3.2-Linear Regression.ipynb

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    "# <font color='deeppink'>LINEAR REGRESSION</font>\n",
    "\n",
    "## <b>1.0 General explanation about <font color='deeppink'>Linear Regression</font> </b>\n",
    "\n",
    "<font size =3 >Regression is the using of the relationship between variables to find best fit line or best equation. Best fit line is used to get the most accurate data which from there, we can make the best prediction. Linear regression is used for continuous data, or two correlated variables."
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    "![alt text](https://cdn-images-1.medium.com/max/1200/1*xz_haBuJRSI2DaveNk-3gw.gif)\n",
    "$$ Y = a_1X_1 + b (randomError) $$"
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   "source": [
    "## <b>1.1 Method used to calculate <font color='deeppink'>Linear Regression</font> line.</b> "
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    "# $$ y = A + Bx $$\n",
    "\n",
    "<font size =4>Method used: </font><font size =4 color='orangered'><b>LEAST SQUARE METHOD</b></font><br><br>\n",
    "\n",
    "- <font size=4> A method to estimate the true value of some quantity <b>based on a consideration of errors </b>in observations or measurements.</font><br><br>\n",
    "\n",
    "- <font size=4> It provides the <b>overall rationale placement of the line of the best fit</b> among the data points being studied. </font><br><br>\n",
    "\n",
    "- <font size =4>AIM:<b> To calculate the values B (slope) and A (y-intercept) in the equation of a line.</b></font>\n"
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    "##  1.2 <font color='orangered'>Least Square Method </font>Explanation <br>\n",
    "- <font size =4> It finds <b> all possible line equations </b>for a given set of data points and select the one <b>which has the least squared sum of errors (residual).</b></font><br><br>\n",
    "\n",
    "- <font size =4><b>ERRORS :</b> the <b>difference</b> between the an observed value <font color='red'><b>(actual)</b></font> and the fitted value provided by a model <font color='red'><b>(predicted)</b></font></font><br><br>\n",
    "\n",
    "- <font size =4> So our equation will produce <b>the value of y with the least value of errors </b></font> <br><br>\n",
    "\n",
    "![alt_text](https://muthu.co/wp-content/uploads/2018/06/Snip20180616_19.png)\n"
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   "source": [
    "## <b>2.0 The manual steps to find the <font color=\"orangered\">Linear Regression:</font>"
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    "\n",
    "<font size =4 >1. You have to build the <b>new equation </b>which consists of the least error values </font>\n",
    "\n",
    "<font size =4 >2. So, find the <b>new slope (B)</b></font>\n",
    "\n",
    "## $$ B = \\frac {n\\sum xy - \\sum x \\sum y} { n\\sum x^2 - (\\sum x)^2} $$\n",
    "\n",
    "<font size =4 >3. Then, calculate the <b>y-intercept </b></font>\n",
    "\n",
    "## $$ A = \\frac {n\\sum y - B\\sum x} { n} $$\n",
    "\n",
    "<font size =4>So, in order to calculate the values of B and A, you first need :</font>\n",
    "## $x^2$, $y^2$, $xy$\n",
    "## $\\sum x$, $\\sum y$, $\\sum x^2$, $\\sum y^2$, $\\sum xy$<br>\n"
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   "source": [
    "## 2.1 Further explanation with video"
   ]
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   "source": [
    "## 3.0 Finding Linear Regression equation <font color=\"deeppink\">using Python.</font>"
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    "## <font color='blue'>STEP 1:</font>\n",
    "\n",
    "<font size =4> Store your data inside a table, which consists of column $x$ and $y$. Then, add 3 more columns inside the table labelled $xy$, $x^2$, and $y^2$. Note that $xy$ is the product of $x$ and $y$, $x^2$ is the square of $x$, and $y^2$ is the square of $y$.</font><br>\n",
    "\n",
    "<font size =4> As we are using python to do the calculation, you can use list to store the values of x and y. It will be easier and faster to handle the data. </font>"
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light",
      "tags": []
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "x= np.arange(0,10,0.1)   # generate random value of x\n",
    "y= (x*2) + (np.random.normal(0,1,len(x))*3)   # generate random value of x\n",
    "\n",
    "plt.xlabel('X')\n",
    "plt.ylabel('Y')\n",
    "plt.scatter(x,y)\n",
    "\n",
    "## Step 1\n",
    "xy=[]\n",
    "x2=[]\n",
    "y2=[]   # create an empty list for each of the new column\n",
    "\n",
    "for m in range(len(x)):\n",
    "    ab = x[m] * y[m]   # calculate x*y\n",
    "    xy.append(ab)      # append each value of x*y into the list\n",
    "# print(\"xy: \"+ str(xy))\n",
    "\n",
    "for i in x:\n",
    "    a= i**2        # calculate x power of 2\n",
    "    x2.append(a)   # append each value of x^2 into the list\n",
    "# print(\"x2: \"+ str(x2))\n",
    "\n",
    "for j in y:\n",
    "    b= j**2        # calculate y power of 2\n",
    "    y2.append(b)   # append each value of y^2 into the list\n",
    "# print(\"y2: \"+ str(y2))\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "jjAzPyPCc4bj"
   },
   "source": [
    "## <font color='blue'>STEP 2:</font>\n",
    "<font size =4> Now add a new row to the bottom of your table. This row should store the total sum of each of column $x$, $y$, $xy$, $x^2$, and $y^2$. Use for loop to get the sum of each column. </font>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "sPP1ILnoc4bk",
    "outputId": "bf6b6a60-03b9-4ad7-e689-dbde2c20035d"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Sum of x: 495.0\n",
      "Sum of y: 1038.3438771091264\n",
      "Sum of xy: 6970.038340745252\n",
      "Sum of x2: 3283.5000000000005\n",
      "Sum of y2: 15837.179789842347\n"
     ]
    }
   ],
   "source": [
    "## Step 2\n",
    "\n",
    "nX=0\n",
    "nY=0\n",
    "nXY=0\n",
    "nX2=0\n",
    "nY2=0   # initialize the sum of each column as 0\n",
    "\n",
    "for i in x:\n",
    "    nX += i   # calculate sum of x\n",
    "print(\"Sum of x: \"+str(nX))   \n",
    "\n",
    "\n",
    "for j in y:\n",
    "    nY += j   # calculate sum of y\n",
    "print(\"Sum of y: \"+str(nY))\n",
    "\n",
    "\n",
    "for k in xy:\n",
    "    nXY += k   # calculate sum of xy\n",
    "print(\"Sum of xy: \"+str(nXY))\n",
    "\n",
    "\n",
    "for m in x2:\n",
    "    nX2 += m   # calculate sum of x2\n",
    "print(\"Sum of x2: \"+str(nX2))\n",
    "\n",
    "\n",
    "for n in y2:   \n",
    "    nY2 += n   # calculate sum of y2\n",
    "print(\"Sum of y2: \"+str(nY2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "FkwnDyToc4bo"
   },
   "source": [
    "## <font color='blue'>STEP 3:</font>\n",
    "\n",
    "<font size =4>Using the following formula, calculate the value of $B$ (slope). Note that $n$ is the sample size (number of item) of the table. Make sure you translate the formula correctly for the calculation. </font>\n",
    "\n",
    "## $$ B = \\frac {n\\sum xy - \\sum x \\sum y} { n\\sum x^2 - (\\sum x)^2} $$\n",
    "\n",
    "<font size =4>Then, calculate the value of $A$ (intercept) using the formula which consists of $B$ that we calculated before. </font> \n",
    "\n",
    "## $$ A = \\frac {n\\sum y - B\\sum x} { n} $$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "6nyU-mKNc4bp",
    "outputId": "8505351f-a629-46b1-a7bf-cb3625287316"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "B (slope)    : 2.1965030291690066\n",
      "A (intercept): -0.4892512232953186\n"
     ]
    }
   ],
   "source": [
    "## Step 3\n",
    "n= len(x)\n",
    "\n",
    "B= 0   # initialize B and A to 0\n",
    "A= 0\n",
    "\n",
    "B = ((n*nXY) - (nX*nY)) / (n*nX2 - (nX**2))\n",
    "A = ((nY) - B*(nX)) / n  # Translate the formula into calculation for A and B\n",
    "\n",
    "print(\"B (slope)    : \"+str(B))\n",
    "print(\"A (intercept): \"+str(A))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "pmmMxZbTc4bs"
   },
   "source": [
    "## <font color='blue'>STEP 4:</font>\n",
    "<font size =4>Insert the values into the equation: </font>\n",
    "## $y = A + Bx$\n",
    "<font size =4> You can use for loop to generate the new $y$, for each value of $x$ to form the linear regression line. Store the value of new $y$ inside a list as we want to use it later on. </font>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "collapsed": true,
    "id": "ogPsAsSFc4bt"
   },
   "outputs": [],
   "source": [
    "## Step 4\n",
    "\n",
    "Y= []\n",
    "for i in range(n):\n",
    "    y0=  A + (B*x[i]) \n",
    "#     y0= A + B*x[i]\n",
    "    Y.append(y0)\n",
    "# print(Y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "Yfp6MlxLc4by"
   },
   "source": [
    "## <font color='blue'>STEP 5:</font>\n",
    "## Use 'plot(x, y)' function from matplotlib to form the linear regression line."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "olTpdj6bc4bz",
    "outputId": "bbe94d0e-e857-4806-b368-75332b004726"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x202fdbc2828>]"
      ]
     },
     "execution_count": 5,
     "metadata": {
      "tags": []
     },
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light",
      "tags": []
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.xlabel('X')\n",
    "plt.ylabel('Y')\n",
    "plt.scatter(x,y)\n",
    "plt.plot(x,Y, c=\"red\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "zfUA2lXyc4b2"
   },
   "source": [
    "## 3.1 <font color=\"deeppink\">Using Python libraries</font> to Construct Linear Regression Equation and Line"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "TRZe2URBc4b3"
   },
   "source": [
    "## <font color='orchid'>STEP 1:</font>\n",
    "<font size =4> Import necessary function and libraries which is <b>numpy, matplotlib, and LinearRegression from sklearn.linear_model</b> </font>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "collapsed": true,
    "id": "9XMkBQbDc4b4"
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from sklearn.linear_model import LinearRegression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "GVzZtPArc4b8"
   },
   "source": [
    "## <font color='orchid'>STEP 2:</font>\n",
    "\n",
    "<font size =4>Store your data inside a list. In this case, we generate formula data by using <b>arange()</b> function from numpy\n",
    "</font>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "collapsed": true,
    "id": "MtZFve3wc4b9"
   },
   "outputs": [],
   "source": [
    "x= np.arange(0,10,0.1)\n",
    "# generate data of x from 1-10 with difference of 0.1 between each data\n",
    "\n",
    "y= 1 + (x*2) + (np.random.normal(0,1,len(x))*3)\n",
    "# generate y based on x value using y=A + Bx + random noise (to make more realistic data)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "LTZRvvt9c4cA"
   },
   "source": [
    "## <font color='orchid'>STEP 3:</font>\n",
    "\n",
    "<font size =4> Plot the scattered (random) data by using <b>scatter()</b> function from matplotlib</font>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "3VIXUXfTc4cB",
    "outputId": "c5ffd1ae-8348-4866-d844-e95e9fa7acc9"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x1d8bfaa3080>"
      ]
     },
     "execution_count": 60,
     "metadata": {
      "tags": []
     },
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light",
      "tags": []
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.xlabel('X')\n",
    "plt.ylabel('Y')   # label the axis\n",
    "\n",
    "plt.scatter(x,y)\n",
    "# plot the points of each (x,y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "B_wjr5z7c4cE"
   },
   "source": [
    "## <font color='orchid'>STEP 4:</font>\n",
    "<font size =4> Transform data into column vector by inserting new axis by using <b>newaxis</b> function from numpy.</font>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "collapsed": true,
    "id": "Nu_PZImKc4cF"
   },
   "outputs": [],
   "source": [
    "x= x[:, np.newaxis]\n",
    "y= y[:, np.newaxis]\n",
    "# transform data into column vector by inserting new axis"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "-OhnpiE2c4cI"
   },
   "source": [
    "## <font color='orchid'>STEP 5:</font>\n",
    "<font size =4> Introduce <b>LinearRegression</b> function to a variable </font>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "collapsed": true,
    "id": "cLWUONDUc4cJ"
   },
   "outputs": [],
   "source": [
    "model= LinearRegression(fit_intercept= True)   # if false, the y intercept will always be 1\n",
    "# import linearRegression module from sklearn"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "67P2OquWc4cM"
   },
   "source": [
    "## <font color='orchid'>STEP 6:</font>\n",
    "<font size =4>Use <b>fit(x,y)</b> function to fit the line into scattered data. </font>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "PpLnSRNXc4cN",
    "outputId": "e807ebf5-50b5-4f27-bdc4-aacefa1148f4"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None, normalize=False)"
      ]
     },
     "execution_count": 63,
     "metadata": {
      "tags": []
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.fit(x,y)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "lyvFO9tsc4cS"
   },
   "source": [
    "## <font color='orchid'>STEP 7:</font>\n",
    "<font size =4> Use <b>predict(x)</b> function to find the value of estimated y based on x, then plot the line using <b>plot()</b> function from matplotlib. </font>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "KkVd2KKvc4cT",
    "outputId": "69463334-8d06-424f-b872-e34f811955fd"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1d8bfacad68>]"
      ]
     },
     "execution_count": 64,
     "metadata": {
      "tags": []
     },
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light",
      "tags": []
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.xlabel('X')\n",
    "plt.ylabel('Y')   # label the axis\n",
    "\n",
    "plt.scatter(x,y)\n",
    "# plot the points of each (x,y)\n",
    "y_pred = model.predict(x)\n",
    "plt.plot(x, y_pred, color='r')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "HbPBxYOVc4cd"
   },
   "source": [
    "## 4.0 <font color=\"deeppink\">Questions</font> about Linear Regression\n",
    "## <font color='palevioletred'>Part 1: Linear Regression with normal calculation.</font>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "RgABkDvZc4ce"
   },
   "source": [
    "<font size =4> Table 1 below shows the amount hours spent for study and the mark achieved by students based on their hours of studying.</font>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "UCU3IZRmc4cf",
    "outputId": "218c1ce9-3633-4547-e90b-2b3ce643f718"
   },
   "outputs": [
    {
     "data": {
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       "        }    #T_974d1630_91a5_11e9_8b94_80a5898a2454row7_col0 {\n",
       "            text-align:  center;\n",
       "        }    #T_974d1630_91a5_11e9_8b94_80a5898a2454row7_col1 {\n",
       "            text-align:  center;\n",
       "        }    #T_974d1630_91a5_11e9_8b94_80a5898a2454row8_col0 {\n",
       "            text-align:  center;\n",
       "        }    #T_974d1630_91a5_11e9_8b94_80a5898a2454row8_col1 {\n",
       "            text-align:  center;\n",
       "        }    #T_974d1630_91a5_11e9_8b94_80a5898a2454row9_col0 {\n",
       "            text-align:  center;\n",
       "        }    #T_974d1630_91a5_11e9_8b94_80a5898a2454row9_col1 {\n",
       "            text-align:  center;\n",
       "        }    #T_974d1630_91a5_11e9_8b94_80a5898a2454row10_col0 {\n",
       "            text-align:  center;\n",
       "        }    #T_974d1630_91a5_11e9_8b94_80a5898a2454row10_col1 {\n",
       "            text-align:  center;\n",
       "        }    #T_974d1630_91a5_11e9_8b94_80a5898a2454row11_col0 {\n",
       "            text-align:  center;\n",
       "        }    #T_974d1630_91a5_11e9_8b94_80a5898a2454row11_col1 {\n",
       "            text-align:  center;\n",
       "        }</style><table id=\"T_974d1630_91a5_11e9_8b94_80a5898a2454\" ><thead>    <tr>        <th class=\"blank level0\" ></th>        <th class=\"col_heading level0 col0\" >Number of hours (x)</th>        <th class=\"col_heading level0 col1\" >Marks achieved in examination (y)</th>    </tr></thead><tbody>\n",
       "                <tr>\n",
       "                        <th id=\"T_974d1630_91a5_11e9_8b94_80a5898a2454level0_row0\" class=\"row_heading level0 row0\" >0</th>\n",
       "                        <td id=\"T_974d1630_91a5_11e9_8b94_80a5898a2454row0_col0\" class=\"data row0 col0\" >2</td>\n",
       "                        <td id=\"T_974d1630_91a5_11e9_8b94_80a5898a2454row0_col1\" class=\"data row0 col1\" >44</td>\n",
       "            </tr>\n",
       "            <tr>\n",
       "                        <th id=\"T_974d1630_91a5_11e9_8b94_80a5898a2454level0_row1\" class=\"row_heading level0 row1\" >1</th>\n",
       "                        <td id=\"T_974d1630_91a5_11e9_8b94_80a5898a2454row1_col0\" class=\"data row1 col0\" >3</td>\n",
       "                        <td id=\"T_974d1630_91a5_11e9_8b94_80a5898a2454row1_col1\" class=\"data row1 col1\" >50</td>\n",
       "            </tr>\n",
       "            <tr>\n",
       "                        <th id=\"T_974d1630_91a5_11e9_8b94_80a5898a2454level0_row2\" class=\"row_heading level0 row2\" >2</th>\n",
       "                        <td id=\"T_974d1630_91a5_11e9_8b94_80a5898a2454row2_col0\" class=\"data row2 col0\" >4</td>\n",
       "                        <td id=\"T_974d1630_91a5_11e9_8b94_80a5898a2454row2_col1\" class=\"data row2 col1\" >60</td>\n",
       "            </tr>\n",
       "            <tr>\n",
       "                        <th id=\"T_974d1630_91a5_11e9_8b94_80a5898a2454level0_row3\" class=\"row_heading level0 row3\" >3</th>\n",
       "                        <td id=\"T_974d1630_91a5_11e9_8b94_80a5898a2454row3_col0\" class=\"data row3 col0\" >4.5</td>\n",
       "                        <td id=\"T_974d1630_91a5_11e9_8b94_80a5898a2454row3_col1\" class=\"data row3 col1\" >54</td>\n",
       "            </tr>\n",
       "            <tr>\n",
       "                        <th id=\"T_974d1630_91a5_11e9_8b94_80a5898a2454level0_row4\" class=\"row_heading level0 row4\" >4</th>\n",
       "                        <td id=\"T_974d1630_91a5_11e9_8b94_80a5898a2454row4_col0\" class=\"data row4 col0\" >5</td>\n",
       "                        <td id=\"T_974d1630_91a5_11e9_8b94_80a5898a2454row4_col1\" class=\"data row4 col1\" >65</td>\n",
       "            </tr>\n",
       "            <tr>\n",
       "                        <th id=\"T_974d1630_91a5_11e9_8b94_80a5898a2454level0_row5\" class=\"row_heading level0 row5\" >5</th>\n",
       "                        <td id=\"T_974d1630_91a5_11e9_8b94_80a5898a2454row5_col0\" class=\"data row5 col0\" >6</td>\n",
       "                        <td id=\"T_974d1630_91a5_11e9_8b94_80a5898a2454row5_col1\" class=\"data row5 col1\" >73</td>\n",
       "            </tr>\n",
       "            <tr>\n",
       "                        <th id=\"T_974d1630_91a5_11e9_8b94_80a5898a2454level0_row6\" class=\"row_heading level0 row6\" >6</th>\n",
       "                        <td id=\"T_974d1630_91a5_11e9_8b94_80a5898a2454row6_col0\" class=\"data row6 col0\" >6.5</td>\n",
       "                        <td id=\"T_974d1630_91a5_11e9_8b94_80a5898a2454row6_col1\" class=\"data row6 col1\" >81</td>\n",
       "            </tr>\n",
       "            <tr>\n",
       "                        <th id=\"T_974d1630_91a5_11e9_8b94_80a5898a2454level0_row7\" class=\"row_heading level0 row7\" >7</th>\n",
       "                        <td id=\"T_974d1630_91a5_11e9_8b94_80a5898a2454row7_col0\" class=\"data row7 col0\" >8</td>\n",
       "                        <td id=\"T_974d1630_91a5_11e9_8b94_80a5898a2454row7_col1\" class=\"data row7 col1\" >89</td>\n",
       "            </tr>\n",
       "            <tr>\n",
       "                        <th id=\"T_974d1630_91a5_11e9_8b94_80a5898a2454level0_row8\" class=\"row_heading level0 row8\" >8</th>\n",
       "                        <td id=\"T_974d1630_91a5_11e9_8b94_80a5898a2454row8_col0\" class=\"data row8 col0\" >8.5</td>\n",
       "                        <td id=\"T_974d1630_91a5_11e9_8b94_80a5898a2454row8_col1\" class=\"data row8 col1\" >84</td>\n",
       "            </tr>\n",
       "            <tr>\n",
       "                        <th id=\"T_974d1630_91a5_11e9_8b94_80a5898a2454level0_row9\" class=\"row_heading level0 row9\" >9</th>\n",
       "                        <td id=\"T_974d1630_91a5_11e9_8b94_80a5898a2454row9_col0\" class=\"data row9 col0\" >9</td>\n",
       "                        <td id=\"T_974d1630_91a5_11e9_8b94_80a5898a2454row9_col1\" class=\"data row9 col1\" >90</td>\n",
       "            </tr>\n",
       "            <tr>\n",
       "                        <th id=\"T_974d1630_91a5_11e9_8b94_80a5898a2454level0_row10\" class=\"row_heading level0 row10\" >10</th>\n",
       "                        <td id=\"T_974d1630_91a5_11e9_8b94_80a5898a2454row10_col0\" class=\"data row10 col0\" >9.5</td>\n",
       "                        <td id=\"T_974d1630_91a5_11e9_8b94_80a5898a2454row10_col1\" class=\"data row10 col1\" >103</td>\n",
       "            </tr>\n",
       "            <tr>\n",
       "                        <th id=\"T_974d1630_91a5_11e9_8b94_80a5898a2454level0_row11\" class=\"row_heading level0 row11\" >11</th>\n",
       "                        <td id=\"T_974d1630_91a5_11e9_8b94_80a5898a2454row11_col0\" class=\"data row11 col0\" >10</td>\n",
       "                        <td id=\"T_974d1630_91a5_11e9_8b94_80a5898a2454row11_col1\" class=\"data row11 col1\" >120</td>\n",
       "            </tr>\n",
       "    </tbody></table>"
      ],
      "text/plain": [
       "<pandas.io.formats.style.Styler at 0x1d8bf302710>"
      ]
     },
     "execution_count": 14,
     "metadata": {
      "tags": []
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "\n",
    "a= [2,3,4,4.5,5,6,6.5,8,8.5,9,9.5,10]\n",
    "b= [44,50,60,54,65,73,81,89,84,90,103,120]\n",
    "\n",
    "df = pd.DataFrame(a, columns = ['Number of hours (x)']); df['Marks achieved in examination (y)'] = b\n",
    "df.style.set_properties(**{'text-align':'center'})"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "NQMs7TTjc4cj"
   },
   "source": [
    "## Question 1:\n",
    "<font size =4> From the following table, add 3 more new columns into the table which consists of $x^2$, $y^2$, and $xy$. Calculate the value of each row of data. </font>\n",
    "## <font color =\"red\">Hint: </font>\n",
    "<font size =4> Use array and for loop for faster calculation of data. </font>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "UhW-gfSkc4ck",
    "outputId": "caf63c90-8d12-4b7c-f52f-1e17a04e94fd"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "xy: [88, 150, 240, 243.0, 325, 438, 526.5, 712, 714.0, 810, 978.5, 1200]\n",
      "x2: [4, 9, 16, 20.25, 25, 36, 42.25, 64, 72.25, 81, 90.25, 100]\n",
      "y2: [1936, 2500, 3600, 2916, 4225, 5329, 6561, 7921, 7056, 8100, 10609, 14400]\n"
     ]
    }
   ],
   "source": [
    "## Task 1\n",
    "\n",
    "x= [2,3,4,4.5,5,6,6.5,8,8.5,9,9.5,10]\n",
    "y= [44,50,60,54,65,73,81,89,84,90,103,120]\n",
    "\n",
    "xy=[]\n",
    "x2=[]\n",
    "y2=[]   # create an empty list for each of the new column\n",
    "\n",
    "for m in range(len(x)):\n",
    "    ab = x[m] * y[m]   # calculate x*y\n",
    "    xy.append(ab)      # append each value of x*y into the list\n",
    "print(\"xy: \"+ str(xy))\n",
    "\n",
    "for i in x:\n",
    "    a= i**2        # calculate x power of 2\n",
    "    x2.append(a)   # append each value of x^2 into the list\n",
    "print(\"x2: \"+ str(x2))\n",
    "\n",
    "for j in y:\n",
    "    b= j**2        # calculate y power of 2\n",
    "    y2.append(b)   # append each value of y^2 into the list\n",
    "print(\"y2: \"+ str(y2))\n",
    "\n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "txavPkPzc4cn"
   },
   "source": [
    "## Question 2:\n",
    "<font size =4 >Add a new row at the bottom part of the table. Calculate the total sum of each of the column, $\\sum x$, $\\sum y$, $\\sum xy$, $\\sum x^2$, and $\\sum y^2$. </font> \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "qrAJ7Vhhc4co",
    "outputId": "ad22f797-0622-462c-c992-f6292f0f46af"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Sum of x: 76.0\n",
      "Sum of y: 913\n",
      "Sum of xy: 6425.0\n",
      "Sum of x2: 560.0\n",
      "Sum of y2: 75153\n"
     ]
    }
   ],
   "source": [
    "## Task 2\n",
    "\n",
    "nX=0\n",
    "nY=0\n",
    "nXY=0\n",
    "nX2=0\n",
    "nY2=0   # initialize the sum of each column as 0\n",
    "\n",
    "for i in x:\n",
    "    nX += i   # calculate sum of x\n",
    "print(\"Sum of x: \"+str(nX))   \n",
    "\n",
    "\n",
    "for j in y:\n",
    "    nY += j   # calculate sum of y\n",
    "print(\"Sum of y: \"+str(nY))\n",
    "\n",
    "\n",
    "for k in xy:\n",
    "    nXY += k   # calculate sum of xy\n",
    "print(\"Sum of xy: \"+str(nXY))\n",
    "\n",
    "\n",
    "for m in x2:\n",
    "    nX2 += m   # calculate sum of x2\n",
    "print(\"Sum of x2: \"+str(nX2))\n",
    "\n",
    "\n",
    "for n in y2:   \n",
    "    nY2 += n   # calculate sum of y2\n",
    "print(\"Sum of y2: \"+str(nY2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "cCANXJsSc4cr"
   },
   "source": [
    "## Question 3:\n",
    "\n",
    "## $$ B = \\frac {n\\sum xy - \\sum x \\sum y} { n\\sum x^2 - (\\sum x)^2} $$\n",
    "\n",
    "## $$ A = \\frac {n\\sum y - B\\sum x} { n} $$\n",
    "\n",
    "<font size =4>Using the following formula, calculate the value of gradient (B). Then using B value, find the value of $y$-intercept (A). Note that $n$ is the sample size (number of item) of the table. </font>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "731ZtqYyc4cs",
    "outputId": "a9ac51c2-e442-4e0e-b16a-1719d90d4bb1"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "24.343220338983052\n",
      "8.169491525423728\n"
     ]
    }
   ],
   "source": [
    "## Task 3\n",
    "\n",
    "n= len(x)\n",
    "\n",
    "A= 0\n",
    "B= 0   # initialize A and B to 0\n",
    "\n",
    "A = ((nY*nX2) - (nX*nXY)) / (n*nX2 - (nX**2))  # Translate the formula into calculation for A and B\n",
    "B = ((n*nXY) - (nX*nY)) / (n*nX2 - (nX**2))\n",
    "\n",
    "print(A)\n",
    "print(B)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "Zu3nRH8Hc4cv"
   },
   "source": [
    "## Question 4:\n",
    "\n",
    "<font size =4> Insert the value of A and B into equation: $y = A + Bx$. Calculate the value of $y$ for each $x$. </font>\n",
    "\n",
    "## <font color =\"red\">Hint: </font>\n",
    "<font size =4> Use array and for loop to calculate the value of Y depending on X value. </font>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "5hNXO-9pc4cw",
    "outputId": "42d75908-0c3f-4f6a-84e5-1e3ea620fc4f"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[40.682203389830505, 48.851694915254235, 57.021186440677965, 61.10593220338983, 65.1906779661017, 73.36016949152543, 77.44491525423729, 89.69915254237287, 93.78389830508473, 97.8686440677966, 101.95338983050848, 106.03813559322035]\n"
     ]
    }
   ],
   "source": [
    "## Task 4\n",
    "\n",
    "Y= []\n",
    "for i in range(n):\n",
    "    y0= A + B*x[i]\n",
    "    Y.append(y0)\n",
    "print(Y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "S2ne5ZGRc4cz"
   },
   "source": [
    "## Question 5:\n",
    "<font size =4> You are finally there! Now you can draw your linear regression line. Congratulations and happy drawing. </font>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "zFJs08yvc4c0",
    "outputId": "86dd9e8f-fa31-4706-ff1e-61a1f2bc6ff7"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light",
      "tags": []
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "## Task 5\n",
    "\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# print(len(y))\n",
    "\n",
    "plt.xlabel(\"x\")\n",
    "plt.ylabel(\"y\")\n",
    "plt.scatter(x,y)\n",
    "# plt.scatter(x,Y, c=\"green\")\n",
    "plt.plot(x,Y, c=\"red\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "UTnFAMd8c4c3"
   },
   "source": [
    "## Question 6:\n",
    "<font size =4> A student studied diligently for 11 hours and sit for an examination. What is likely to be his/her mark achieved? </font>\n",
    "## <font color =\"red\">Hint: </font>\n",
    "<font size =4> You have to use the equation of the regression line and find the value of $y$ based on a certain value of $x$. </font>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "LRoEsn-sc4c4",
    "outputId": "8977b10e-92ea-48ab-8dd8-f4e7c6fc936e"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mark achieved: 114.20762711864407\n"
     ]
    }
   ],
   "source": [
    "## Task 6\n",
    "y0= A + B*11\n",
    "print(\"Mark achieved: \"+ str(y0))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "JEG65_1Hc4c7"
   },
   "source": [
    "## Question 7:\n",
    "<font size =4> A student has achieved a mark of 95 for his examination. Can you find what is approximately the hours taken by him to study for the examination? </font>\n",
    "## <font color =\"red\">Hint: </font>\n",
    "<font size =4> You have to modify the equation of the regression line to find a specific value of $x$ based on a certain value of $y$. </font>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "GHwts_CKc4c-",
    "outputId": "b33852ab-5d97-46e4-800e-289130e8e728"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Hours studied: 8.648858921161825\n"
     ]
    }
   ],
   "source": [
    "## Task 7:\n",
    "# 95= A + B*x \n",
    "# B*x = 95 - A\n",
    "x= (95 - A) / B   # conversion of equation so that we can find the value of x\n",
    "\n",
    "print(\"Hours studied: \"+str(x))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "jZlplvupc4dA"
   },
   "source": [
    "# <font color='palevioletred'>Part 2: Linear Regression with Python Libraries</font>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "VDcJuHdZc4dB"
   },
   "source": [
    "## Question 8:\n",
    "<font size =4> From the same Table 1, we want to recreate the linear regression line, but using Python Libraries. Firstly, import certain Python libraries to be used for these questions. The libraries are <b>numpy, matplotlib.pyplot, and LinearRegression from sklearn.linear_model</b> </font>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "collapsed": true,
    "id": "_RaJBq-bc4dC"
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from sklearn.linear_model import LinearRegression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "collapsed": true,
    "id": "sjSC3_Efc4dG"
   },
   "outputs": [],
   "source": [
    "# Task1\n",
    "import numpy as np\n",
    "\n",
    "x= [2,3,4,4.5,5,6,6.5,8,8.5,9,9.5,10]\n",
    "y= [44,50,60,54,65,73,81,89,84,90,103,120]   # put the data into a list for easier to handle the data\n",
    "\n",
    "x= np.array(x)   # intialize type as array\n",
    "y= np.array(y)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "pV4DgrDRc4dK"
   },
   "source": [
    "## Question 9:\n",
    "<font size =4 >Store the data x and y into lists. One for x, and another one for y. Initialize them as array by using array() function from numpy. Then, plot the following data into a graph. </font>\n",
    "## <font color =\"red\">Hint: </font>\n",
    "<font size =4 >Use scatter() and show() function for the plotting.</font>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "_cllxNS7c4dL",
    "outputId": "4f54bc0e-e153-4be1-cf4d-5c43895e394b"
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light",
      "tags": []
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "x= [2,3,4,4.5,5,6,6.5,8,8.5,9,9.5,10]\n",
    "y= [44,50,60,54,65,73,81,89,84,90,103,120]   # store the data into a list\n",
    "\n",
    "x= np.array(x)   # intialize type as array so that it is compatible with other functions \n",
    "y= np.array(y)\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "plt.scatter(x,y)\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "uQIw8vUEc4dP"
   },
   "source": [
    "## Question 10:\n",
    "<font size =4 >Construct a best-fit line along the scattered data so that we can predict the mark achieved by students according to the amount of hours spent on studying. </font>\n",
    "## <font color =\"red\"> Hint: </font>\n",
    "<font size =4> <b>Import library:</b> numpy, sklearn.linear_model, LinearRegression </font><br>\n",
    "<font size =4 ><b>Use function:</b> newaxis, fit(), predict() </font>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "5MiifyLxc4dQ",
    "outputId": "420d7760-7baa-4349-88d0-8ea167c13319"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light",
      "tags": []
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.linear_model import LinearRegression\n",
    "\n",
    "plt.scatter(x,y)   # plot the scattered data\n",
    "\n",
    "x1= x[:, np.newaxis] \n",
    "y1= y[:, np.newaxis]   # transform data into column vector by inserting new axis\n",
    "\n",
    "model= LinearRegression(fit_intercept= True)   # import linearRegression module from sklearn\n",
    "\n",
    "model.fit(x1,y1)\n",
    "y_pred = model.predict(x1)\n",
    "\n",
    "plt.plot(x1, y_pred, color='r')\n",
    "plt.xlabel(\"X\")   # label x-axis\n",
    "plt.ylabel(\"Y\")   # label y-axis\n",
    "plt.title(\"Linear Regression\")   # label title\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "HQltAgyTc4dT"
   },
   "source": [
    "# project: check this link to analyse diabet dataset with linear regression model."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "iLhN96tdc4dU"
   },
   "source": [
    "https://scikit-learn.org/stable/auto_examples/linear_model/plot_ols.html?fbclid=IwAR2pnt3b6I3LV-82Qv7-0c0GcVLxpUka4m-HCnOUdiLCMGAnylWfH4kd34A#sphx-glr-auto-examples-linear-model-plot-ols-py"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "XjsxqRrTc4dV"
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "colab": {
   "name": "[FollowTemplate] Linear Regression.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
}