Holts linear trend method.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Holt’s linear trend method\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 122,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Day</th>\n",
       "      <th>Value</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>39</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2</td>\n",
       "      <td>44</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>3</td>\n",
       "      <td>40</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4</td>\n",
       "      <td>45</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5</td>\n",
       "      <td>41</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>6</td>\n",
       "      <td>46</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>7</td>\n",
       "      <td>42</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>8</td>\n",
       "      <td>47</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>9</td>\n",
       "      <td>43</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>10</td>\n",
       "      <td>48</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>11</td>\n",
       "      <td>44</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>12</td>\n",
       "      <td>48</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>13</td>\n",
       "      <td>45</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>14</td>\n",
       "      <td>50</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    Day  Value\n",
       "0     1     39\n",
       "1     2     44\n",
       "2     3     40\n",
       "3     4     45\n",
       "4     5     41\n",
       "5     6     46\n",
       "6     7     42\n",
       "7     8     47\n",
       "8     9     43\n",
       "9    10     48\n",
       "10   11     44\n",
       "11   12     48\n",
       "12   13     45\n",
       "13   14     50"
      ]
     },
     "execution_count": 122,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import pandas as pd\n",
    "import warnings \n",
    "warnings.filterwarnings('ignore')\n",
    "\n",
    "\n",
    "col_names =  ['Day', 'Value']\n",
    "data  = pd.DataFrame(columns = col_names)\n",
    "\n",
    "data['Day'] = [1,2,3,4,5,6,7,8,9,10,11,12,13,14]\n",
    "data['Value'] = [39,44,40,45,41,46,42,47,43,48,44,48,45,50]\n",
    "data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Holt (1957) extended simple exponential smoothing to allow the forecasting of data with a trend. This method involves a forecast equation and two smoothing equations (one for the level and one for the trend):**\n",
    "\n",
    "\n",
    "\n",
    "\\begin{align*}\n",
    "  \\text{Forecast equation}&& \\hat{y}_{t+h|t} &= \\ell_{t} + hb_{t} \\\\\n",
    "  \\text{Level equation}   && \\ell_{t} &= \\alpha y_{t} + (1 - \\alpha)(\\ell_{t-1} + b_{t-1})\\\\\n",
    "  \\text{Trend equation}   && b_{t}    &= \\beta^*(\\ell_{t} - \\ell_{t-1}) + (1 -\\beta^*)b_{t-1},\n",
    "\\end{align*}\n",
    "\n",
    "\n",
    "where  \n",
    "ℓt\n",
    "  denotes an estimate of the level of the series at time  t\n",
    " ,  \n",
    "bt\n",
    "  denotes an estimate of the trend (slope) of the series at time  t\n",
    " ,  \n",
    "α\n",
    "  is the smoothing parameter for the level,  \n",
    "0\n",
    "≤\n",
    "α\n",
    "≤\n",
    "1\n",
    " , and  \n",
    "β\n",
    "∗\n",
    "  is the smoothing parameter for the trend,  \n",
    "0\n",
    "≤\n",
    "β\n",
    "∗\n",
    "≤\n",
    "1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 123,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
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ABvipxgaFp8itE3O8EVmsc70pRh3vNeRSRR7v+WwfbxW5L0XuwVkRUuRKSo37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\n",
      "text/plain": [
       "<Figure size 576x396 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import seaborn as sns\n",
    "import matplotlib.pyplot as plt\n",
    "sns.pointplot(x='Day', y='Value', data=data)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There is an overall **increasing trend** and hence we can make use of Holts method"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We normally obtain the initial level and slope values by **MINIMIZING SUM SQUARED ERROR OVER PERIODS T (here 14)**\n",
    "\n",
    "Obtain initial estimates l0 and b0 by fitting a least squares trend line to the historical data.\n",
    "\n",
    "** y-intercept = l0 ; slope = b0**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 124,
   "metadata": {},
   "outputs": [],
   "source": [
    "### FINDING THE SLOPE AND GRADIENT\n",
    "\n",
    "x_mean = sum(data['Day'])/len(data)\n",
    "y_mean = sum(data['Value'])/len(data)\n",
    "\n",
    "numerator = []\n",
    "denominator = []\n",
    "for i in range(1,len(data)):\n",
    "    x_val = (data['Day'][i] - x_mean)\n",
    "    y_val = (data['Value'][i] - y_mean)\n",
    "    numerator.append(x_val * y_val)\n",
    "    denominator.append(x_val * x_val)\n",
    "b0 = sum(numerator)/sum(denominator)\n",
    "l0 = y_mean - (b0*x_mean)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "** Equation :**     y = 0.484(x) + 40.796"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 125,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "SLOPE IS b0: 0.4842876421823789\n",
      "INTERCEPT IS l0: 40.796414112203585\n"
     ]
    }
   ],
   "source": [
    "print(\"SLOPE IS b0:\",    b0)\n",
    "print(\"INTERCEPT IS l0:\",l0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 126,
   "metadata": {},
   "outputs": [],
   "source": [
    "#### CONSIDER THE PARAMETERS ALPHA = 0.2 AND BETA = 0.1 ####\n",
    "\n",
    "alpha = 0.2\n",
    "beta = 0.1\n",
    "l = [0] * (len(data)+1)\n",
    "b = [0] * (len(data)+1)\n",
    "l[0] = (l0)\n",
    "b[0] = (b0)\n",
    "forecast = []\n",
    "\n",
    "for i in range(0,len(data)):\n",
    "    forecast.append(b[i] + l[i])\n",
    "    l[i+1] = (alpha*data['Value'][i]) + (1-alpha)*(b[i]+l[i])\n",
    "    b[i+1] = beta*(l[i+1] - l[i]) + (1-beta)*b[i]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 127,
   "metadata": {},
   "outputs": [],
   "source": [
    "data['Level Lt'] = l[1:]\n",
    "data['Slope Bt'] = b[1:]\n",
    "data['Forecast'] = forecast"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Applying Holt’s linear method with  \n",
    "α =\n",
    "0.2\n",
    "  and  \n",
    "β =\n",
    "0.1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 128,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Day</th>\n",
       "      <th>Value</th>\n",
       "      <th>Level Lt</th>\n",
       "      <th>Slope Bt</th>\n",
       "      <th>Forecast</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0</td>\n",
       "      <td>NA</td>\n",
       "      <td>40.796414</td>\n",
       "      <td>0.484288</td>\n",
       "      <td>NA</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>39</td>\n",
       "      <td>40.824561</td>\n",
       "      <td>0.438674</td>\n",
       "      <td>41.2807</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2</td>\n",
       "      <td>44</td>\n",
       "      <td>41.810588</td>\n",
       "      <td>0.493409</td>\n",
       "      <td>41.2632</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>3</td>\n",
       "      <td>40</td>\n",
       "      <td>41.843198</td>\n",
       "      <td>0.447329</td>\n",
       "      <td>42.304</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>4</td>\n",
       "      <td>45</td>\n",
       "      <td>42.832421</td>\n",
       "      <td>0.501518</td>\n",
       "      <td>42.2905</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>5</td>\n",
       "      <td>41</td>\n",
       "      <td>42.867152</td>\n",
       "      <td>0.454840</td>\n",
       "      <td>43.3339</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>6</td>\n",
       "      <td>46</td>\n",
       "      <td>43.857593</td>\n",
       "      <td>0.508400</td>\n",
       "      <td>43.322</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>7</td>\n",
       "      <td>42</td>\n",
       "      <td>43.892794</td>\n",
       "      <td>0.461080</td>\n",
       "      <td>44.366</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>8</td>\n",
       "      <td>47</td>\n",
       "      <td>44.883099</td>\n",
       "      <td>0.514002</td>\n",
       "      <td>44.3539</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>9</td>\n",
       "      <td>43</td>\n",
       "      <td>44.917682</td>\n",
       "      <td>0.466060</td>\n",
       "      <td>45.3971</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>10</td>\n",
       "      <td>48</td>\n",
       "      <td>45.906994</td>\n",
       "      <td>0.518386</td>\n",
       "      <td>45.3837</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>11</td>\n",
       "      <td>44</td>\n",
       "      <td>45.940303</td>\n",
       "      <td>0.469878</td>\n",
       "      <td>46.4254</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>12</td>\n",
       "      <td>48</td>\n",
       "      <td>46.728145</td>\n",
       "      <td>0.501674</td>\n",
       "      <td>46.4102</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>13</td>\n",
       "      <td>45</td>\n",
       "      <td>46.783856</td>\n",
       "      <td>0.457078</td>\n",
       "      <td>47.2298</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>14</td>\n",
       "      <td>50</td>\n",
       "      <td>47.792747</td>\n",
       "      <td>0.512259</td>\n",
       "      <td>47.2409</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    Day Value   Level Lt  Slope Bt Forecast\n",
       "0     0    NA  40.796414  0.484288       NA\n",
       "1     1    39  40.824561  0.438674  41.2807\n",
       "2     2    44  41.810588  0.493409  41.2632\n",
       "3     3    40  41.843198  0.447329   42.304\n",
       "4     4    45  42.832421  0.501518  42.2905\n",
       "5     5    41  42.867152  0.454840  43.3339\n",
       "6     6    46  43.857593  0.508400   43.322\n",
       "7     7    42  43.892794  0.461080   44.366\n",
       "8     8    47  44.883099  0.514002  44.3539\n",
       "9     9    43  44.917682  0.466060  45.3971\n",
       "10   10    48  45.906994  0.518386  45.3837\n",
       "11   11    44  45.940303  0.469878  46.4254\n",
       "12   12    48  46.728145  0.501674  46.4102\n",
       "13   13    45  46.783856  0.457078  47.2298\n",
       "14   14    50  47.792747  0.512259  47.2409"
      ]
     },
     "execution_count": 128,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.loc[-1] = [0, 'NA' ,40.796414112203585, 0.4842876421823789,'NA' ]  # adding a row\n",
    "data.index = data.index + 1  # shifting index\n",
    "data = data.sort_index()  # sorting by index\n",
    "data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Lets calculate the error"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 129,
   "metadata": {},
   "outputs": [],
   "source": [
    "data = data[1:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 130,
   "metadata": {},
   "outputs": [],
   "source": [
    "error = []\n",
    "error_sq = []\n",
    "for i in range(1,len(data)+1):\n",
    "    e = data['Value'][i] - data['Forecast'][i]\n",
    "    error.append(e)\n",
    "    error_sq.append(e*e)\n",
    "data['Error'] = error\n",
    "data['Error_Square'] = error_sq"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 131,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Day</th>\n",
       "      <th>Value</th>\n",
       "      <th>Level Lt</th>\n",
       "      <th>Slope Bt</th>\n",
       "      <th>Forecast</th>\n",
       "      <th>Error</th>\n",
       "      <th>Error_Square</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>39</td>\n",
       "      <td>40.824561</td>\n",
       "      <td>0.438674</td>\n",
       "      <td>41.2807</td>\n",
       "      <td>-2.280702</td>\n",
       "      <td>5.201600</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2</td>\n",
       "      <td>44</td>\n",
       "      <td>41.810588</td>\n",
       "      <td>0.493409</td>\n",
       "      <td>41.2632</td>\n",
       "      <td>2.736765</td>\n",
       "      <td>7.489883</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>3</td>\n",
       "      <td>40</td>\n",
       "      <td>41.843198</td>\n",
       "      <td>0.447329</td>\n",
       "      <td>42.304</td>\n",
       "      <td>-2.303997</td>\n",
       "      <td>5.308402</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>4</td>\n",
       "      <td>45</td>\n",
       "      <td>42.832421</td>\n",
       "      <td>0.501518</td>\n",
       "      <td>42.2905</td>\n",
       "      <td>2.709473</td>\n",
       "      <td>7.341247</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>5</td>\n",
       "      <td>41</td>\n",
       "      <td>42.867152</td>\n",
       "      <td>0.454840</td>\n",
       "      <td>43.3339</td>\n",
       "      <td>-2.333940</td>\n",
       "      <td>5.447274</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>6</td>\n",
       "      <td>46</td>\n",
       "      <td>43.857593</td>\n",
       "      <td>0.508400</td>\n",
       "      <td>43.322</td>\n",
       "      <td>2.678009</td>\n",
       "      <td>7.171730</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>7</td>\n",
       "      <td>42</td>\n",
       "      <td>43.892794</td>\n",
       "      <td>0.461080</td>\n",
       "      <td>44.366</td>\n",
       "      <td>-2.365993</td>\n",
       "      <td>5.597922</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>8</td>\n",
       "      <td>47</td>\n",
       "      <td>44.883099</td>\n",
       "      <td>0.514002</td>\n",
       "      <td>44.3539</td>\n",
       "      <td>2.646126</td>\n",
       "      <td>7.001981</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>9</td>\n",
       "      <td>43</td>\n",
       "      <td>44.917682</td>\n",
       "      <td>0.466060</td>\n",
       "      <td>45.3971</td>\n",
       "      <td>-2.397102</td>\n",
       "      <td>5.746098</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>10</td>\n",
       "      <td>48</td>\n",
       "      <td>45.906994</td>\n",
       "      <td>0.518386</td>\n",
       "      <td>45.3837</td>\n",
       "      <td>2.616258</td>\n",
       "      <td>6.844806</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>11</td>\n",
       "      <td>44</td>\n",
       "      <td>45.940303</td>\n",
       "      <td>0.469878</td>\n",
       "      <td>46.4254</td>\n",
       "      <td>-2.425379</td>\n",
       "      <td>5.882464</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>12</td>\n",
       "      <td>48</td>\n",
       "      <td>46.728145</td>\n",
       "      <td>0.501674</td>\n",
       "      <td>46.4102</td>\n",
       "      <td>1.589819</td>\n",
       "      <td>2.527523</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>13</td>\n",
       "      <td>45</td>\n",
       "      <td>46.783856</td>\n",
       "      <td>0.457078</td>\n",
       "      <td>47.2298</td>\n",
       "      <td>-2.229819</td>\n",
       "      <td>4.972095</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>14</td>\n",
       "      <td>50</td>\n",
       "      <td>47.792747</td>\n",
       "      <td>0.512259</td>\n",
       "      <td>47.2409</td>\n",
       "      <td>2.759066</td>\n",
       "      <td>7.612448</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    Day Value   Level Lt  Slope Bt Forecast     Error  Error_Square\n",
       "1     1    39  40.824561  0.438674  41.2807 -2.280702      5.201600\n",
       "2     2    44  41.810588  0.493409  41.2632  2.736765      7.489883\n",
       "3     3    40  41.843198  0.447329   42.304 -2.303997      5.308402\n",
       "4     4    45  42.832421  0.501518  42.2905  2.709473      7.341247\n",
       "5     5    41  42.867152  0.454840  43.3339 -2.333940      5.447274\n",
       "6     6    46  43.857593  0.508400   43.322  2.678009      7.171730\n",
       "7     7    42  43.892794  0.461080   44.366 -2.365993      5.597922\n",
       "8     8    47  44.883099  0.514002  44.3539  2.646126      7.001981\n",
       "9     9    43  44.917682  0.466060  45.3971 -2.397102      5.746098\n",
       "10   10    48  45.906994  0.518386  45.3837  2.616258      6.844806\n",
       "11   11    44  45.940303  0.469878  46.4254 -2.425379      5.882464\n",
       "12   12    48  46.728145  0.501674  46.4102  1.589819      2.527523\n",
       "13   13    45  46.783856  0.457078  47.2298 -2.229819      4.972095\n",
       "14   14    50  47.792747  0.512259  47.2409  2.759066      7.612448"
      ]
     },
     "execution_count": 131,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 134,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "6.010390950769211"
      ]
     },
     "execution_count": 134,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sum(data['Error_Square'])/ len(data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 133,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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I2/KBVb6rP9kA49+eBVTSZu/eoJk2QRBEAHSbbTjRYBSeeytcEkvklQ1GNMtcIhfPsnNS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\nQgghIvH/AXZhcooKOilbAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 576x396 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "sns.pointplot(x='Day', y='Value', data=data, ax=ax)\n",
    "sns.pointplot(x='Day', y='Forecast', data=data, ax=ax, color='r')\n",
    "sns.plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# LOOKS LIKE WE ARE ABLE TO CAPTURE THE TREND (UPWARD)"
   ]
  }
 ],
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