3.0-Covariance.ipynb

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    "# <font color = \"orange\">Covariance</font>"
   ]
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    "## 1.0 General Explanation about <font color = \"orange\">Covariance</font>\n",
    "\n",
    "-  Covariance measure the total variation of two variables from their expected value (mean).\n",
    "-  Covariance is a measure of the joint probability of two variables.\n",
    "-  Covariance does not indicate the strength of the relationship nor the dependency between the variables.\n",
    "-  The relationship between the two concpets can be expected using the formula:"
   ]
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   "source": [
    "### 1.1 Further Explanation for <font color = \"orange\">Covariance</font>"
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    "%%HTML\n",
    "\n",
    "<iframe width=\"700\" height=\"350\" src=\"https://www.youtube.com/embed/0nZT9fqr2MU\" frameborder=\"0\" allow=\"accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen></iframe>"
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    "### 1.2 Formula for <font color = \"orange\">Covariance</font>\n",
    "<img src = \"1st.png\" height = 500 width = 300>\n",
    "\n",
    "\n",
    "-  Cov(x, y) = covariance between variables\n",
    "-  n = number of sample\n",
    "-  x = values of x-variable\n",
    "-  y = values of y-variable\n",
    "\n",
    "<font color = \"blue\">Step 1: Find the mean of **x**, and the mean of **y**</font></br>\n",
    "<font color = \"blue\">Step 2: Find the difference of each value of x from mean of **x**, and the difference of each value of y from mean of **y**</font></br>\n",
    "<font color = \"blue\">Step 3: Multiply the results obtain</font></br>\n",
    "<font color = \"blue\">Step 4: Find the covariance</font></br>"
   ]
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    "## 2.0 Example for <font color = \"orange\">Covariance</font>\n",
    "Study was conducted to investigate the relationship between <font color = \"red\"><strong>score in Data Science</strong></font> and <font color = \"red\"><strong>weight in kilograms</strong></font> among students."
   ]
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Score( /50)</th>\n",
       "      <th>Weight(kg)</th>\n",
       "    </tr>\n",
       "  </thead>\n",
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      "text/plain": [
       "    Score( /50)  Weight(kg)\n",
       "0             3          30\n",
       "1             5          32\n",
       "2             8          34\n",
       "3            10          35\n",
       "4            13          38\n",
       "5            15          39\n",
       "6            18          41\n",
       "7            20          43\n",
       "8            28          44\n",
       "9            32          46\n",
       "10           35          47\n",
       "11           39          50\n",
       "12           40          51\n",
       "13           40          53\n",
       "14           42          54\n",
       "15           43          58\n",
       "16           45          60\n",
       "17           46          65\n",
       "18           47          66\n",
       "19           48          70"
      ]
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     "metadata": {
      "tags": []
     },
     "output_type": "execute_result"
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   ],
   "source": [
    "#creating table using pandas library by extracting .csv file\n",
    "import pandas as pd\n",
    "\n",
    "pd.read_csv('1st.csv', delimiter = ',')"
   ]
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       "                    70\n",
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       "        "
      ],
      "text/plain": [
       "<pandas.formats.style.Styler at 0x9d6c978>"
      ]
     },
     "execution_count": 63,
     "metadata": {
      "tags": []
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#creating table using pandas library by inserting data\n",
    "import pandas as pd\n",
    "\n",
    "score = [3, 5, 8, 10, 13, 15, 18, 20, 28, 32, 35, 39, 40, 40, 42, 43, 45, 46, 47, 48]\n",
    "weight = [30, 32, 34, 35, 38, 39, 41, 43, 44, 46, 47, 50, 51, 53, 54, 58, 60, 65, 66, 70]\n",
    "\n",
    "question_table = pd.DataFrame(score, columns = ['Score ( /50)']); question_table['Weight (kg)'] = weight\n",
    "question_table\n",
    "question_table.style.set_properties(**{'text-align': 'center'})"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "Meni2yPYcF2-"
   },
   "source": [
    "### 2.1 Calculating the <font color = \"orange\">Covariance</font> step by step"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "UsTni3kVcF2_"
   },
   "outputs": [],
   "source": [
    "# score = [3, 5, 8, 10, 13, 15, 18, 20, 28, 32, 35, 39, 40, 40, 42, 43, 45, 46, 47, 48]\n",
    "weight = [30, 32, 34, 35, 38, 39, 41, 43, 44, 46, 47, 50, 51, 53, 54, 58, 60, 65, 66, 70]\n",
    "\n",
    "#1st Step: Find the mean of x and the mean of y\n",
    "meanScore = sum(score) / len(score)\n",
    "meanWeight = sum(weight) / len(weight)\n",
    "\n",
    "print \"1. Mean of score in Data Science among students is \", meanScore\n",
    "print \"2. Mean of weight (kg) among students is \", meanWeight\n",
    "\n",
    "#2nd Step: Find the difference of each value of x (assign as a) and y (assign as b) from their means.\n",
    "a = []\n",
    "for i in score:\n",
    "    differentFromMeanScore = i - meanScore\n",
    "    a.append(differentFromMeanScore)\n",
    "    #print \"List of a is \", a\n",
    "\n",
    "b = []\n",
    "for j in weight:\n",
    "    differentFromMeanWeight = j - meanWeight\n",
    "    b.append(differentFromMeanWeight)\n",
    "    #print \"List of b is \", b\n",
    "    \n",
    "#3rd Step: Multiply the results obtained\n",
    "ab = []\n",
    "for k in range (len(a)):\n",
    "    ab.append(a[k]*b[k])\n",
    "    #print \"List of (a x b) is \", ab\n",
    "\n",
    "#4th Step: Find the covariance\n",
    "covariance = sum(ab) / float(len(ab) - 1)\n",
    "print \"3. The covariance is \", covariance"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "_RoAmlrFcF3D"
   },
   "source": [
    "### 2.2 Calculating the <font color = \"orange\">Covariance</font> using NUMPY"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "gFD76BjVcF3E",
    "outputId": "4d428027-e130-4516-8a54-cd521efce0c5"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1. The covariance of (score, score) is  246.871052632\n",
      "2. The covariance of (weight, weight) is  138.694736842\n",
      "3. The covariance of (score, weight) is \n",
      "[[ 246.87105263  175.86315789]\n",
      " [ 175.86315789  138.69473684]]\n",
      "4. The covariance of (weight, score) is \n",
      "[[ 138.69473684  175.86315789]\n",
      " [ 175.86315789  246.87105263]]\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "\n",
    "print \"1. The covariance of (score, score) is \", np.cov(score)\n",
    "print \"2. The covariance of (weight, weight) is \", np.cov(weight)\n",
    "print \"3. The covariance of (score, weight) is \"\n",
    "print (np.cov(score, weight))\n",
    "print \"4. The covariance of (weight, score) is \"\n",
    "print (np.cov(weight, score))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "HdLx0wRncF3H"
   },
   "source": [
    "## 3.0 Question for <font color = \"orange\">Covariance</font>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true,
    "id": "xpuPsz7xcF3J"
   },
   "source": [
    "### <font color =\"orange\">Question 1</font>\n",
    "Table below shows a list of 25 students with the days they present to class in one semester and the GPA they got for that semester. A student who has many absence has a decrease in GPA. By referring to table below, create list for Days Present as x and GPA as y."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "0G-qpn1lcF3L",
    "outputId": "82795e20-558b-4ad1-a88b-b63892946f39"
   },
   "outputs": [
    {
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       "            #T_21ab1cee_7bb5_11e9_95c8_782bcb97f042row16_col0 {\n",
       "            \n",
       "                text-align:  center;\n",
       "            \n",
       "            }\n",
       "        \n",
       "            #T_21ab1cee_7bb5_11e9_95c8_782bcb97f042row16_col1 {\n",
       "            \n",
       "                text-align:  center;\n",
       "            \n",
       "            }\n",
       "        \n",
       "            #T_21ab1cee_7bb5_11e9_95c8_782bcb97f042row17_col0 {\n",
       "            \n",
       "                text-align:  center;\n",
       "            \n",
       "            }\n",
       "        \n",
       "            #T_21ab1cee_7bb5_11e9_95c8_782bcb97f042row17_col1 {\n",
       "            \n",
       "                text-align:  center;\n",
       "            \n",
       "            }\n",
       "        \n",
       "            #T_21ab1cee_7bb5_11e9_95c8_782bcb97f042row18_col0 {\n",
       "            \n",
       "                text-align:  center;\n",
       "            \n",
       "            }\n",
       "        \n",
       "            #T_21ab1cee_7bb5_11e9_95c8_782bcb97f042row18_col1 {\n",
       "            \n",
       "                text-align:  center;\n",
       "            \n",
       "            }\n",
       "        \n",
       "            #T_21ab1cee_7bb5_11e9_95c8_782bcb97f042row19_col0 {\n",
       "            \n",
       "                text-align:  center;\n",
       "            \n",
       "            }\n",
       "        \n",
       "            #T_21ab1cee_7bb5_11e9_95c8_782bcb97f042row19_col1 {\n",
       "            \n",
       "                text-align:  center;\n",
       "            \n",
       "            }\n",
       "        \n",
       "            #T_21ab1cee_7bb5_11e9_95c8_782bcb97f042row20_col0 {\n",
       "            \n",
       "                text-align:  center;\n",
       "            \n",
       "            }\n",
       "        \n",
       "            #T_21ab1cee_7bb5_11e9_95c8_782bcb97f042row20_col1 {\n",
       "            \n",
       "                text-align:  center;\n",
       "            \n",
       "            }\n",
       "        \n",
       "            #T_21ab1cee_7bb5_11e9_95c8_782bcb97f042row21_col0 {\n",
       "            \n",
       "                text-align:  center;\n",
       "            \n",
       "            }\n",
       "        \n",
       "            #T_21ab1cee_7bb5_11e9_95c8_782bcb97f042row21_col1 {\n",
       "            \n",
       "                text-align:  center;\n",
       "            \n",
       "            }\n",
       "        \n",
       "            #T_21ab1cee_7bb5_11e9_95c8_782bcb97f042row22_col0 {\n",
       "            \n",
       "                text-align:  center;\n",
       "            \n",
       "            }\n",
       "        \n",
       "            #T_21ab1cee_7bb5_11e9_95c8_782bcb97f042row22_col1 {\n",
       "            \n",
       "                text-align:  center;\n",
       "            \n",
       "            }\n",
       "        \n",
       "            #T_21ab1cee_7bb5_11e9_95c8_782bcb97f042row23_col0 {\n",
       "            \n",
       "                text-align:  center;\n",
       "            \n",
       "            }\n",
       "        \n",
       "            #T_21ab1cee_7bb5_11e9_95c8_782bcb97f042row23_col1 {\n",
       "            \n",
       "                text-align:  center;\n",
       "            \n",
       "            }\n",
       "        \n",
       "            #T_21ab1cee_7bb5_11e9_95c8_782bcb97f042row24_col0 {\n",
       "            \n",
       "                text-align:  center;\n",
       "            \n",
       "            }\n",
       "        \n",
       "            #T_21ab1cee_7bb5_11e9_95c8_782bcb97f042row24_col1 {\n",
       "            \n",
       "                text-align:  center;\n",
       "            \n",
       "            }\n",
       "        \n",
       "        </style>\n",
       "\n",
       "        <table id=\"T_21ab1cee_7bb5_11e9_95c8_782bcb97f042\" None>\n",
       "        \n",
       "\n",
       "        <thead>\n",
       "            \n",
       "            <tr>\n",
       "                \n",
       "                <th class=\"blank\">\n",
       "                \n",
       "                <th class=\"col_heading level0 col0\">Days Present\n",
       "                \n",
       "                <th class=\"col_heading level0 col1\">GPA\n",
       "                \n",
       "            </tr>\n",
       "            \n",
       "        </thead>\n",
       "        <tbody>\n",
       "            \n",
       "            <tr>\n",
       "                \n",
       "                <th id=\"T_21ab1cee_7bb5_11e9_95c8_782bcb97f042\" class=\"row_heading level1 row0\">\n",
       "                    0\n",
       "                \n",
       "                <td id=\"T_21ab1cee_7bb5_11e9_95c8_782bcb97f042row0_col0\" class=\"data row0 col0\">\n",
       "                    180\n",
       "                \n",
       "                <td id=\"T_21ab1cee_7bb5_11e9_95c8_782bcb97f042row0_col1\" class=\"data row0 col1\">\n",
       "                    4\n",
       "                \n",
       "            </tr>\n",
       "            \n",
       "            <tr>\n",
       "                \n",
       "                <th id=\"T_21ab1cee_7bb5_11e9_95c8_782bcb97f042\" class=\"row_heading level1 row1\">\n",
       "                    1\n",
       "                \n",
       "                <td id=\"T_21ab1cee_7bb5_11e9_95c8_782bcb97f042row1_col0\" class=\"data row1 col0\">\n",
       "                    150\n",
       "                \n",
       "                <td id=\"T_21ab1cee_7bb5_11e9_95c8_782bcb97f042row1_col1\" class=\"data row1 col1\">\n",
       "                    2.5\n",
       "                \n",
       "            </tr>\n",
       "            \n",
       "            <tr>\n",
       "                \n",
       "                <th id=\"T_21ab1cee_7bb5_11e9_95c8_782bcb97f042\" class=\"row_heading level1 row2\">\n",
       "                    2\n",
       "                \n",
       "                <td id=\"T_21ab1cee_7bb5_11e9_95c8_782bcb97f042row2_col0\" class=\"data row2 col0\">\n",
       "                    170\n",
       "                \n",
       "                <td id=\"T_21ab1cee_7bb5_11e9_95c8_782bcb97f042row2_col1\" class=\"data row2 col1\">\n",
       "                    4\n",
       "                \n",
       "            </tr>\n",
       "            \n",
       "            <tr>\n",
       "                \n",
       "                <th id=\"T_21ab1cee_7bb5_11e9_95c8_782bcb97f042\" class=\"row_heading level1 row3\">\n",
       "                    3\n",
       "                \n",
       "                <td id=\"T_21ab1cee_7bb5_11e9_95c8_782bcb97f042row3_col0\" class=\"data row3 col0\">\n",
       "                    180\n",
       "                \n",
       "                <td id=\"T_21ab1cee_7bb5_11e9_95c8_782bcb97f042row3_col1\" class=\"data row3 col1\">\n",
       "                    3.9\n",
       "                \n",
       "            </tr>\n",
       "            \n",
       "            <tr>\n",
       "                \n",
       "                <th id=\"T_21ab1cee_7bb5_11e9_95c8_782bcb97f042\" class=\"row_heading level1 row4\">\n",
       "                    4\n",
       "                \n",
       "                <td id=\"T_21ab1cee_7bb5_11e9_95c8_782bcb97f042row4_col0\" class=\"data row4 col0\">\n",
       "                    177\n",
       "                \n",
       "                <td id=\"T_21ab1cee_7bb5_11e9_95c8_782bcb97f042row4_col1\" class=\"data row4 col1\">\n",
       "                    3.75\n",
       "                \n",
       "            </tr>\n",
       "            \n",
       "            <tr>\n",
       "                \n",
       "                <th id=\"T_21ab1cee_7bb5_11e9_95c8_782bcb97f042\" class=\"row_heading level1 row5\">\n",
       "                    5\n",
       "                \n",
       "                <td id=\"T_21ab1cee_7bb5_11e9_95c8_782bcb97f042row5_col0\" class=\"data row5 col0\">\n",
       "                    180\n",
       "                \n",
       "                <td id=\"T_21ab1cee_7bb5_11e9_95c8_782bcb97f042row5_col1\" class=\"data row5 col1\">\n",
       "                    3.8\n",
       "                \n",
       "            </tr>\n",
       "            \n",
       "            <tr>\n",
       "                \n",
       "                <th id=\"T_21ab1cee_7bb5_11e9_95c8_782bcb97f042\" class=\"row_heading level1 row6\">\n",
       "                    6\n",
       "                \n",
       "                <td id=\"T_21ab1cee_7bb5_11e9_95c8_782bcb97f042row6_col0\" class=\"data row6 col0\">\n",
       "                    140\n",
       "                \n",
       "                <td id=\"T_21ab1cee_7bb5_11e9_95c8_782bcb97f042row6_col1\" class=\"data row6 col1\">\n",
       "                    2.9\n",
       "                \n",
       "            </tr>\n",
       "            \n",
       "            <tr>\n",
       "                \n",
       "                <th id=\"T_21ab1cee_7bb5_11e9_95c8_782bcb97f042\" class=\"row_heading level1 row7\">\n",
       "                    7\n",
       "                \n",
       "                <td id=\"T_21ab1cee_7bb5_11e9_95c8_782bcb97f042row7_col0\" class=\"data row7 col0\">\n",
       "                    169\n",
       "                \n",
       "                <td id=\"T_21ab1cee_7bb5_11e9_95c8_782bcb97f042row7_col1\" class=\"data row7 col1\">\n",
       "                    3.1\n",
       "                \n",
       "            </tr>\n",
       "            \n",
       "            <tr>\n",
       "                \n",
       "                <th id=\"T_21ab1cee_7bb5_11e9_95c8_782bcb97f042\" class=\"row_heading level1 row8\">\n",
       "                    8\n",
       "                \n",
       "                <td id=\"T_21ab1cee_7bb5_11e9_95c8_782bcb97f042row8_col0\" class=\"data row8 col0\">\n",
       "                    168\n",
       "                \n",
       "                <td id=\"T_21ab1cee_7bb5_11e9_95c8_782bcb97f042row8_col1\" class=\"data row8 col1\">\n",
       "                    3.25\n",
       "                \n",
       "            </tr>\n",
       "            \n",
       "            <tr>\n",
       "                \n",
       "                <th id=\"T_21ab1cee_7bb5_11e9_95c8_782bcb97f042\" class=\"row_heading level1 row9\">\n",
       "                    9\n",
       "                \n",
       "                <td id=\"T_21ab1cee_7bb5_11e9_95c8_782bcb97f042row9_col0\" class=\"data row9 col0\">\n",
       "                    152\n",
       "                \n",
       "                <td id=\"T_21ab1cee_7bb5_11e9_95c8_782bcb97f042row9_col1\" class=\"data row9 col1\">\n",
       "                    3.4\n",
       "                \n",
       "            </tr>\n",
       "            \n",
       "            <tr>\n",
       "                \n",
       "                <th id=\"T_21ab1cee_7bb5_11e9_95c8_782bcb97f042\" class=\"row_heading level1 row10\">\n",
       "                    10\n",
       "                \n",
       "                <td id=\"T_21ab1cee_7bb5_11e9_95c8_782bcb97f042row10_col0\" class=\"data row10 col0\">\n",
       "                    150\n",
       "                \n",
       "                <td id=\"T_21ab1cee_7bb5_11e9_95c8_782bcb97f042row10_col1\" class=\"data row10 col1\">\n",
       "                    3.3\n",
       "                \n",
       "            </tr>\n",
       "            \n",
       "            <tr>\n",
       "                \n",
       "                <th id=\"T_21ab1cee_7bb5_11e9_95c8_782bcb97f042\" class=\"row_heading level1 row11\">\n",
       "                    11\n",
       "                \n",
       "                <td id=\"T_21ab1cee_7bb5_11e9_95c8_782bcb97f042row11_col0\" class=\"data row11 col0\">\n",
       "                    170\n",
       "                \n",
       "                <td id=\"T_21ab1cee_7bb5_11e9_95c8_782bcb97f042row11_col1\" class=\"data row11 col1\">\n",
       "                    3.9\n",
       "                \n",
       "            </tr>\n",
       "            \n",
       "            <tr>\n",
       "                \n",
       "                <th id=\"T_21ab1cee_7bb5_11e9_95c8_782bcb97f042\" class=\"row_heading level1 row12\">\n",
       "                    12\n",
       "                \n",
       "                <td id=\"T_21ab1cee_7bb5_11e9_95c8_782bcb97f042row12_col0\" class=\"data row12 col0\">\n",
       "                    109\n",
       "                \n",
       "                <td id=\"T_21ab1cee_7bb5_11e9_95c8_782bcb97f042row12_col1\" class=\"data row12 col1\">\n",
       "                    1.35\n",
       "                \n",
       "            </tr>\n",
       "            \n",
       "            <tr>\n",
       "                \n",
       "                <th id=\"T_21ab1cee_7bb5_11e9_95c8_782bcb97f042\" class=\"row_heading level1 row13\">\n",
       "                    13\n",
       "                \n",
       "                <td id=\"T_21ab1cee_7bb5_11e9_95c8_782bcb97f042row13_col0\" class=\"data row13 col0\">\n",
       "                    180\n",
       "                \n",
       "                <td id=\"T_21ab1cee_7bb5_11e9_95c8_782bcb97f042row13_col1\" class=\"data row13 col1\">\n",
       "                    4\n",
       "                \n",
       "            </tr>\n",
       "            \n",
       "            <tr>\n",
       "                \n",
       "                <th id=\"T_21ab1cee_7bb5_11e9_95c8_782bcb97f042\" class=\"row_heading level1 row14\">\n",
       "                    14\n",
       "                \n",
       "                <td id=\"T_21ab1cee_7bb5_11e9_95c8_782bcb97f042row14_col0\" class=\"data row14 col0\">\n",
       "                    108\n",
       "                \n",
       "                <td id=\"T_21ab1cee_7bb5_11e9_95c8_782bcb97f042row14_col1\" class=\"data row14 col1\">\n",
       "                    1\n",
       "                \n",
       "            </tr>\n",
       "            \n",
       "            <tr>\n",
       "                \n",
       "                <th id=\"T_21ab1cee_7bb5_11e9_95c8_782bcb97f042\" class=\"row_heading level1 row15\">\n",
       "                    15\n",
       "                \n",
       "                <td id=\"T_21ab1cee_7bb5_11e9_95c8_782bcb97f042row15_col0\" class=\"data row15 col0\">\n",
       "                    175\n",
       "                \n",
       "                <td id=\"T_21ab1cee_7bb5_11e9_95c8_782bcb97f042row15_col1\" class=\"data row15 col1\">\n",
       "                    3.85\n",
       "                \n",
       "            </tr>\n",
       "            \n",
       "            <tr>\n",
       "                \n",
       "                <th id=\"T_21ab1cee_7bb5_11e9_95c8_782bcb97f042\" class=\"row_heading level1 row16\">\n",
       "                    16\n",
       "                \n",
       "                <td id=\"T_21ab1cee_7bb5_11e9_95c8_782bcb97f042row16_col0\" class=\"data row16 col0\">\n",
       "                    144\n",
       "                \n",
       "                <td id=\"T_21ab1cee_7bb5_11e9_95c8_782bcb97f042row16_col1\" class=\"data row16 col1\">\n",
       "                    2.98\n",
       "                \n",
       "            </tr>\n",
       "            \n",
       "            <tr>\n",
       "                \n",
       "                <th id=\"T_21ab1cee_7bb5_11e9_95c8_782bcb97f042\" class=\"row_heading level1 row17\">\n",
       "                    17\n",
       "                \n",
       "                <td id=\"T_21ab1cee_7bb5_11e9_95c8_782bcb97f042row17_col0\" class=\"data row17 col0\">\n",
       "                    120\n",
       "                \n",
       "                <td id=\"T_21ab1cee_7bb5_11e9_95c8_782bcb97f042row17_col1\" class=\"data row17 col1\">\n",
       "                    2.75\n",
       "                \n",
       "            </tr>\n",
       "            \n",
       "            <tr>\n",
       "                \n",
       "                <th id=\"T_21ab1cee_7bb5_11e9_95c8_782bcb97f042\" class=\"row_heading level1 row18\">\n",
       "                    18\n",
       "                \n",
       "                <td id=\"T_21ab1cee_7bb5_11e9_95c8_782bcb97f042row18_col0\" class=\"data row18 col0\">\n",
       "                    133\n",
       "                \n",
       "                <td id=\"T_21ab1cee_7bb5_11e9_95c8_782bcb97f042row18_col1\" class=\"data row18 col1\">\n",
       "                    2.75\n",
       "                \n",
       "            </tr>\n",
       "            \n",
       "            <tr>\n",
       "                \n",
       "                <th id=\"T_21ab1cee_7bb5_11e9_95c8_782bcb97f042\" class=\"row_heading level1 row19\">\n",
       "                    19\n",
       "                \n",
       "                <td id=\"T_21ab1cee_7bb5_11e9_95c8_782bcb97f042row19_col0\" class=\"data row19 col0\">\n",
       "                    160\n",
       "                \n",
       "                <td id=\"T_21ab1cee_7bb5_11e9_95c8_782bcb97f042row19_col1\" class=\"data row19 col1\">\n",
       "                    3.6\n",
       "                \n",
       "            </tr>\n",
       "            \n",
       "            <tr>\n",
       "                \n",
       "                <th id=\"T_21ab1cee_7bb5_11e9_95c8_782bcb97f042\" class=\"row_heading level1 row20\">\n",
       "                    20\n",
       "                \n",
       "                <td id=\"T_21ab1cee_7bb5_11e9_95c8_782bcb97f042row20_col0\" class=\"data row20 col0\">\n",
       "                    160\n",
       "                \n",
       "                <td id=\"T_21ab1cee_7bb5_11e9_95c8_782bcb97f042row20_col1\" class=\"data row20 col1\">\n",
       "                    3.5\n",
       "                \n",
       "            </tr>\n",
       "            \n",
       "            <tr>\n",
       "                \n",
       "                <th id=\"T_21ab1cee_7bb5_11e9_95c8_782bcb97f042\" class=\"row_heading level1 row21\">\n",
       "                    21\n",
       "                \n",
       "                <td id=\"T_21ab1cee_7bb5_11e9_95c8_782bcb97f042row21_col0\" class=\"data row21 col0\">\n",
       "                    159\n",
       "                \n",
       "                <td id=\"T_21ab1cee_7bb5_11e9_95c8_782bcb97f042row21_col1\" class=\"data row21 col1\">\n",
       "                    3.5\n",
       "                \n",
       "            </tr>\n",
       "            \n",
       "            <tr>\n",
       "                \n",
       "                <th id=\"T_21ab1cee_7bb5_11e9_95c8_782bcb97f042\" class=\"row_heading level1 row22\">\n",
       "                    22\n",
       "                \n",
       "                <td id=\"T_21ab1cee_7bb5_11e9_95c8_782bcb97f042row22_col0\" class=\"data row22 col0\">\n",
       "                    165\n",
       "                \n",
       "                <td id=\"T_21ab1cee_7bb5_11e9_95c8_782bcb97f042row22_col1\" class=\"data row22 col1\">\n",
       "                    3.5\n",
       "                \n",
       "            </tr>\n",
       "            \n",
       "            <tr>\n",
       "                \n",
       "                <th id=\"T_21ab1cee_7bb5_11e9_95c8_782bcb97f042\" class=\"row_heading level1 row23\">\n",
       "                    23\n",
       "                \n",
       "                <td id=\"T_21ab1cee_7bb5_11e9_95c8_782bcb97f042row23_col0\" class=\"data row23 col0\">\n",
       "                    180\n",
       "                \n",
       "                <td id=\"T_21ab1cee_7bb5_11e9_95c8_782bcb97f042row23_col1\" class=\"data row23 col1\">\n",
       "                    3.85\n",
       "                \n",
       "            </tr>\n",
       "            \n",
       "            <tr>\n",
       "                \n",
       "                <th id=\"T_21ab1cee_7bb5_11e9_95c8_782bcb97f042\" class=\"row_heading level1 row24\">\n",
       "                    24\n",
       "                \n",
       "                <td id=\"T_21ab1cee_7bb5_11e9_95c8_782bcb97f042row24_col0\" class=\"data row24 col0\">\n",
       "                    149\n",
       "                \n",
       "                <td id=\"T_21ab1cee_7bb5_11e9_95c8_782bcb97f042row24_col1\" class=\"data row24 col1\">\n",
       "                    2.95\n",
       "                \n",
       "            </tr>\n",
       "            \n",
       "        </tbody>\n",
       "        </table>\n",
       "        "
      ],
      "text/plain": [
       "<pandas.formats.style.Styler at 0xa2de780>"
      ]
     },
     "execution_count": 136,
     "metadata": {
      "tags": []
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "x = [180, 150, 170, 180, 177, 180, 140, 169, 168, 152, 150, 170, 109, 180, 108, 175, 144, 120, 133, 160, 160, 159, 165, 180, 149]\n",
    "y = [4.00, 2.50, 4.00, 3.90, 3.75, 3.80, 2.90, 3.10, 3.25, 3.40, 3.30, 3.90, 1.35, 4.00, 1.00, 3.85, 2.98, 2.75, 2.75, 3.60, 3.50, 3.50, 3.50, 3.85, 2.95]\n",
    "\n",
    "\n",
    "df = pd.DataFrame(x, columns = ['Days Present']); df['GPA'] = y\n",
    "df.style.set_properties(**{'text-align':'center'})\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "8jcnNKm9cF3S"
   },
   "source": [
    "### <font color = \"orange\">Question 2</font>\n",
    "\n",
    "By referring to previous table in Question 1, find:\n",
    "-  Mean of x (as meanX) and mean of y (as meanY)\n",
    "-  The difference for each value in x from mean of x (as a), and each value in y from mean of y\n",
    "-  Product of the results obtain\n",
    "-  Covariance and print it."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "xeDQWdX1cF3T",
    "outputId": "fc251ce9-0fdc-4386-a25c-7651faf1b92c"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "12.4971714286\n"
     ]
    }
   ],
   "source": [
    "#1. Create the list of Days Present (as x) and GPA (as y)\n",
    "x = [180, 150, 170, 180, 177, 180, 140, 169, 168, 152, 150, 170, 109, 180, 108, 175, 144, 120, 133, 160, 160, 159, 165, 180, 149, 180, 160, 155, 156, 145, 122, 131, 156, 166, 170, 155, 158, 170, 160, 165, 159, 119, 168, 175, 161, 160, 160, 150, 140, 148]\n",
    "y = [4.00, 2.50, 4.00, 3.90, 3.75, 3.80, 2.90, 3.10, 3.25, 3.40, 3.30, 3.90, 1.35, 4.00, 1.00, 3.85, 2.98, 2.75, 2.75, 3.60, 3.50, 3.50, 3.50, 3.85, 2.95, 3.95, 3.65, 3.55, 3.58, 2.98, 1.50, 1.75, 2.20, 3.00, 3.00, 3.00, 3.15, 3.90, 3.15, 3.85, 2.70, 1.00, 3.25, 3.90, 2.80, 3.50, 3.40, 2.30, 2.50, 2.35]\n",
    "\n",
    "#2.1 Find mean of x (as meanX) and mean of y (as meanY)\n",
    "meanX = sum(x) / len (x)\n",
    "meanY = sum(y) / len (y)\n",
    "\n",
    "#2.2 Find the difference of each value of x form mean of x (as a), and each value in y from mean of y (as b)\n",
    "a = []\n",
    "\n",
    "for i in x:\n",
    "    differenceFromMeanX = i - meanX\n",
    "    a.append(differenceFromMeanX)\n",
    "\n",
    "b = []\n",
    "\n",
    "for j in y:\n",
    "    differenceFromMeanY = j - meanY\n",
    "    b.append(differenceFromMeanY)\n",
    "\n",
    "#2.3 Find the product of the a and b (a x b)\n",
    "ab = []\n",
    "\n",
    "for k in range(len(a)):\n",
    "    ab.append(a[k]*b[k])\n",
    "\n",
    "#2.4 Find the covariance and print it\n",
    "covariance = sum (ab) / float(len(ab) - 1)\n",
    "print covariance"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "mmFAe1S-cF3W"
   },
   "source": [
    "### <font color = \"orange\">Question 3</font>\n",
    "\n",
    "By referring to table in Question 1, import **NUMPY** and use it to find the covariance of x and y, compare with your step by step result."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "r1yLdzB2cF3X",
    "outputId": "2c0266fe-830d-4fad-f509-c2f43e68ae07"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3. The covariance of x and y is \n",
      "[[ 342.10653061   12.49717143]\n",
      " [  12.49717143    0.6085718 ]]\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "\n",
    "print \"3. The covariance of x and y is \"\n",
    "print (np.cov(x, y))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "Ew9CewnecF3g"
   },
   "source": [
    "### <font color = \"maroon\">Question 4</font>\n",
    "\n",
    "Taller people tend to weigh more and shorter people tend to weigh less. By referring to table below, create a list of Height (as x) and a list of Weight (as y). Let see the covariance between these two variable."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "Uj4QPArAcF3h",
    "outputId": "6d775a45-57d5-4270-c661-a82ac2d58bb2"
   },
   "outputs": [
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       "                    7\n",
       "                \n",
       "                <td id=\"T_bb346cf0_7bab_11e9_ab81_782bcb97f042row7_col0\" class=\"data row7 col0\">\n",
       "                    8\n",
       "                \n",
       "                <td id=\"T_bb346cf0_7bab_11e9_ab81_782bcb97f042row7_col1\" class=\"data row7 col1\">\n",
       "                    171\n",
       "                \n",
       "                <td id=\"T_bb346cf0_7bab_11e9_ab81_782bcb97f042row7_col2\" class=\"data row7 col2\">\n",
       "                    68\n",
       "                \n",
       "            </tr>\n",
       "            \n",
       "            <tr>\n",
       "                \n",
       "                <th id=\"T_bb346cf0_7bab_11e9_ab81_782bcb97f042\" class=\"row_heading level2 row8\">\n",
       "                    8\n",
       "                \n",
       "                <td id=\"T_bb346cf0_7bab_11e9_ab81_782bcb97f042row8_col0\" class=\"data row8 col0\">\n",
       "                    9\n",
       "                \n",
       "                <td id=\"T_bb346cf0_7bab_11e9_ab81_782bcb97f042row8_col1\" class=\"data row8 col1\">\n",
       "                    163.9\n",
       "                \n",
       "                <td id=\"T_bb346cf0_7bab_11e9_ab81_782bcb97f042row8_col2\" class=\"data row8 col2\">\n",
       "                    65\n",
       "                \n",
       "            </tr>\n",
       "            \n",
       "            <tr>\n",
       "                \n",
       "                <th id=\"T_bb346cf0_7bab_11e9_ab81_782bcb97f042\" class=\"row_heading level2 row9\">\n",
       "                    9\n",
       "                \n",
       "                <td id=\"T_bb346cf0_7bab_11e9_ab81_782bcb97f042row9_col0\" class=\"data row9 col0\">\n",
       "                    10\n",
       "                \n",
       "                <td id=\"T_bb346cf0_7bab_11e9_ab81_782bcb97f042row9_col1\" class=\"data row9 col1\">\n",
       "                    151\n",
       "                \n",
       "                <td id=\"T_bb346cf0_7bab_11e9_ab81_782bcb97f042row9_col2\" class=\"data row9 col2\">\n",
       "                    78\n",
       "                \n",
       "            </tr>\n",
       "            \n",
       "            <tr>\n",
       "                \n",
       "                <th id=\"T_bb346cf0_7bab_11e9_ab81_782bcb97f042\" class=\"row_heading level2 row10\">\n",
       "                    10\n",
       "                \n",
       "                <td id=\"T_bb346cf0_7bab_11e9_ab81_782bcb97f042row10_col0\" class=\"data row10 col0\">\n",
       "                    11\n",
       "                \n",
       "                <td id=\"T_bb346cf0_7bab_11e9_ab81_782bcb97f042row10_col1\" class=\"data row10 col1\">\n",
       "                    149.9\n",
       "                \n",
       "                <td id=\"T_bb346cf0_7bab_11e9_ab81_782bcb97f042row10_col2\" class=\"data row10 col2\">\n",
       "                    50\n",
       "                \n",
       "            </tr>\n",
       "            \n",
       "            <tr>\n",
       "                \n",
       "                <th id=\"T_bb346cf0_7bab_11e9_ab81_782bcb97f042\" class=\"row_heading level2 row11\">\n",
       "                    11\n",
       "                \n",
       "                <td id=\"T_bb346cf0_7bab_11e9_ab81_782bcb97f042row11_col0\" class=\"data row11 col0\">\n",
       "                    12\n",
       "                \n",
       "                <td id=\"T_bb346cf0_7bab_11e9_ab81_782bcb97f042row11_col1\" class=\"data row11 col1\">\n",
       "                    149.9\n",
       "                \n",
       "                <td id=\"T_bb346cf0_7bab_11e9_ab81_782bcb97f042row11_col2\" class=\"data row11 col2\">\n",
       "                    62\n",
       "                \n",
       "            </tr>\n",
       "            \n",
       "            <tr>\n",
       "                \n",
       "                <th id=\"T_bb346cf0_7bab_11e9_ab81_782bcb97f042\" class=\"row_heading level2 row12\">\n",
       "                    12\n",
       "                \n",
       "                <td id=\"T_bb346cf0_7bab_11e9_ab81_782bcb97f042row12_col0\" class=\"data row12 col0\">\n",
       "                    13\n",
       "                \n",
       "                <td id=\"T_bb346cf0_7bab_11e9_ab81_782bcb97f042row12_col1\" class=\"data row12 col1\">\n",
       "                    164\n",
       "                \n",
       "                <td id=\"T_bb346cf0_7bab_11e9_ab81_782bcb97f042row12_col2\" class=\"data row12 col2\">\n",
       "                    57\n",
       "                \n",
       "            </tr>\n",
       "            \n",
       "            <tr>\n",
       "                \n",
       "                <th id=\"T_bb346cf0_7bab_11e9_ab81_782bcb97f042\" class=\"row_heading level2 row13\">\n",
       "                    13\n",
       "                \n",
       "                <td id=\"T_bb346cf0_7bab_11e9_ab81_782bcb97f042row13_col0\" class=\"data row13 col0\">\n",
       "                    14\n",
       "                \n",
       "                <td id=\"T_bb346cf0_7bab_11e9_ab81_782bcb97f042row13_col1\" class=\"data row13 col1\">\n",
       "                    180\n",
       "                \n",
       "                <td id=\"T_bb346cf0_7bab_11e9_ab81_782bcb97f042row13_col2\" class=\"data row13 col2\">\n",
       "                    85\n",
       "                \n",
       "            </tr>\n",
       "            \n",
       "            <tr>\n",
       "                \n",
       "                <th id=\"T_bb346cf0_7bab_11e9_ab81_782bcb97f042\" class=\"row_heading level2 row14\">\n",
       "                    14\n",
       "                \n",
       "                <td id=\"T_bb346cf0_7bab_11e9_ab81_782bcb97f042row14_col0\" class=\"data row14 col0\">\n",
       "                    15\n",
       "                \n",
       "                <td id=\"T_bb346cf0_7bab_11e9_ab81_782bcb97f042row14_col1\" class=\"data row14 col1\">\n",
       "                    167\n",
       "                \n",
       "                <td id=\"T_bb346cf0_7bab_11e9_ab81_782bcb97f042row14_col2\" class=\"data row14 col2\">\n",
       "                    51\n",
       "                \n",
       "            </tr>\n",
       "            \n",
       "        </tbody>\n",
       "        </table>\n",
       "        "
      ],
      "text/plain": [
       "<pandas.formats.style.Styler at 0x9f50828>"
      ]
     },
     "execution_count": 81,
     "metadata": {
      "tags": []
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import pandas as pd\n",
    "\n",
    "people = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]\n",
    "height = [173.0, 173.0, 162.0, 163.0, 152.0, 172.0, 170.0, 171.0, 163.9, 151.0, 149.9, 149.9, 164.0, 180.0, 167.0]\n",
    "weight = [50, 73, 53, 85, 74, 62, 75, 68, 65, 78, 50, 62, 57, 85, 51]\n",
    "\n",
    "df = pd.DataFrame(people, columns = ['People']); df[('Height (cm)')] = height; df[('Weight (kg)')] = weight\n",
    "df.style.set_properties(**{'text-align':'center'})\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "km9UaaV-cF3k"
   },
   "source": [
    "### <font color = \"maroon\">Question 5</font>\n",
    "\n",
    "By referring to table in Question 4, find:\n",
    "-  Mean of x (as meanX) and mean of y (as meanY)\n",
    "-  The difference for each value in x from mean of x (as a), and each value in y from mean of y\n",
    "-  Product of the results obtain\n",
    "-  Covariance and print it."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "oabjuDm1cF3l",
    "outputId": "9c402948-2bd5-413d-b170-d014469e460d"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "17.9519047619\n"
     ]
    }
   ],
   "source": [
    "#4. Create the list of Height and the Weight\n",
    "height = [173.0, 173.0, 162.0, 163.0, 152.0, 172.0, 170.0, 171.0, 163.9, 151.0, 149.9, 149.9, 164.0, 180.0, 167.0]\n",
    "weight = [50, 73, 53, 85, 74, 62, 75, 68, 65, 78, 50, 62, 57, 85, 51]\n",
    "\n",
    "#5.1 Find mean of x, and mean of y\n",
    "meanHeight = sum(height) / len(height)\n",
    "meanWeight = sum(weight) / len(weight)\n",
    "\n",
    "#5.2 Find the difference for each value of x from mean of x (as a), and each value of y from mean of y (as b)\n",
    "c = []\n",
    "\n",
    "for i in height:\n",
    "    c.append(i - meanHeight)\n",
    "\n",
    "d = []\n",
    "\n",
    "for j in weight:\n",
    "    d.append(j - meanWeight)\n",
    "    \n",
    "#5.3 Find the product of the results obtained\n",
    "heightWeight = []\n",
    "\n",
    "for k in range(len(c)):\n",
    "    heightWeight.append(c[k]*d[k])\n",
    "\n",
    "#5.4 Find the covariance and print it\n",
    "covariance = sum(heightWeight) / float(len(heightWeight) - 1)\n",
    "print covariance"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "Ee15ETlKcF3o"
   },
   "source": [
    "### <font color = \"maroon\">Question 6</font>\n",
    "\n",
    "By referring to table in Question 4, import **NUMPY** and use it to find the covariance of x and y, compare with your step by step result."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "_hFZA1t4cF3p",
    "outputId": "aedd41b8-0eb0-41a3-d02f-4fbc5b4a351d"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "6. The covariance of height and weight is \n",
      "[[  92.24552381   17.95190476]\n",
      " [  17.95190476  148.83809524]]\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "\n",
    "print \"6. The covariance of height and weight is \"\n",
    "print (np.cov(height, weight))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "Okj7YpuucF3s"
   },
   "source": [
    "### <font color = \"darkorchid\">Question 7</font>\n",
    "Taller people have larger shoe sizes and shorter people have smaller shoe sizes. By referring to the table provided, find:\n",
    "\n",
    "-  Mean of x (as meanX) and mean of y (as meanY)\n",
    "-  The difference for each value in x from mean of x (as a), and each value in y from mean of y\n",
    "-  Product of the results obtain\n",
    "-  Covariance and print it."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "l4rtbdvtcF3t",
    "outputId": "40f35ca6-e4f6-4b80-c4e7-d5669db1e2cc"
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "        <style  type=\"text/css\" >\n",
       "        \n",
       "        \n",
       "        </style>\n",
       "\n",
       "        <table id=\"T_7700b89e_7baf_11e9_902a_782bcb97f042\" None>\n",
       "        \n",
       "\n",
       "        <thead>\n",
       "            \n",
       "            <tr>\n",
       "                \n",
       "                <th class=\"blank\">\n",
       "                \n",
       "                <th class=\"col_heading level0 col0\">People\n",
       "                \n",
       "                <th class=\"col_heading level0 col1\">Height (cm)\n",
       "                \n",
       "                <th class=\"col_heading level0 col2\">Shoe Size\n",
       "                \n",
       "            </tr>\n",
       "            \n",
       "        </thead>\n",
       "        <tbody>\n",
       "            \n",
       "            <tr>\n",
       "                \n",
       "                <th id=\"T_7700b89e_7baf_11e9_902a_782bcb97f042\" class=\"row_heading level2 row0\">\n",
       "                    0\n",
       "                \n",
       "                <td id=\"T_7700b89e_7baf_11e9_902a_782bcb97f042row0_col0\" class=\"data row0 col0\">\n",
       "                    1\n",
       "                \n",
       "                <td id=\"T_7700b89e_7baf_11e9_902a_782bcb97f042row0_col1\" class=\"data row0 col1\">\n",
       "                    173\n",
       "                \n",
       "                <td id=\"T_7700b89e_7baf_11e9_902a_782bcb97f042row0_col2\" class=\"data row0 col2\">\n",
       "                    6\n",
       "                \n",
       "            </tr>\n",
       "            \n",
       "            <tr>\n",
       "                \n",
       "                <th id=\"T_7700b89e_7baf_11e9_902a_782bcb97f042\" class=\"row_heading level2 row1\">\n",
       "                    1\n",
       "                \n",
       "                <td id=\"T_7700b89e_7baf_11e9_902a_782bcb97f042row1_col0\" class=\"data row1 col0\">\n",
       "                    2\n",
       "                \n",
       "                <td id=\"T_7700b89e_7baf_11e9_902a_782bcb97f042row1_col1\" class=\"data row1 col1\">\n",
       "                    173\n",
       "                \n",
       "                <td id=\"T_7700b89e_7baf_11e9_902a_782bcb97f042row1_col2\" class=\"data row1 col2\">\n",
       "                    9\n",
       "                \n",
       "            </tr>\n",
       "            \n",
       "            <tr>\n",
       "                \n",
       "                <th id=\"T_7700b89e_7baf_11e9_902a_782bcb97f042\" class=\"row_heading level2 row2\">\n",
       "                    2\n",
       "                \n",
       "                <td id=\"T_7700b89e_7baf_11e9_902a_782bcb97f042row2_col0\" class=\"data row2 col0\">\n",
       "                    3\n",
       "                \n",
       "                <td id=\"T_7700b89e_7baf_11e9_902a_782bcb97f042row2_col1\" class=\"data row2 col1\">\n",
       "                    162\n",
       "                \n",
       "                <td id=\"T_7700b89e_7baf_11e9_902a_782bcb97f042row2_col2\" class=\"data row2 col2\">\n",
       "                    7\n",
       "                \n",
       "            </tr>\n",
       "            \n",
       "            <tr>\n",
       "                \n",
       "                <th id=\"T_7700b89e_7baf_11e9_902a_782bcb97f042\" class=\"row_heading level2 row3\">\n",
       "                    3\n",
       "                \n",
       "                <td id=\"T_7700b89e_7baf_11e9_902a_782bcb97f042row3_col0\" class=\"data row3 col0\">\n",
       "                    4\n",
       "                \n",
       "                <td id=\"T_7700b89e_7baf_11e9_902a_782bcb97f042row3_col1\" class=\"data row3 col1\">\n",
       "                    163\n",
       "                \n",
       "                <td id=\"T_7700b89e_7baf_11e9_902a_782bcb97f042row3_col2\" class=\"data row3 col2\">\n",
       "                    8\n",
       "                \n",
       "            </tr>\n",
       "            \n",
       "            <tr>\n",
       "                \n",
       "                <th id=\"T_7700b89e_7baf_11e9_902a_782bcb97f042\" class=\"row_heading level2 row4\">\n",
       "                    4\n",
       "                \n",
       "                <td id=\"T_7700b89e_7baf_11e9_902a_782bcb97f042row4_col0\" class=\"data row4 col0\">\n",
       "                    5\n",
       "                \n",
       "                <td id=\"T_7700b89e_7baf_11e9_902a_782bcb97f042row4_col1\" class=\"data row4 col1\">\n",
       "                    152\n",
       "                \n",
       "                <td id=\"T_7700b89e_7baf_11e9_902a_782bcb97f042row4_col2\" class=\"data row4 col2\">\n",
       "                    11\n",
       "                \n",
       "            </tr>\n",
       "            \n",
       "            <tr>\n",
       "                \n",
       "                <th id=\"T_7700b89e_7baf_11e9_902a_782bcb97f042\" class=\"row_heading level2 row5\">\n",
       "                    5\n",
       "                \n",
       "                <td id=\"T_7700b89e_7baf_11e9_902a_782bcb97f042row5_col0\" class=\"data row5 col0\">\n",
       "                    6\n",
       "                \n",
       "                <td id=\"T_7700b89e_7baf_11e9_902a_782bcb97f042row5_col1\" class=\"data row5 col1\">\n",
       "                    172\n",
       "                \n",
       "                <td id=\"T_7700b89e_7baf_11e9_902a_782bcb97f042row5_col2\" class=\"data row5 col2\">\n",
       "                    10\n",
       "                \n",
       "            </tr>\n",
       "            \n",
       "            <tr>\n",
       "                \n",
       "                <th id=\"T_7700b89e_7baf_11e9_902a_782bcb97f042\" class=\"row_heading level2 row6\">\n",
       "                    6\n",
       "                \n",
       "                <td id=\"T_7700b89e_7baf_11e9_902a_782bcb97f042row6_col0\" class=\"data row6 col0\">\n",
       "                    7\n",
       "                \n",
       "                <td id=\"T_7700b89e_7baf_11e9_902a_782bcb97f042row6_col1\" class=\"data row6 col1\">\n",
       "                    170\n",
       "                \n",
       "                <td id=\"T_7700b89e_7baf_11e9_902a_782bcb97f042row6_col2\" class=\"data row6 col2\">\n",
       "                    8\n",
       "                \n",
       "            </tr>\n",
       "            \n",
       "            <tr>\n",
       "                \n",
       "                <th id=\"T_7700b89e_7baf_11e9_902a_782bcb97f042\" class=\"row_heading level2 row7\">\n",
       "                    7\n",
       "                \n",
       "                <td id=\"T_7700b89e_7baf_11e9_902a_782bcb97f042row7_col0\" class=\"data row7 col0\">\n",
       "                    8\n",
       "                \n",
       "                <td id=\"T_7700b89e_7baf_11e9_902a_782bcb97f042row7_col1\" class=\"data row7 col1\">\n",
       "                    171\n",
       "                \n",
       "                <td id=\"T_7700b89e_7baf_11e9_902a_782bcb97f042row7_col2\" class=\"data row7 col2\">\n",
       "                    7\n",
       "                \n",
       "            </tr>\n",
       "            \n",
       "            <tr>\n",
       "                \n",
       "                <th id=\"T_7700b89e_7baf_11e9_902a_782bcb97f042\" class=\"row_heading level2 row8\">\n",
       "                    8\n",
       "                \n",
       "                <td id=\"T_7700b89e_7baf_11e9_902a_782bcb97f042row8_col0\" class=\"data row8 col0\">\n",
       "                    9\n",
       "                \n",
       "                <td id=\"T_7700b89e_7baf_11e9_902a_782bcb97f042row8_col1\" class=\"data row8 col1\">\n",
       "                    163.9\n",
       "                \n",
       "                <td id=\"T_7700b89e_7baf_11e9_902a_782bcb97f042row8_col2\" class=\"data row8 col2\">\n",
       "                    7\n",
       "                \n",
       "            </tr>\n",
       "            \n",
       "            <tr>\n",
       "                \n",
       "                <th id=\"T_7700b89e_7baf_11e9_902a_782bcb97f042\" class=\"row_heading level2 row9\">\n",
       "                    9\n",
       "                \n",
       "                <td id=\"T_7700b89e_7baf_11e9_902a_782bcb97f042row9_col0\" class=\"data row9 col0\">\n",
       "                    10\n",
       "                \n",
       "                <td id=\"T_7700b89e_7baf_11e9_902a_782bcb97f042row9_col1\" class=\"data row9 col1\">\n",
       "                    151\n",
       "                \n",
       "                <td id=\"T_7700b89e_7baf_11e9_902a_782bcb97f042row9_col2\" class=\"data row9 col2\">\n",
       "                    6\n",
       "                \n",
       "            </tr>\n",
       "            \n",
       "            <tr>\n",
       "                \n",
       "                <th id=\"T_7700b89e_7baf_11e9_902a_782bcb97f042\" class=\"row_heading level2 row10\">\n",
       "                    10\n",
       "                \n",
       "                <td id=\"T_7700b89e_7baf_11e9_902a_782bcb97f042row10_col0\" class=\"data row10 col0\">\n",
       "                    11\n",
       "                \n",
       "                <td id=\"T_7700b89e_7baf_11e9_902a_782bcb97f042row10_col1\" class=\"data row10 col1\">\n",
       "                    149.9\n",
       "                \n",
       "                <td id=\"T_7700b89e_7baf_11e9_902a_782bcb97f042row10_col2\" class=\"data row10 col2\">\n",
       "                    4\n",
       "                \n",
       "            </tr>\n",
       "            \n",
       "            <tr>\n",
       "                \n",
       "                <th id=\"T_7700b89e_7baf_11e9_902a_782bcb97f042\" class=\"row_heading level2 row11\">\n",
       "                    11\n",
       "                \n",
       "                <td id=\"T_7700b89e_7baf_11e9_902a_782bcb97f042row11_col0\" class=\"data row11 col0\">\n",
       "                    12\n",
       "                \n",
       "                <td id=\"T_7700b89e_7baf_11e9_902a_782bcb97f042row11_col1\" class=\"data row11 col1\">\n",
       "                    149.9\n",
       "                \n",
       "                <td id=\"T_7700b89e_7baf_11e9_902a_782bcb97f042row11_col2\" class=\"data row11 col2\">\n",
       "                    4\n",
       "                \n",
       "            </tr>\n",
       "            \n",
       "            <tr>\n",
       "                \n",
       "                <th id=\"T_7700b89e_7baf_11e9_902a_782bcb97f042\" class=\"row_heading level2 row12\">\n",
       "                    12\n",
       "                \n",
       "                <td id=\"T_7700b89e_7baf_11e9_902a_782bcb97f042row12_col0\" class=\"data row12 col0\">\n",
       "                    13\n",
       "                \n",
       "                <td id=\"T_7700b89e_7baf_11e9_902a_782bcb97f042row12_col1\" class=\"data row12 col1\">\n",
       "                    164\n",
       "                \n",
       "                <td id=\"T_7700b89e_7baf_11e9_902a_782bcb97f042row12_col2\" class=\"data row12 col2\">\n",
       "                    10\n",
       "                \n",
       "            </tr>\n",
       "            \n",
       "            <tr>\n",
       "                \n",
       "                <th id=\"T_7700b89e_7baf_11e9_902a_782bcb97f042\" class=\"row_heading level2 row13\">\n",
       "                    13\n",
       "                \n",
       "                <td id=\"T_7700b89e_7baf_11e9_902a_782bcb97f042row13_col0\" class=\"data row13 col0\">\n",
       "                    14\n",
       "                \n",
       "                <td id=\"T_7700b89e_7baf_11e9_902a_782bcb97f042row13_col1\" class=\"data row13 col1\">\n",
       "                    180\n",
       "                \n",
       "                <td id=\"T_7700b89e_7baf_11e9_902a_782bcb97f042row13_col2\" class=\"data row13 col2\">\n",
       "                    10.5\n",
       "                \n",
       "            </tr>\n",
       "            \n",
       "            <tr>\n",
       "                \n",
       "                <th id=\"T_7700b89e_7baf_11e9_902a_782bcb97f042\" class=\"row_heading level2 row14\">\n",
       "                    14\n",
       "                \n",
       "                <td id=\"T_7700b89e_7baf_11e9_902a_782bcb97f042row14_col0\" class=\"data row14 col0\">\n",
       "                    15\n",
       "                \n",
       "                <td id=\"T_7700b89e_7baf_11e9_902a_782bcb97f042row14_col1\" class=\"data row14 col1\">\n",
       "                    167\n",
       "                \n",
       "                <td id=\"T_7700b89e_7baf_11e9_902a_782bcb97f042row14_col2\" class=\"data row14 col2\">\n",
       "                    6\n",
       "                \n",
       "            </tr>\n",
       "            \n",
       "        </tbody>\n",
       "        </table>\n",
       "        "
      ],
      "text/plain": [
       "<pandas.formats.style.Styler at 0xa2de048>"
      ]
     },
     "execution_count": 95,
     "metadata": {
      "tags": []
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import pandas as pd\n",
    "\n",
    "people = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]\n",
    "height = [173.0, 173.0, 162.0, 163.0, 152.0, 172.0, 170.0, 171.0, 163.9, 151.0, 149.9, 149.9, 164.0, 180.0, 167.0]\n",
    "shoesize = [6.0, 9.0, 7.0, 8.0, 11.0, 10.0, 8.0, 7.0, 7.0, 6.0, 4.0, 4.0, 10.0, 10.5, 6]\n",
    "\n",
    "df = pd.DataFrame(people, columns = ['People']); df[('Height (cm)')] = height; df[('Shoe Size')] = shoesize\n",
    "df.style.set_properties(**{'text-align':'center'})\n",
    "df.style.format({'height':\"{:.2%}\"})\n",
    "df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "yJT_Z1TPcF3z",
    "outputId": "c80ff83f-a8a2-439e-8e85-6faaf367bb3e"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "9.97404761905\n"
     ]
    }
   ],
   "source": [
    "people = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]\n",
    "height = [173.0, 173.0, 162.0, 163.0, 152.0, 172.0, 170.0, 171.0, 163.9, 151.0, 149.9, 149.9, 164.0, 180.0, 167.0]\n",
    "shoesize = [6.0, 9.0, 7.0, 8.0, 11.0, 10.0, 8.0, 7.0, 7.0, 6.0, 4.0, 4.0, 10.0, 10.5, 6]\n",
    "\n",
    "#8.1 Find the mean of height (as meanHeight) and mean of shoesize (meanShoesize)\n",
    "meanHeight = sum(height) / len(height)\n",
    "meanShoesize = sum(shoesize) / len(shoesize)\n",
    "\n",
    "#8.2 Find the difference for each value in height from mean of height (as e), and each value in shoe size from mean of shoe size (as f)\n",
    "e = []\n",
    "for i in height:\n",
    "    e.append(i - meanHeight)\n",
    "\n",
    "f = []\n",
    "for j in shoesize:\n",
    "    f.append(j - meanShoesize)\n",
    "\n",
    "#8.3 Find the product of the results obtained\n",
    "ef = []\n",
    "for k in range(len(e)):\n",
    "    ef.append(e[k]*f[k])\n",
    "\n",
    "#8.4 Find the covariance and print it\n",
    "covariance = sum(ef) / float(len(ef) - 1)\n",
    "print covariance"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "PMFiKGkNcF32"
   },
   "source": [
    "### <font color=\"darkorchid\">Question 8</font>\n",
    "\n",
    "By referring to table in Question 7, import **NUMPY** and use it to find the covariance of x and y, compare with your step by step result."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "B-xfReqzcF33",
    "outputId": "d16104a0-f1da-43a9-9ea7-db2390b3e35c"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "9. The covariance is \n",
      "[[ 92.24552381   9.97404762]\n",
      " [  9.97404762   4.88809524]]\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "\n",
    "print \"9. The covariance is \"\n",
    "print (np.cov(height, shoesize))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "a94pPhv4cF36"
   },
   "source": [
    "### <font color = \"green\">Question 9</font>\n",
    "\n",
    "Believe it or not, chickens have a quite an impressive lifespan! The maximum age of a chicken is around 25 years. It's very rare for a chicken to live that long, however, because they are so vulnerable to predators and disease. Due to their vulnerability, the average age of a backyard chicken is only 3 or 4 years. Although with special protection and care it would not be unreasonable to expect 7 or 8 years. Average production of egg is 8 eggs per 10 days.\n",
    "\n",
    "If a chicken increases in age, the amount of eggs it produces decrease. By considering the chicken have special protection and care, generate a list of random numbers for the age of 20 chicken and the egg produced. Then, find the covariance of these two data using **NUMPY**."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "nX-zkgOUcF37",
    "outputId": "c3184073-c5c3-4046-9a8f-d567427992bb"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The age of chicken are : [4, 8, 3, 7, 1, 2, 9, 9, 7, 4, 6, 1, 1, 8, 1, 1, 6, 7, 1, 1]\n",
      "The amount of eggs produced are : [5, 7, 8, 6, 9, 4, 1, 1, 8, 9, 3, 9, 3, 0, 3, 3, 5, 6, 9, 10]\n",
      "The covariance between age of chicken and amount of eggs produced is \n",
      "[[ 9.60789474 -4.11315789]\n",
      " [-4.11315789  9.62894737]]\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "import random\n",
    "\n",
    "age = []\n",
    "egg = []\n",
    "\n",
    "for i in range (20):\n",
    "    age.append(random.randint(1, 9))\n",
    "    egg.append(random.randint(0, 10))\n",
    "\n",
    "print \"The age of chicken are :\", age\n",
    "print \"The amount of eggs produced are :\", egg\n",
    "\n",
    "print \"The covariance between age of chicken and amount of eggs produced is \"\n",
    "print (np.cov(age, egg))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "yTpHddr6cF4B"
   },
   "source": [
    "### <font color = \"crimson\">Question 10</font>\n",
    "\n",
    "Generate 20 random values for m in range (40, 60). Then, create list n which every value in m is connected with n using formula <em>n = 2m + 1</em>. Find the covariance of these two data using **NUMPY**."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "95GMOAK0cF4C",
    "outputId": "5ff921e6-8cec-465a-e6b1-10da935981e5"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[55, 41, 54, 52, 49, 42, 52, 54, 51, 48, 58, 40, 51, 46, 48, 44, 47, 40, 53, 42]\n",
      "[111, 83, 109, 105, 99, 85, 105, 109, 103, 97, 117, 81, 103, 93, 97, 89, 95, 81, 107, 85]\n",
      "[[  29.71315789   59.42631579]\n",
      " [  59.42631579  118.85263158]]\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "import random\n",
    "\n",
    "m = []\n",
    "n = []\n",
    "\n",
    "for i in range (20):\n",
    "    m.append(random.randint(40, 60))\n",
    "print m\n",
    "\n",
    "for j in m:\n",
    "    n.append((2*j) + 1)\n",
    "print n\n",
    "       \n",
    "print (np.cov(m, n))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "PtPHPQfacF4I"
   },
   "source": [
    "### <font color = \"crimson\">Question 11</font>\n",
    "\n",
    "Using the data of m and n in <font color = \"crimson\">Question 11</font>, draw a scatter plot of m and n."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "ZP8MmWx3cF4J",
    "outputId": "88d649b3-7de0-4b1c-de0b-dce7640b75b6"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " \n",
      "2 x + 1\n"
     ]
    },
    {
     "data": {
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g6Y5HItIplZaWMvl7F/H+e+8xJbUvS+9fwrpXf89vnn2GoUOHtqhviYh0Lkcb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\nl7RzB4NCv/kAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x66d7ac8>"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "plt.scatter(m, n, c = \"crimson\", s = 100, marker = \"p\" )\n",
    "plt.xlabel(\"m\", fontsize = 12); plt.ylabel(\"n\", fontsize = 12)\n",
    "plt.xticks(size = 10); plt.yticks(size = 10)\n",
    "plt.title(\"m versus n\", fontsize = 15)\n",
    "\n",
    "equation = np.poly1d(np.polyfit(m, n, 1))\n",
    "print equation\n",
    "\n",
    "mm = np.arange(40, 60, 0.1)\n",
    "nn = (2 * mm) + 1\n",
    "\n",
    "plt.plot(mm, nn)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "TPo3qtvbcF4N"
   },
   "source": [
    "### <font color = mediumturquoise>Question 12</font>\n",
    "\n",
    "List of x and y are given. Generate 30 random number from list x and y and assign it as two new list randomX and randomY. Then, draw a scatter plot of randomX and randomY with the line of best fit drawn on the scatter diagram. Try to get the best fit of line!\n",
    "\n",
    "\n",
    "x = [180, 150, 170, 180, 177, 180, 140, 169, 168, 152, 150, 170, 109, 180, 108, 175, 144, 120, 133, 160, 160, 159, 165, 180, 149, 180, 160, 155, 156, 145, 122, 131, 156, 166, 170, 155, 158, 170, 160, 165, 159, 119, 168, 175, 161, 160, 160, 150, 140, 148]\n",
    "\n",
    "y = [4.00, 2.50, 4.00, 3.90, 3.75, 3.80, 2.90, 3.10, 3.25, 3.40, 3.30, 3.90, 1.35, 4.00, 1.00, 3.85, 2.98, 2.75, 2.75, 3.60, 3.50, 3.50, 3.50, 3.85, 2.95, 3.95, 3.65, 3.55, 3.58, 2.98, 1.50, 1.75, 2.20, 3.00, 3.00, 3.00, 3.15, 3.90, 3.15, 3.85, 2.70, 1.00, 3.25, 3.90, 2.80, 3.50, 3.40, 2.30, 2.50, 2.35]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "CMMbb9sZcF4O",
    "outputId": "2dc0104d-eac2-4887-cc02-9876761f4891"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "randomX =  [180, 133, 160, 109, 150, 145, 145, 168, 170, 155, 180, 180, 144, 140, 122, 148, 156, 180, 119, 119, 175, 145, 133, 145, 180, 160, 160, 170, 122, 150]\n",
      "randomY =  [3.65, 2.8, 2.8, 3.9, 3.15, 3.85, 3.5, 2.3, 3.5, 2.95, 3.85, 3.15, 3.0, 3.8, 2.98, 3.85, 3.9, 3.58, 3.9, 3.1, 3.1, 3.5, 3.5, 2.8, 3.1, 3.4, 3.5, 4.0, 3.85, 3.4]\n",
      " \n",
      "-0.002309 x + 3.738\n"
     ]
    },
    {
     "data": {
      "image/png": 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WGk2wFruUmIiEoWFDOPdc+OMfYe1a+Phjn5DUrw+jR0OXLpCQsJkmTaYzYMAk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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f54978>"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = [180, 150, 170, 180, 177, 180, 140, 169, 168, 152, 150, 170, 109, 180, 108, 175, 144, 120, 133, 160, 160, 159, 165, 180, 149, 180, 160, 155, 156, 145, 122, 131, 156, 166, 170, 155, 158, 170, 160, 165, 159, 119, 168, 175, 161, 160, 160, 150, 140, 148]\n",
    "y = [4.00, 2.50, 4.00, 3.90, 3.75, 3.80, 2.90, 3.10, 3.25, 3.40, 3.30, 3.90, 1.35, 4.00, 1.00, 3.85, 2.98, 2.75, 2.75, 3.60, 3.50, 3.50, 3.50, 3.85, 2.95, 3.95, 3.65, 3.55, 3.58, 2.98, 1.50, 1.75, 2.20, 3.00, 3.00, 3.00, 3.15, 3.90, 3.15, 3.85, 2.70, 1.00, 3.25, 3.90, 2.80, 3.50, 3.40, 2.30, 2.50, 2.35]\n",
    "\n",
    "import random\n",
    "\n",
    "randomX = []\n",
    "randomY = []\n",
    "\n",
    "for i in range (30):\n",
    "    randomX.append(random.choice(x))\n",
    "    randomY.append(random.choice(y))\n",
    "print \"randomX = \", randomX\n",
    "print \"randomY = \", randomY\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "plt.scatter(randomX, randomY, c = \"mediumturquoise\", s = 100, marker = \"p\")\n",
    "plt.xlabel(\"RandomX\", fontsize = 12); plt.ylabel(\"RandomY\", fontsize = 12)\n",
    "plt.xticks(size = 10); plt.yticks(size = 10)\n",
    "plt.title(\"RandomX vs RandomY\", fontsize = 12)\n",
    "\n",
    "import numpy as np\n",
    "\n",
    "equation = np.poly1d(np.polyfit(randomX, randomY, 1))\n",
    "print equation\n",
    "\n",
    "randomXX = np.arange(110, 190, 0.1)\n",
    "randomYY = ((-0.01075 * randomXX) + 4.974)\n",
    "\n",
    "plt.plot(randomXX, randomYY)\n",
    "\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "colab": {
   "name": "3.0-Covariance.ipynb",
   "provenance": []
  },
  "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": "3.9.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}