{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "# import numpy for doing the math/making matrices\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "# [[1, 2, 1.5], [3, 4, 5], [10, 5, 2]]\n",
    "arr = [[2, 3, 4, 6], [2, 2.5, 4, 4.5]]\n",
    "arr2 = [[1, 2, 1.5], [3, 4, 5], [10, 5, 2]]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.9166666666666665\n",
      "[[2.91666667 1.91666667]\n",
      " [1.91666667 1.41666667]]\n",
      "[[ 0.25        0.25       -1.25      ]\n",
      " [ 0.25        1.         -4.        ]\n",
      " [-1.25       -4.         16.33333333]]\n"
     ]
    }
   ],
   "source": [
    "# calculate the variance/covariance\n",
    "# np.var(arr, ddof = 1)\n",
    "# np.cov(arr)\n",
    "# ddof = 1 means use bessel's correction\n",
    "print(np.var(arr[0], ddof = 1))\n",
    "print(np.cov(arr))\n",
    "print(np.cov(arr2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 1.          0.5        -0.61858957]\n",
      " [ 0.5         1.         -0.98974332]\n",
      " [-0.61858957 -0.98974332  1.        ]]\n"
     ]
    }
   ],
   "source": [
    "# calculate the coref values\n",
    "# np.corrcoef(arr)\n",
    "print(np.corrcoef(arr2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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