ies2-statistics.ipynb

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     "text": [
      "Observations:\n",
      "[0, 3, 4]\n",
      "[1, 2, 4]\n",
      "[3, 4, 5]\n",
      "\n",
      "Mean of each observation:\n",
      "[2.3333333333333335, 2.3333333333333335, 4.0]\n",
      "\n",
      "General mean:\n",
      "2.8888888888888893\n",
      "\n",
      "Variance of each observation:\n",
      "[4.333333333333334, 2.333333333333333, 1.0]\n",
      "\n",
      "Standard deviation of each observation:\n",
      "[2.081665999466133, 1.5275252316519465, 1.0]\n",
      "\n",
      "Covariance matrix:\n",
      "[4.333333333333334, 2.833333333333333, 2.0]\n",
      "[2.833333333333333, 2.333333333333333, 1.5]\n",
      "[2.0, 1.5, 1.0]\n",
      "\n",
      "Correlation matrix:\n",
      "[0.9999999999999998, 0.8910421112136304, 0.9607689228305226]\n",
      "[0.8910421112136304, 1.0, 0.9819805060619659]\n",
      "[0.9607689228305226, 0.9819805060619659, 1.0]\n",
      "\n",
      "Covariance matrix:\n",
      "[[4.33333333 2.83333333 2.        ]\n",
      " [2.83333333 2.33333333 1.5       ]\n",
      " [2.         1.5        1.        ]]\n",
      "\n",
      "Correlation matrix:\n",
      "[[1.         0.89104211 0.96076892]\n",
      " [0.89104211 1.         0.98198051]\n",
      " [0.96076892 0.98198051 1.        ]]\n",
      "\n"
     ]
    }
   ],
   "source": [
    "################################################################################\n",
    "\n",
    "# Importing Math module\n",
    "import math\n",
    "# Importing numpy library\n",
    "import numpy as np\n",
    "\n",
    "################################################################################\n",
    "\n",
    "# Function to find mean.\n",
    "def mean(arr):\n",
    "  sum = 0\n",
    "  for a in arr:\n",
    "    sum += a\n",
    "  return sum / len(arr)\n",
    "\n",
    "# Function to find variance.\n",
    "def variance(arr, mean, gl):\n",
    "  sum = 0\n",
    "  for a in arr:\n",
    "    sum += pow(a - mean, 2)\n",
    "  return sum / gl\n",
    "\n",
    "# Function to find standard deviation.\n",
    "def stddev(variance):\n",
    "  return math.sqrt(variance)\n",
    "\n",
    "# Function to find covariance.\n",
    "def covariance(arr1, arr2, mean1, mean2, n, gl):\n",
    "  sum = 0\n",
    "  for i in range(n):\n",
    "    sum += (arr1[i] - mean1) * (arr2[i] - mean2)\n",
    "  return sum / gl\n",
    "\n",
    "# Function to find correlation.\n",
    "def correlation(arr1, arr2, mean1, mean2, sd1, sd2, n, gl):\n",
    "  sum = 0\n",
    "  for i in range(n):\n",
    "    sum += (arr1[i] - mean1) * (arr2[i] - mean2)\n",
    "  return sum / (gl * sd1 * sd2)\n",
    "\n",
    "################################################################################\n",
    "\n",
    "# Observations\n",
    "arrs =[\n",
    "  [0, 3, 4],\n",
    "  [1, 2, 4],\n",
    "  [3, 4, 5],\n",
    "]\n",
    "# Number of observations\n",
    "numob = len(arrs)\n",
    "# Number of variables\n",
    "numov = len(arrs[0])\n",
    "# Degrees of freedom\n",
    "gl = numov - 1\n",
    "# Means\n",
    "means = []\n",
    "# General mean\n",
    "gmean = 0\n",
    "# Variances\n",
    "variances = []\n",
    "# Standard deviations\n",
    "stddevs = []\n",
    "# Covariance\n",
    "obs_covariance = 0\n",
    "# Covariance matrix\n",
    "mcov = []\n",
    "for i in range(numov):\n",
    "  aux = []\n",
    "  for j in range(numov):\n",
    "    aux.append(0)\n",
    "  mcov.append(aux)\n",
    "# Correlation matrix\n",
    "mcorr = []\n",
    "for i in range(numov):\n",
    "  aux = []\n",
    "  for j in range(numov):\n",
    "    aux.append(0)\n",
    "  mcorr.append(aux)\n",
    "\n",
    "print('Observations:')\n",
    "for o in arrs:\n",
    "  print(o)\n",
    "print()\n",
    "\n",
    "################################################################################\n",
    "\n",
    "# Find means\n",
    "print('Mean of each observation:')\n",
    "for arr in arrs:\n",
    "  m = mean(arr)\n",
    "  means.append(m)\n",
    "print(means, end='\\n\\n')\n",
    "\n",
    "# Find general mean\n",
    "print('General mean:')\n",
    "gmean = sum(means) / numob\n",
    "# Variables:\n",
    "print(gmean, end='\\n\\n')\n",
    "\n",
    "# Find variances\n",
    "print('Variance of each observation:')\n",
    "for i, arr in enumerate(arrs):\n",
    "  v = variance(arr, means[i], gl)\n",
    "  variances.append(v)\n",
    "print(variances, end='\\n\\n')\n",
    "\n",
    "# Find standard deviation\n",
    "print('Standard deviation of each observation:')\n",
    "for variance in variances:\n",
    "  sd = stddev(variance)\n",
    "  stddevs.append(sd)\n",
    "print(stddevs, end='\\n\\n')\n",
    "\n",
    "# Find covariance matrix\n",
    "print('Covariance matrix:')\n",
    "for i in range(numob):\n",
    "  for j in range(numob):\n",
    "    mcov[i][j] = covariance(arrs[i], arrs[j], means[i], means[j], numov, gl)\n",
    "for i in mcov:\n",
    "  print(i)\n",
    "print()\n",
    "\n",
    "# Find correlation matrix\n",
    "print('Correlation matrix:')\n",
    "for i in range(numob):\n",
    "  for j in range(numob):\n",
    "    mcorr[i][j] = correlation(arrs[i], arrs[j], means[i], means[j],\n",
    "      stddevs[i], stddevs[j], numov, gl)\n",
    "for i in mcorr:\n",
    "  print(i)\n",
    "print()\n",
    "\n",
    "# Find covariance matrix\n",
    "x = np.array(arrs)\n",
    "print('Covariance matrix:')\n",
    "print(np.cov(x), end='\\n\\n')\n",
    "\n",
    "# Find correlation matrix\n",
    "print('Correlation matrix:')\n",
    "print(np.corrcoef(x), end='\\n\\n')\n",
    "\n",
    "################################################################################\n"
   ]
  }
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