      <td>35.3</td>\n",
       "      <td>24</td>\n",
       "      <td>r</td>\n",
       "      <td>bz</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>male</td>\n",
       "      <td>39</td>\n",
       "      <td>3100</td>\n",
       "      <td>50.0</td>\n",
       "      <td>33.0</td>\n",
       "      <td>34.0</td>\n",
       "      <td>17</td>\n",
       "      <td>r</td>\n",
       "      <td>bz</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>male</td>\n",
       "      <td>40</td>\n",
       "      <td>4000</td>\n",
       "      <td>53.0</td>\n",
       "      <td>35.0</td>\n",
       "      <td>36.0</td>\n",
       "      <td>41</td>\n",
       "      <td>r</td>\n",
       "      <td>bz</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>male</td>\n",
       "      <td>40</td>\n",
       "      <td>3800</td>\n",
       "      <td>52.0</td>\n",
       "      <td>34.0</td>\n",
       "      <td>35.0</td>\n",
       "      <td>43</td>\n",
       "      <td>r</td>\n",
       "      <td>bz</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      Sex  Gestation  Weight  Length  Head  Chest  Mother.s.age type region\n",
       "1  female         40    2800    50.0  31.0   30.0            25    r     bz\n",
       "2  female         38    3250    50.0  36.0   35.3            24    r     bz\n",
       "3    male         39    3100    50.0  33.0   34.0            17    r     bz\n",
       "4    male         40    4000    53.0  35.0   36.0            41    r     bz\n",
       "5    male         40    3800    52.0  34.0   35.0            43    r     bz"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "birth = pd.read_csv('data/02-birth.txt', sep='\\s+', skiprows=[13], header=13) # sep='\\s+' - один и более пробелов\n",
    "birth.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "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": [
    "plt.scatter(x=birth.Head, y=birth.Chest, c='black', edgecolors='white')\n",
    "plt.xlabel('Head')\n",
    "plt.ylabel('Chest')\n",
    "plt.savefig('data/birth-scatterplot.jpeg', dpi=500)\n",
    "plt.savefig('data/birth-scatterplot.svg')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "corr coeff: 0.6685676720438418\n",
      "p-value: 3.804056856828032e-53\n"
     ]
    }
   ],
   "source": [
    "corrpearsonbirth, p = pearsonr(x=birth['Head'].values,y=birth['Chest'].values)\n",
    "print(f'corr coeff: {corrpearsonbirth}\\np-value: {p}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Ttest_indResult(statistic=6.3472541812738195, pvalue=3.673477687821116e-10)"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ttest_ind(birth['Head'].values, birth['Chest'].values)"
   ]
  }
 ],
 "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": "3.8.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}