{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "08a1d994",
   "metadata": {},
   "source": [
    "<img src=\"./images/shouke_logo.png\"\n",
    "     style=\"float: right\"\n",
    "     width=100\n",
    "     style=\"padding-bottom:100px;\"/>\n",
    "<br>\n",
    "<br>\n",
    "\n",
    "<table style=\"float:center;\">\n",
    "    <tr>\n",
    "        <td>\n",
    "            <img src='./images/python-logo.png'width=120>\n",
    "        </td>\n",
    "        <td>\n",
    "            <img src='./images/pandas-logo.png'width=150>\n",
    "        </td>\n",
    "        <td>\n",
    "            <img src='./images/scikit_learn_logo.png'width=150>\n",
    "        </td>\n",
    "    </tr>\n",
    "</table>\n",
    "\n",
    "<h1 style='text-align: center;'>Normalizing the Data</h1>\n",
    "<h3 style='text-align: center;'>Shouke Wei, Ph.D. Professor</h3>\n",
    "<h4 style='text-align: center;'>Email: shouke.wei@gmail.com</h4>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f8ae5c5d",
   "metadata": {},
   "source": [
    "## Objective \n",
    "- learn how to normalize the features, save and load the normalization scaler for new data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "94abd9b5",
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>year</th>\n",
       "      <th>gdp</th>\n",
       "      <th>pop</th>\n",
       "      <th>finv</th>\n",
       "      <th>trade</th>\n",
       "      <th>fexpen</th>\n",
       "      <th>uinc</th>\n",
       "      <th>prov_hn</th>\n",
       "      <th>prov_js</th>\n",
       "      <th>prov_sd</th>\n",
       "      <th>prov_zj</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>2000</td>\n",
       "      <td>1.074125</td>\n",
       "      <td>8.650000</td>\n",
       "      <td>0.314513</td>\n",
       "      <td>1.408147</td>\n",
       "      <td>0.108032</td>\n",
       "      <td>0.976157</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2001</td>\n",
       "      <td>1.203925</td>\n",
       "      <td>8.733000</td>\n",
       "      <td>0.348443</td>\n",
       "      <td>1.501391</td>\n",
       "      <td>0.132133</td>\n",
       "      <td>1.041519</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2002</td>\n",
       "      <td>1.350242</td>\n",
       "      <td>8.842000</td>\n",
       "      <td>0.385078</td>\n",
       "      <td>1.830169</td>\n",
       "      <td>0.152108</td>\n",
       "      <td>1.113720</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>2003</td>\n",
       "      <td>1.584464</td>\n",
       "      <td>8.963000</td>\n",
       "      <td>0.481320</td>\n",
       "      <td>2.346735</td>\n",
       "      <td>0.169563</td>\n",
       "      <td>1.238043</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>2004</td>\n",
       "      <td>1.886462</td>\n",
       "      <td>9.052298</td>\n",
       "      <td>0.587002</td>\n",
       "      <td>2.955899</td>\n",
       "      <td>0.185295</td>\n",
       "      <td>1.362765</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   year       gdp       pop      finv     trade    fexpen      uinc  prov_hn  \\\n",
       "0  2000  1.074125  8.650000  0.314513  1.408147  0.108032  0.976157      0.0   \n",
       "1  2001  1.203925  8.733000  0.348443  1.501391  0.132133  1.041519      0.0   \n",
       "2  2002  1.350242  8.842000  0.385078  1.830169  0.152108  1.113720      0.0   \n",
       "3  2003  1.584464  8.963000  0.481320  2.346735  0.169563  1.238043      0.0   \n",
       "4  2004  1.886462  9.052298  0.587002  2.955899  0.185295  1.362765      0.0   \n",
       "\n",
       "   prov_js  prov_sd  prov_zj  \n",
       "0      0.0      0.0      0.0  \n",
       "1      0.0      0.0      0.0  \n",
       "2      0.0      0.0      0.0  \n",
       "3      0.0      0.0      0.0  \n",
       "4      0.0      0.0      0.0  "
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# import required packages\n",
    "import pandas as pd\n",
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn.preprocessing import MinMaxScaler\n",
    "\n",
    "# read data\n",
    "df = pd.read_csv('./data/gdp_china_encoded.csv')\n",
    "\n",
    "# show the first 5 rows\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c46350e0",
   "metadata": {},
   "source": [
    "### Slice data into features X and target y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "4fadde18",
   "metadata": {},
   "outputs": [],
   "source": [
    "X = df.drop(['gdp'],axis=1)\n",
    "y = df['gdp']"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "913af9d8",
   "metadata": {},
   "source": [
    "### Split train and test data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "06608307",
   "metadata": {},
   "outputs": [],
   "source": [
    "X_train, X_test, y_train, y_test = train_test_split(X, y,test_size=0.30, random_state=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "7fbd1ef3",
   "metadata": {},
   "outputs": [
    {
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       "      <th></th>\n",
       "      <th>year</th>\n",
       "      <th>pop</th>\n",
       "      <th>finv</th>\n",
       "      <th>trade</th>\n",
       "      <th>fexpen</th>\n",
       "      <th>uinc</th>\n",
       "      <th>prov_hn</th>\n",
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       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>66</th>\n",
       "      <td>2009</td>\n",
       "      <td>5.276</td>\n",
       "      <td>1.074232</td>\n",
       "      <td>1.282390</td>\n",
       "      <td>0.265335</td>\n",
       "      <td>2.461081</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
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       "    <tr>\n",
       "      <th>54</th>\n",
       "      <td>2016</td>\n",
       "      <td>9.947</td>\n",
       "      <td>5.332294</td>\n",
       "      <td>1.547657</td>\n",
       "      <td>0.875521</td>\n",
       "      <td>3.401208</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>36</th>\n",
       "      <td>2017</td>\n",
       "      <td>7.656</td>\n",
       "      <td>5.327700</td>\n",
       "      <td>3.999750</td>\n",
       "      <td>1.062103</td>\n",
       "      <td>4.362180</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>45</th>\n",
       "      <td>2007</td>\n",
       "      <td>9.367</td>\n",
       "      <td>1.253770</td>\n",
       "      <td>0.931296</td>\n",
       "      <td>0.226185</td>\n",
       "      <td>1.426470</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>52</th>\n",
       "      <td>2014</td>\n",
       "      <td>9.789</td>\n",
       "      <td>4.249555</td>\n",
       "      <td>1.701122</td>\n",
       "      <td>0.717731</td>\n",
       "      <td>2.922194</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
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       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75</th>\n",
       "      <td>2018</td>\n",
       "      <td>5.155</td>\n",
       "      <td>3.169770</td>\n",
       "      <td>2.851160</td>\n",
       "      <td>0.862953</td>\n",
       "      <td>5.557430</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>2009</td>\n",
       "      <td>10.130</td>\n",
       "      <td>1.293312</td>\n",
       "      <td>4.174383</td>\n",
       "      <td>0.433437</td>\n",
       "      <td>2.157472</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>72</th>\n",
       "      <td>2015</td>\n",
       "      <td>5.539</td>\n",
       "      <td>2.732332</td>\n",
       "      <td>2.159908</td>\n",
       "      <td>0.664598</td>\n",
       "      <td>4.371448</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>2012</td>\n",
       "      <td>10.594</td>\n",
       "      <td>1.875150</td>\n",
       "      <td>6.211629</td>\n",
       "      <td>0.738786</td>\n",
       "      <td>3.022671</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>37</th>\n",
       "      <td>2018</td>\n",
       "      <td>7.723</td>\n",
       "      <td>5.327680</td>\n",
       "      <td>4.379350</td>\n",
       "      <td>1.165735</td>\n",
       "      <td>4.720000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>66 rows × 10 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "    year     pop      finv     trade    fexpen      uinc  prov_hn  prov_js  \\\n",
       "66  2009   5.276  1.074232  1.282390  0.265335  2.461081      0.0      0.0   \n",
       "54  2016   9.947  5.332294  1.547657  0.875521  3.401208      0.0      0.0   \n",
       "36  2017   7.656  5.327700  3.999750  1.062103  4.362180      0.0      1.0   \n",
       "45  2007   9.367  1.253770  0.931296  0.226185  1.426470      0.0      0.0   \n",
       "52  2014   9.789  4.249555  1.701122  0.717731  2.922194      0.0      0.0   \n",
       "..   ...     ...       ...       ...       ...       ...      ...      ...   \n",
       "75  2018   5.155  3.169770  2.851160  0.862953  5.557430      0.0      0.0   \n",
       "9   2009  10.130  1.293312  4.174383  0.433437  2.157472      0.0      0.0   \n",
       "72  2015   5.539  2.732332  2.159908  0.664598  4.371448      0.0      0.0   \n",
       "12  2012  10.594  1.875150  6.211629  0.738786  3.022671      0.0      0.0   \n",
       "37  2018   7.723  5.327680  4.379350  1.165735  4.720000      0.0      1.0   \n",
       "\n",
       "    prov_sd  prov_zj  \n",
       "66      0.0      1.0  \n",
       "54      1.0      0.0  \n",
       "36      0.0      0.0  \n",
       "45      1.0      0.0  \n",
       "52      1.0      0.0  \n",
       "..      ...      ...  \n",
       "75      0.0      1.0  \n",
       "9       0.0      0.0  \n",
       "72      0.0      1.0  \n",
       "12      0.0      0.0  \n",
       "37      0.0      0.0  \n",
       "\n",
       "[66 rows x 10 columns]"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_train"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4dbaa7bf",
   "metadata": {},
   "source": [
    "## 1. Normalization and Standardization"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "337e30a2",
   "metadata": {},
   "source": [
    "The terms standardize and normalize are used interchangeably in data preprocessing, although in statistics, the latter term also has other connotations.\n",
    "\n",
    "The process of normalization involves transforming the data to a smaller or common range such as [−1,1] or [0, 1]."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9950ac4c",
   "metadata": {},
   "source": [
    "## 2. Why data normalization?\n",
    "\n",
    "Normalization:\n",
    " \n",
    "- gives all attributes an equal weight\n",
    "- avoids dependence on the measurement units\n",
    "- particularly useful for machine learning training or\n",
    "- helps speed up the learning phase\n",
    "\n",
    "In a linear regression model, it can help too though it is not necessary."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d4099149",
   "metadata": {},
   "source": [
    "## 3. Methods for data normalization\n",
    "#### Min-max normalization: \n",
    "$$x'=\\frac{x - min(x)}{max(x) - min(x)}$$\n",
    "\n",
    "$$x'=\\frac{x - min(x)}{max(x) - min(x)}(new\\_max(x)-new\\_min(x)) + new\\_min(x)$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4942006e",
   "metadata": {},
   "source": [
    "#### Mean normalization\n",
    "\n",
    "$$x'=\\frac{x - mean(x)}{max(x) - min(x)}$$ \n",
    "\n",
    "#### Z-score normalization / Standardization\n",
    "\n",
    "$$x'=\\frac{x - \\mu}{\\sigma}$$\n",
    "\n",
    "$$μ: \\text{the mean of the variable,}$$\n",
    "$$σ: \\text{is the standard deviation of the variable.}$$\n",
    "\n",
    "#### Scaling to unit length\n",
    "\n",
    "$$x'=\\frac{x}{||x||}$$\n",
    "$$||x||: \\text{the Euclidean length of the variable}.$$\n",
    "\n",
    "#### Decimal scaling \n",
    "$$x'=\\frac{x}{10^j}$$\n",
    "\n",
    "$$ j: \\text{the smallest integer such that max(|x'|)<1}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d1d00a4d",
   "metadata": {},
   "source": [
    "## 4. Sklearn built-in methods for data normalization"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "66f5d61e",
   "metadata": {},
   "source": [
    "### (1) MinMaxScaler\n",
    "- Transform features by scaling each feature to a given range\n",
    "\n",
    "### (2) MaxAbsScaler \n",
    "- Scale each feature by its maximum absolute value [-1, 1] by dividing through the largest maximum value\n",
    "\n",
    "### (3) RobustScaler\n",
    "- Scale features using statistics that are robust to outliers.It subtracts the column median and divides by the interquartile range.\n",
    "\n",
    "### (4) StandardScaler\n",
    "- StandardScaler scales each column to have 0 mean and unit variance.\n",
    "\n",
    "### (5) Normalizer\n",
    "Normalize samples individually to unit norm. The normalizer operates on the rows rather than the columns. It applies l2 normalization by default.\n",
    "\n",
    "Reference: https://scikit-learn.org/stable/modules/classes.html#module-sklearn.preprocessing"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bc734084",
   "metadata": {},
   "source": [
    "###  `MinMaxScaler` Example:"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "830de60c",
   "metadata": {},
   "source": [
    "#### (1) Normaliz the trainning dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "8d211be1",
   "metadata": {},
   "outputs": [
    {
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       "      <th></th>\n",
       "      <th>year</th>\n",
       "      <th>pop</th>\n",
       "      <th>finv</th>\n",
       "      <th>trade</th>\n",
       "      <th>fexpen</th>\n",
       "      <th>uinc</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>66</th>\n",
       "      <td>2009</td>\n",
       "      <td>5.276</td>\n",
       "      <td>1.074232</td>\n",
       "      <td>1.282390</td>\n",
       "      <td>0.265335</td>\n",
       "      <td>2.461081</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>54</th>\n",
       "      <td>2016</td>\n",
       "      <td>9.947</td>\n",
       "      <td>5.332294</td>\n",
       "      <td>1.547657</td>\n",
       "      <td>0.875521</td>\n",
       "      <td>3.401208</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>36</th>\n",
       "      <td>2017</td>\n",
       "      <td>7.656</td>\n",
       "      <td>5.327700</td>\n",
       "      <td>3.999750</td>\n",
       "      <td>1.062103</td>\n",
       "      <td>4.362180</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>45</th>\n",
       "      <td>2007</td>\n",
       "      <td>9.367</td>\n",
       "      <td>1.253770</td>\n",
       "      <td>0.931296</td>\n",
       "      <td>0.226185</td>\n",
       "      <td>1.426470</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>52</th>\n",
       "      <td>2014</td>\n",
       "      <td>9.789</td>\n",
       "      <td>4.249555</td>\n",
       "      <td>1.701122</td>\n",
       "      <td>0.717731</td>\n",
       "      <td>2.922194</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75</th>\n",
       "      <td>2018</td>\n",
       "      <td>5.155</td>\n",
       "      <td>3.169770</td>\n",
       "      <td>2.851160</td>\n",
       "      <td>0.862953</td>\n",
       "      <td>5.557430</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>2009</td>\n",
       "      <td>10.130</td>\n",
       "      <td>1.293312</td>\n",
       "      <td>4.174383</td>\n",
       "      <td>0.433437</td>\n",
       "      <td>2.157472</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>72</th>\n",
       "      <td>2015</td>\n",
       "      <td>5.539</td>\n",
       "      <td>2.732332</td>\n",
       "      <td>2.159908</td>\n",
       "      <td>0.664598</td>\n",
       "      <td>4.371448</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>2012</td>\n",
       "      <td>10.594</td>\n",
       "      <td>1.875150</td>\n",
       "      <td>6.211629</td>\n",
       "      <td>0.738786</td>\n",
       "      <td>3.022671</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>37</th>\n",
       "      <td>2018</td>\n",
       "      <td>7.723</td>\n",
       "      <td>5.327680</td>\n",
       "      <td>4.379350</td>\n",
       "      <td>1.165735</td>\n",
       "      <td>4.720000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>66 rows × 6 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "    year     pop      finv     trade    fexpen      uinc\n",
       "66  2009   5.276  1.074232  1.282390  0.265335  2.461081\n",
       "54  2016   9.947  5.332294  1.547657  0.875521  3.401208\n",
       "36  2017   7.656  5.327700  3.999750  1.062103  4.362180\n",
       "45  2007   9.367  1.253770  0.931296  0.226185  1.426470\n",
       "52  2014   9.789  4.249555  1.701122  0.717731  2.922194\n",
       "..   ...     ...       ...       ...       ...       ...\n",
       "75  2018   5.155  3.169770  2.851160  0.862953  5.557430\n",
       "9   2009  10.130  1.293312  4.174383  0.433437  2.157472\n",
       "72  2015   5.539  2.732332  2.159908  0.664598  4.371448\n",
       "12  2012  10.594  1.875150  6.211629  0.738786  3.022671\n",
       "37  2018   7.723  5.327680  4.379350  1.165735  4.720000\n",
       "\n",
       "[66 rows x 6 columns]"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# slice the continous features from the training data\n",
    "X_train_continuous = X_train.loc[:,'year':'uinc']\n",
    "X_train_continuous"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "329a6000",
   "metadata": {},
   "outputs": [
    {
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       "    <tr>\n",
       "      <th>52</th>\n",
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       "    <tr>\n",
       "      <th>72</th>\n",
       "      <td>0.833333</td>\n",
       "      <td>0.135939</td>\n",
       "      <td>0.481940</td>\n",
       "      <td>0.299806</td>\n",
       "      <td>0.406242</td>\n",
       "      <td>0.766576</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>0.666667</td>\n",
       "      <td>0.935908</td>\n",
       "      <td>0.322718</td>\n",
       "      <td>0.867170</td>\n",
       "      <td>0.454738</td>\n",
       "      <td>0.501111</td>\n",
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       "    <tr>\n",
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       "      <td>0.964026</td>\n",
       "      <td>0.610595</td>\n",
       "      <td>0.733827</td>\n",
       "      <td>0.835178</td>\n",
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      "text/plain": [
       "        year       pop      finv     trade    fexpen      uinc\n",
       "66  0.500000  0.094319  0.173947  0.176927  0.145251  0.390579\n",
       "54  0.888889  0.833518  0.964883  0.214073  0.544119  0.575614\n",
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       "45  0.388889  0.741731  0.207296  0.127763  0.119660  0.186948\n",
       "52  0.777778  0.808514  0.763764  0.235562  0.440974  0.481335\n",
       "..       ...       ...       ...       ...       ...       ...\n",
       "75  1.000000  0.075170  0.563194  0.396602  0.535903  1.000000\n",
       "9   0.500000  0.862478  0.214641  0.581894  0.255137  0.330823\n",
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       "37  1.000000  0.481564  0.964026  0.610595  0.733827  0.835178\n",
       "\n",
       "[66 rows x 6 columns]"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# to learn the underlying parameters of the scaler from the training data-set\n",
    "min_max_scaler = MinMaxScaler().fit(X_train_continuous)\n",
    "\n",
    "#  transform the training data-set to range [0,1]\n",
    "X_train_continuous_scaled = min_max_scaler.transform(X_train_continuous)\n",
    "\n",
    "# convert it into dataframe\n",
    "X_train_continuous_scaled = pd.DataFrame(X_train_continuous_scaled,index=X_train_continuous.index,\n",
    "                                        columns=X_train_continuous.columns)\n",
    "X_train_continuous_scaled"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "96d85fb7",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
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       "    <tr>\n",
       "      <th>75</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.075170</td>\n",
       "      <td>0.563194</td>\n",
       "      <td>0.396602</td>\n",
       "      <td>0.535903</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
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       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>0.500000</td>\n",
       "      <td>0.862478</td>\n",
       "      <td>0.214641</td>\n",
       "      <td>0.581894</td>\n",
       "      <td>0.255137</td>\n",
       "      <td>0.330823</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
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       "    <tr>\n",
       "      <th>72</th>\n",
       "      <td>0.833333</td>\n",
       "      <td>0.135939</td>\n",
       "      <td>0.481940</td>\n",
       "      <td>0.299806</td>\n",
       "      <td>0.406242</td>\n",
       "      <td>0.766576</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
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       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>0.666667</td>\n",
       "      <td>0.935908</td>\n",
       "      <td>0.322718</td>\n",
       "      <td>0.867170</td>\n",
       "      <td>0.454738</td>\n",
       "      <td>0.501111</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
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       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
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       "  </tbody>\n",
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       "<p>66 rows × 10 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "        year       pop      finv     trade    fexpen      uinc  prov_hn  \\\n",
       "66  0.500000  0.094319  0.173947  0.176927  0.145251  0.390579      0.0   \n",
       "54  0.888889  0.833518  0.964883  0.214073  0.544119  0.575614      0.0   \n",
       "36  0.944444  0.470961  0.964029  0.557440  0.666084  0.764752      0.0   \n",
       "45  0.388889  0.741731  0.207296  0.127763  0.119660  0.186948      0.0   \n",
       "52  0.777778  0.808514  0.763764  0.235562  0.440974  0.481335      0.0   \n",
       "..       ...       ...       ...       ...       ...       ...      ...   \n",
       "75  1.000000  0.075170  0.563194  0.396602  0.535903  1.000000      0.0   \n",
       "9   0.500000  0.862478  0.214641  0.581894  0.255137  0.330823      0.0   \n",
       "72  0.833333  0.135939  0.481940  0.299806  0.406242  0.766576      0.0   \n",
       "12  0.666667  0.935908  0.322718  0.867170  0.454738  0.501111      0.0   \n",
       "37  1.000000  0.481564  0.964026  0.610595  0.733827  0.835178      0.0   \n",
       "\n",
       "    prov_js  prov_sd  prov_zj  \n",
       "66      0.0      0.0      1.0  \n",
       "54      0.0      1.0      0.0  \n",
       "36      1.0      0.0      0.0  \n",
       "45      0.0      1.0      0.0  \n",
       "52      0.0      1.0      0.0  \n",
       "..      ...      ...      ...  \n",
       "75      0.0      0.0      1.0  \n",
       "9       0.0      0.0      0.0  \n",
       "72      0.0      0.0      1.0  \n",
       "12      0.0      0.0      0.0  \n",
       "37      1.0      0.0      0.0  \n",
       "\n",
       "[66 rows x 10 columns]"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# diplay the full scaled train dataset \n",
    "X_train_scaled = X_train.copy()\n",
    "X_train_scaled.loc[:,'year':'uinc'] = X_train_continuous_scaled\n",
    "X_train_scaled"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c61f9138",
   "metadata": {},
   "source": [
    "#### (2) Normaliz the testing dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "965240a1",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>year</th>\n",
       "      <th>pop</th>\n",
       "      <th>finv</th>\n",
       "      <th>trade</th>\n",
       "      <th>fexpen</th>\n",
       "      <th>uinc</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>40</th>\n",
       "      <td>0.111111</td>\n",
       "      <td>0.696629</td>\n",
       "      <td>0.039111</td>\n",
       "      <td>0.036688</td>\n",
       "      <td>0.028066</td>\n",
       "      <td>0.056056</td>\n",
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       "    <tr>\n",
       "      <th>31</th>\n",
       "      <td>0.666667</td>\n",
       "      <td>0.512739</td>\n",
       "      <td>0.547526</td>\n",
       "      <td>0.481719</td>\n",
       "      <td>0.431193</td>\n",
       "      <td>0.490291</td>\n",
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       "    <tr>\n",
       "      <th>46</th>\n",
       "      <td>0.444444</td>\n",
       "      <td>0.749644</td>\n",
       "      <td>0.261131</td>\n",
       "      <td>0.151409</td>\n",
       "      <td>0.148605</td>\n",
       "      <td>0.227113</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>58</th>\n",
       "      <td>0.055556</td>\n",
       "      <td>0.007754</td>\n",
       "      <td>0.027068</td>\n",
       "      <td>0.035371</td>\n",
       "      <td>0.010851</td>\n",
       "      <td>0.112156</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>77</th>\n",
       "      <td>0.055556</td>\n",
       "      <td>0.771483</td>\n",
       "      <td>0.003089</td>\n",
       "      <td>0.000578</td>\n",
       "      <td>0.005052</td>\n",
       "      <td>0.009864</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>49</th>\n",
       "      <td>0.611111</td>\n",
       "      <td>0.784460</td>\n",
       "      <td>0.471284</td>\n",
       "      <td>0.210696</td>\n",
       "      <td>0.298783</td>\n",
       "      <td>0.354778</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>87</th>\n",
       "      <td>0.611111</td>\n",
       "      <td>0.745055</td>\n",
       "      <td>0.304467</td>\n",
       "      <td>0.026858</td>\n",
       "      <td>0.249544</td>\n",
       "      <td>0.264300</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>44</th>\n",
       "      <td>0.333333</td>\n",
       "      <td>0.732553</td>\n",
       "      <td>0.180803</td>\n",
       "      <td>0.103640</td>\n",
       "      <td>0.091655</td>\n",
       "      <td>0.146158</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>88</th>\n",
       "      <td>0.666667</td>\n",
       "      <td>0.747903</td>\n",
       "      <td>0.372843</td>\n",
       "      <td>0.043088</td>\n",
       "      <td>0.299066</td>\n",
       "      <td>0.308541</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>90</th>\n",
       "      <td>0.777778</td>\n",
       "      <td>0.752651</td>\n",
       "      <td>0.546188</td>\n",
       "      <td>0.053241</td>\n",
       "      <td>0.365891</td>\n",
       "      <td>0.372103</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>67</th>\n",
       "      <td>0.555556</td>\n",
       "      <td>0.121380</td>\n",
       "      <td>0.204294</td>\n",
       "      <td>0.237688</td>\n",
       "      <td>0.181500</td>\n",
       "      <td>0.444669</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>0.444444</td>\n",
       "      <td>0.487735</td>\n",
       "      <td>0.258616</td>\n",
       "      <td>0.378848</td>\n",
       "      <td>0.184089</td>\n",
       "      <td>0.273840</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>74</th>\n",
       "      <td>0.944444</td>\n",
       "      <td>0.062035</td>\n",
       "      <td>0.563162</td>\n",
       "      <td>0.355903</td>\n",
       "      <td>0.464050</td>\n",
       "      <td>0.915100</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>84</th>\n",
       "      <td>0.444444</td>\n",
       "      <td>0.751543</td>\n",
       "      <td>0.169272</td>\n",
       "      <td>0.014353</td>\n",
       "      <td>0.120951</td>\n",
       "      <td>0.166605</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>32</th>\n",
       "      <td>0.722222</td>\n",
       "      <td>0.515746</td>\n",
       "      <td>0.650043</td>\n",
       "      <td>0.475029</td>\n",
       "      <td>0.481579</td>\n",
       "      <td>0.527854</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>55</th>\n",
       "      <td>0.944444</td>\n",
       "      <td>0.732553</td>\n",
       "      <td>0.999799</td>\n",
       "      <td>0.248336</td>\n",
       "      <td>0.577012</td>\n",
       "      <td>0.630277</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>39</th>\n",
       "      <td>0.055556</td>\n",
       "      <td>0.690141</td>\n",
       "      <td>0.026208</td>\n",
       "      <td>0.030915</td>\n",
       "      <td>0.021080</td>\n",
       "      <td>0.045954</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>0.555556</td>\n",
       "      <td>0.911695</td>\n",
       "      <td>0.264619</td>\n",
       "      <td>0.741384</td>\n",
       "      <td>0.326203</td>\n",
       "      <td>0.376546</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.111111</td>\n",
       "      <td>0.658649</td>\n",
       "      <td>0.045937</td>\n",
       "      <td>0.253633</td>\n",
       "      <td>0.071237</td>\n",
       "      <td>0.125392</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>38</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.683336</td>\n",
       "      <td>0.021424</td>\n",
       "      <td>0.026322</td>\n",
       "      <td>0.011883</td>\n",
       "      <td>0.033926</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>53</th>\n",
       "      <td>0.833333</td>\n",
       "      <td>0.817693</td>\n",
       "      <td>0.871813</td>\n",
       "      <td>0.207203</td>\n",
       "      <td>0.511095</td>\n",
       "      <td>0.527062</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>73</th>\n",
       "      <td>0.888889</td>\n",
       "      <td>0.144010</td>\n",
       "      <td>0.536787</td>\n",
       "      <td>0.308322</td>\n",
       "      <td>0.427701</td>\n",
       "      <td>0.835909</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.418895</td>\n",
       "      <td>0.022146</td>\n",
       "      <td>0.050256</td>\n",
       "      <td>0.010458</td>\n",
       "      <td>0.040032</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>89</th>\n",
       "      <td>0.722222</td>\n",
       "      <td>0.749011</td>\n",
       "      <td>0.458983</td>\n",
       "      <td>0.049350</td>\n",
       "      <td>0.336712</td>\n",
       "      <td>0.334089</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>94</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.740624</td>\n",
       "      <td>0.801175</td>\n",
       "      <td>0.074534</td>\n",
       "      <td>0.574353</td>\n",
       "      <td>0.533536</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>35</th>\n",
       "      <td>0.888889</td>\n",
       "      <td>0.525241</td>\n",
       "      <td>0.896903</td>\n",
       "      <td>0.468056</td>\n",
       "      <td>0.624309</td>\n",
       "      <td>0.696451</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>33</th>\n",
       "      <td>0.777778</td>\n",
       "      <td>0.519069</td>\n",
       "      <td>0.753419</td>\n",
       "      <td>0.482110</td>\n",
       "      <td>0.525635</td>\n",
       "      <td>0.582191</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>48</th>\n",
       "      <td>0.555556</td>\n",
       "      <td>0.776705</td>\n",
       "      <td>0.406844</td>\n",
       "      <td>0.176662</td>\n",
       "      <td>0.242760</td>\n",
       "      <td>0.298763</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>70</th>\n",
       "      <td>0.722222</td>\n",
       "      <td>0.129451</td>\n",
       "      <td>0.360436</td>\n",
       "      <td>0.288562</td>\n",
       "      <td>0.281029</td>\n",
       "      <td>0.635990</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        year       pop      finv     trade    fexpen      uinc\n",
       "40  0.111111  0.696629  0.039111  0.036688  0.028066  0.056056\n",
       "31  0.666667  0.512739  0.547526  0.481719  0.431193  0.490291\n",
       "46  0.444444  0.749644  0.261131  0.151409  0.148605  0.227113\n",
       "58  0.055556  0.007754  0.027068  0.035371  0.010851  0.112156\n",
       "77  0.055556  0.771483  0.003089  0.000578  0.005052  0.009864\n",
       "49  0.611111  0.784460  0.471284  0.210696  0.298783  0.354778\n",
       "87  0.611111  0.745055  0.304467  0.026858  0.249544  0.264300\n",
       "44  0.333333  0.732553  0.180803  0.103640  0.091655  0.146158\n",
       "88  0.666667  0.747903  0.372843  0.043088  0.299066  0.308541\n",
       "90  0.777778  0.752651  0.546188  0.053241  0.365891  0.372103\n",
       "67  0.555556  0.121380  0.204294  0.237688  0.181500  0.444669\n",
       "27  0.444444  0.487735  0.258616  0.378848  0.184089  0.273840\n",
       "74  0.944444  0.062035  0.563162  0.355903  0.464050  0.915100\n",
       "84  0.444444  0.751543  0.169272  0.014353  0.120951  0.166605\n",
       "32  0.722222  0.515746  0.650043  0.475029  0.481579  0.527854\n",
       "55  0.944444  0.732553  0.999799  0.248336  0.577012  0.630277\n",
       "39  0.055556  0.690141  0.026208  0.030915  0.021080  0.045954\n",
       "10  0.555556  0.911695  0.264619  0.741384  0.326203  0.376546\n",
       "2   0.111111  0.658649  0.045937  0.253633  0.071237  0.125392\n",
       "38  0.000000  0.683336  0.021424  0.026322  0.011883  0.033926\n",
       "53  0.833333  0.817693  0.871813  0.207203  0.511095  0.527062\n",
       "73  0.888889  0.144010  0.536787  0.308322  0.427701  0.835909\n",
       "19  0.000000  0.418895  0.022146  0.050256  0.010458  0.040032\n",
       "89  0.722222  0.749011  0.458983  0.049350  0.336712  0.334089\n",
       "94  1.000000  0.740624  0.801175  0.074534  0.574353  0.533536\n",
       "35  0.888889  0.525241  0.896903  0.468056  0.624309  0.696451\n",
       "33  0.777778  0.519069  0.753419  0.482110  0.525635  0.582191\n",
       "48  0.555556  0.776705  0.406844  0.176662  0.242760  0.298763\n",
       "70  0.722222  0.129451  0.360436  0.288562  0.281029  0.635990"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# slice the continous features from the testing data\n",
    "X_test_continuous = X_test.loc[:,'year':'uinc']\n",
    "#  transforme the testing data-set to range [0,1] using the training scaler\n",
    "X_test_continuous_scaled = min_max_scaler.transform(X_test_continuous)\n",
    "\n",
    "# convert it into dataframe\n",
    "X_test_continuous_scaled = pd.DataFrame(X_test_continuous_scaled,index=X_test_continuous.index,\n",
    "                                        columns=X_test_continuous.columns)\n",
    "X_test_continuous_scaled"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "51fecee3",
   "metadata": {},
   "outputs": [
    {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>year</th>\n",
       "      <th>pop</th>\n",
       "      <th>finv</th>\n",
       "      <th>trade</th>\n",
       "      <th>fexpen</th>\n",
       "      <th>uinc</th>\n",
       "      <th>prov_hn</th>\n",
       "      <th>prov_js</th>\n",
       "      <th>prov_sd</th>\n",
       "      <th>prov_zj</th>\n",
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       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>40</th>\n",
       "      <td>0.111111</td>\n",
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       "      <td>0.039111</td>\n",
       "      <td>0.036688</td>\n",
       "      <td>0.028066</td>\n",
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       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
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       "    <tr>\n",
       "      <th>31</th>\n",
       "      <td>0.666667</td>\n",
       "      <td>0.512739</td>\n",
       "      <td>0.547526</td>\n",
       "      <td>0.481719</td>\n",
       "      <td>0.431193</td>\n",
       "      <td>0.490291</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>46</th>\n",
       "      <td>0.444444</td>\n",
       "      <td>0.749644</td>\n",
       "      <td>0.261131</td>\n",
       "      <td>0.151409</td>\n",
       "      <td>0.148605</td>\n",
       "      <td>0.227113</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>58</th>\n",
       "      <td>0.055556</td>\n",
       "      <td>0.007754</td>\n",
       "      <td>0.027068</td>\n",
       "      <td>0.035371</td>\n",
       "      <td>0.010851</td>\n",
       "      <td>0.112156</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>77</th>\n",
       "      <td>0.055556</td>\n",
       "      <td>0.771483</td>\n",
       "      <td>0.003089</td>\n",
       "      <td>0.000578</td>\n",
       "      <td>0.005052</td>\n",
       "      <td>0.009864</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>49</th>\n",
       "      <td>0.611111</td>\n",
       "      <td>0.784460</td>\n",
       "      <td>0.471284</td>\n",
       "      <td>0.210696</td>\n",
       "      <td>0.298783</td>\n",
       "      <td>0.354778</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>87</th>\n",
       "      <td>0.611111</td>\n",
       "      <td>0.745055</td>\n",
       "      <td>0.304467</td>\n",
       "      <td>0.026858</td>\n",
       "      <td>0.249544</td>\n",
       "      <td>0.264300</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>44</th>\n",
       "      <td>0.333333</td>\n",
       "      <td>0.732553</td>\n",
       "      <td>0.180803</td>\n",
       "      <td>0.103640</td>\n",
       "      <td>0.091655</td>\n",
       "      <td>0.146158</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>88</th>\n",
       "      <td>0.666667</td>\n",
       "      <td>0.747903</td>\n",
       "      <td>0.372843</td>\n",
       "      <td>0.043088</td>\n",
       "      <td>0.299066</td>\n",
       "      <td>0.308541</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>90</th>\n",
       "      <td>0.777778</td>\n",
       "      <td>0.752651</td>\n",
       "      <td>0.546188</td>\n",
       "      <td>0.053241</td>\n",
       "      <td>0.365891</td>\n",
       "      <td>0.372103</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>67</th>\n",
       "      <td>0.555556</td>\n",
       "      <td>0.121380</td>\n",
       "      <td>0.204294</td>\n",
       "      <td>0.237688</td>\n",
       "      <td>0.181500</td>\n",
       "      <td>0.444669</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>0.444444</td>\n",
       "      <td>0.487735</td>\n",
       "      <td>0.258616</td>\n",
       "      <td>0.378848</td>\n",
       "      <td>0.184089</td>\n",
       "      <td>0.273840</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>74</th>\n",
       "      <td>0.944444</td>\n",
       "      <td>0.062035</td>\n",
       "      <td>0.563162</td>\n",
       "      <td>0.355903</td>\n",
       "      <td>0.464050</td>\n",
       "      <td>0.915100</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>84</th>\n",
       "      <td>0.444444</td>\n",
       "      <td>0.751543</td>\n",
       "      <td>0.169272</td>\n",
       "      <td>0.014353</td>\n",
       "      <td>0.120951</td>\n",
       "      <td>0.166605</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>32</th>\n",
       "      <td>0.722222</td>\n",
       "      <td>0.515746</td>\n",
       "      <td>0.650043</td>\n",
       "      <td>0.475029</td>\n",
       "      <td>0.481579</td>\n",
       "      <td>0.527854</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>55</th>\n",
       "      <td>0.944444</td>\n",
       "      <td>0.732553</td>\n",
       "      <td>0.999799</td>\n",
       "      <td>0.248336</td>\n",
       "      <td>0.577012</td>\n",
       "      <td>0.630277</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>39</th>\n",
       "      <td>0.055556</td>\n",
       "      <td>0.690141</td>\n",
       "      <td>0.026208</td>\n",
       "      <td>0.030915</td>\n",
       "      <td>0.021080</td>\n",
       "      <td>0.045954</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>0.555556</td>\n",
       "      <td>0.911695</td>\n",
       "      <td>0.264619</td>\n",
       "      <td>0.741384</td>\n",
       "      <td>0.326203</td>\n",
       "      <td>0.376546</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.111111</td>\n",
       "      <td>0.658649</td>\n",
       "      <td>0.045937</td>\n",
       "      <td>0.253633</td>\n",
       "      <td>0.071237</td>\n",
       "      <td>0.125392</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>38</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.683336</td>\n",
       "      <td>0.021424</td>\n",
       "      <td>0.026322</td>\n",
       "      <td>0.011883</td>\n",
       "      <td>0.033926</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>53</th>\n",
       "      <td>0.833333</td>\n",
       "      <td>0.817693</td>\n",
       "      <td>0.871813</td>\n",
       "      <td>0.207203</td>\n",
       "      <td>0.511095</td>\n",
       "      <td>0.527062</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>73</th>\n",
       "      <td>0.888889</td>\n",
       "      <td>0.144010</td>\n",
       "      <td>0.536787</td>\n",
       "      <td>0.308322</td>\n",
       "      <td>0.427701</td>\n",
       "      <td>0.835909</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.418895</td>\n",
       "      <td>0.022146</td>\n",
       "      <td>0.050256</td>\n",
       "      <td>0.010458</td>\n",
       "      <td>0.040032</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>89</th>\n",
       "      <td>0.722222</td>\n",
       "      <td>0.749011</td>\n",
       "      <td>0.458983</td>\n",
       "      <td>0.049350</td>\n",
       "      <td>0.336712</td>\n",
       "      <td>0.334089</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>94</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.740624</td>\n",
       "      <td>0.801175</td>\n",
       "      <td>0.074534</td>\n",
       "      <td>0.574353</td>\n",
       "      <td>0.533536</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>35</th>\n",
       "      <td>0.888889</td>\n",
       "      <td>0.525241</td>\n",
       "      <td>0.896903</td>\n",
       "      <td>0.468056</td>\n",
       "      <td>0.624309</td>\n",
       "      <td>0.696451</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>33</th>\n",
       "      <td>0.777778</td>\n",
       "      <td>0.519069</td>\n",
       "      <td>0.753419</td>\n",
       "      <td>0.482110</td>\n",
       "      <td>0.525635</td>\n",
       "      <td>0.582191</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>48</th>\n",
       "      <td>0.555556</td>\n",
       "      <td>0.776705</td>\n",
       "      <td>0.406844</td>\n",
       "      <td>0.176662</td>\n",
       "      <td>0.242760</td>\n",
       "      <td>0.298763</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>70</th>\n",
       "      <td>0.722222</td>\n",
       "      <td>0.129451</td>\n",
       "      <td>0.360436</td>\n",
       "      <td>0.288562</td>\n",
       "      <td>0.281029</td>\n",
       "      <td>0.635990</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        year       pop      finv     trade    fexpen      uinc  prov_hn  \\\n",
       "40  0.111111  0.696629  0.039111  0.036688  0.028066  0.056056      0.0   \n",
       "31  0.666667  0.512739  0.547526  0.481719  0.431193  0.490291      0.0   \n",
       "46  0.444444  0.749644  0.261131  0.151409  0.148605  0.227113      0.0   \n",
       "58  0.055556  0.007754  0.027068  0.035371  0.010851  0.112156      0.0   \n",
       "77  0.055556  0.771483  0.003089  0.000578  0.005052  0.009864      1.0   \n",
       "49  0.611111  0.784460  0.471284  0.210696  0.298783  0.354778      0.0   \n",
       "87  0.611111  0.745055  0.304467  0.026858  0.249544  0.264300      1.0   \n",
       "44  0.333333  0.732553  0.180803  0.103640  0.091655  0.146158      0.0   \n",
       "88  0.666667  0.747903  0.372843  0.043088  0.299066  0.308541      1.0   \n",
       "90  0.777778  0.752651  0.546188  0.053241  0.365891  0.372103      1.0   \n",
       "67  0.555556  0.121380  0.204294  0.237688  0.181500  0.444669      0.0   \n",
       "27  0.444444  0.487735  0.258616  0.378848  0.184089  0.273840      0.0   \n",
       "74  0.944444  0.062035  0.563162  0.355903  0.464050  0.915100      0.0   \n",
       "84  0.444444  0.751543  0.169272  0.014353  0.120951  0.166605      1.0   \n",
       "32  0.722222  0.515746  0.650043  0.475029  0.481579  0.527854      0.0   \n",
       "55  0.944444  0.732553  0.999799  0.248336  0.577012  0.630277      0.0   \n",
       "39  0.055556  0.690141  0.026208  0.030915  0.021080  0.045954      0.0   \n",
       "10  0.555556  0.911695  0.264619  0.741384  0.326203  0.376546      0.0   \n",
       "2   0.111111  0.658649  0.045937  0.253633  0.071237  0.125392      0.0   \n",
       "38  0.000000  0.683336  0.021424  0.026322  0.011883  0.033926      0.0   \n",
       "53  0.833333  0.817693  0.871813  0.207203  0.511095  0.527062      0.0   \n",
       "73  0.888889  0.144010  0.536787  0.308322  0.427701  0.835909      0.0   \n",
       "19  0.000000  0.418895  0.022146  0.050256  0.010458  0.040032      0.0   \n",
       "89  0.722222  0.749011  0.458983  0.049350  0.336712  0.334089      1.0   \n",
       "94  1.000000  0.740624  0.801175  0.074534  0.574353  0.533536      1.0   \n",
       "35  0.888889  0.525241  0.896903  0.468056  0.624309  0.696451      0.0   \n",
       "33  0.777778  0.519069  0.753419  0.482110  0.525635  0.582191      0.0   \n",
       "48  0.555556  0.776705  0.406844  0.176662  0.242760  0.298763      0.0   \n",
       "70  0.722222  0.129451  0.360436  0.288562  0.281029  0.635990      0.0   \n",
       "\n",
       "    prov_js  prov_sd  prov_zj  \n",
       "40      0.0      1.0      0.0  \n",
       "31      1.0      0.0      0.0  \n",
       "46      0.0      1.0      0.0  \n",
       "58      0.0      0.0      1.0  \n",
       "77      0.0      0.0      0.0  \n",
       "49      0.0      1.0      0.0  \n",
       "87      0.0      0.0      0.0  \n",
       "44      0.0      1.0      0.0  \n",
       "88      0.0      0.0      0.0  \n",
       "90      0.0      0.0      0.0  \n",
       "67      0.0      0.0      1.0  \n",
       "27      1.0      0.0      0.0  \n",
       "74      0.0      0.0      1.0  \n",
       "84      0.0      0.0      0.0  \n",
       "32      1.0      0.0      0.0  \n",
       "55      0.0      1.0      0.0  \n",
       "39      0.0      1.0      0.0  \n",
       "10      0.0      0.0      0.0  \n",
       "2       0.0      0.0      0.0  \n",
       "38      0.0      1.0      0.0  \n",
       "53      0.0      1.0      0.0  \n",
       "73      0.0      0.0      1.0  \n",
       "19      1.0      0.0      0.0  \n",
       "89      0.0      0.0      0.0  \n",
       "94      0.0      0.0      0.0  \n",
       "35      1.0      0.0      0.0  \n",
       "33      1.0      0.0      0.0  \n",
       "48      0.0      1.0      0.0  \n",
       "70      0.0      0.0      1.0  "
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# diplay the full scaled train dataset \n",
    "X_test_scaled = X_test.copy()\n",
    "X_test_scaled.loc[:,'year':'uinc'] = X_test_continuous_scaled\n",
    "X_test_scaled"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7aac1d46",
   "metadata": {},
   "source": [
    "## 7. Save and load the training scaler"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "e4937531",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['mm_scaler']"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import joblib\n",
    "joblib.dump(min_max_scaler,'mm_scaler')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "d0a0c572",
   "metadata": {},
   "outputs": [],
   "source": [
    "import joblib\n",
    "mm_scaler = joblib.load('mm_scaler')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "1332cbc1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1.11111111e-01, 6.96629213e-01, 3.91109924e-02, 3.66880369e-02,\n",
       "        2.80658336e-02, 5.60560888e-02],\n",
       "       [6.66666667e-01, 5.12739357e-01, 5.47525660e-01, 4.81719398e-01,\n",
       "        4.31192786e-01, 4.90290710e-01],\n",
       "       [4.44444444e-01, 7.49643931e-01, 2.61131077e-01, 1.51408782e-01,\n",
       "        1.48605435e-01, 2.27112677e-01],\n",
       "       [5.55555556e-02, 7.75439152e-03, 2.70675105e-02, 3.53714159e-02,\n",
       "        1.08511200e-02, 1.12155675e-01],\n",
       "       [5.55555556e-02, 7.71482830e-01, 3.08939634e-03, 5.78018498e-04,\n",
       "        5.05165395e-03, 9.86379321e-03],\n",
       "       [6.11111111e-01, 7.84459566e-01, 4.71284143e-01, 2.10695512e-01,\n",
       "        2.98782975e-01, 3.54778102e-01],\n",
       "       [6.11111111e-01, 7.45054597e-01, 3.04466957e-01, 2.68583659e-02,\n",
       "        2.49544384e-01, 2.64299509e-01],\n",
       "       [3.33333333e-01, 7.32552619e-01, 1.80803243e-01, 1.03640173e-01,\n",
       "        9.16553580e-02, 1.46157577e-01],\n",
       "       [6.66666667e-01, 7.47903149e-01, 3.72842512e-01, 4.30876725e-02,\n",
       "        2.99066019e-01, 3.08540932e-01],\n",
       "       [7.77777778e-01, 7.52650736e-01, 5.46187701e-01, 5.32412770e-02,\n",
       "        3.65891269e-01, 3.72102526e-01],\n",
       "       [5.55555556e-01, 1.21379965e-01, 2.04293577e-01, 2.37688015e-01,\n",
       "        1.81500017e-01, 4.44668993e-01],\n",
       "       [4.44444444e-01, 4.87735401e-01, 2.58616392e-01, 3.78847655e-01,\n",
       "        1.84089251e-01, 2.73839731e-01],\n",
       "       [9.44444444e-01, 6.20351321e-02, 5.63162106e-01, 3.55902600e-01,\n",
       "        4.64050109e-01, 9.15100051e-01],\n",
       "       [4.44444444e-01, 7.51542966e-01, 1.69272246e-01, 1.43526835e-02,\n",
       "        1.20951421e-01, 1.66604537e-01],\n",
       "       [7.22222222e-01, 5.15746162e-01, 6.50043391e-01, 4.75028989e-01,\n",
       "        4.81578590e-01, 5.27853859e-01],\n",
       "       [9.44444444e-01, 7.32552619e-01, 9.99799390e-01, 2.48335520e-01,\n",
       "        5.77011575e-01, 6.30277019e-01],\n",
       "       [5.55555556e-02, 6.90140845e-01, 2.62082304e-02, 3.09146826e-02,\n",
       "        2.10799348e-02, 4.59537506e-02],\n",
       "       [5.55555556e-01, 9.11694888e-01, 2.64618908e-01, 7.41384232e-01,\n",
       "        3.26202971e-01, 3.76545523e-01],\n",
       "       [1.11111111e-01, 6.58648520e-01, 4.59367528e-02, 2.53632717e-01,\n",
       "        7.12369492e-02, 1.25392359e-01],\n",
       "       [0.00000000e+00, 6.83335971e-01, 2.14236782e-02, 2.63224027e-02,\n",
       "        1.18826301e-02, 3.39259298e-02],\n",
       "       [8.33333333e-01, 8.17692673e-01, 8.71812713e-01, 2.07203245e-01,\n",
       "        5.11094943e-01, 5.27062449e-01],\n",
       "       [8.88888889e-01, 1.44010128e-01, 5.36786887e-01, 3.08322356e-01,\n",
       "        4.27701471e-01, 8.35909435e-01],\n",
       "       [0.00000000e+00, 4.18895395e-01, 2.21456890e-02, 5.02564960e-02,\n",
       "        1.04576035e-02, 4.00324437e-02],\n",
       "       [7.22222222e-01, 7.49010919e-01, 4.58983397e-01, 4.93503389e-02,\n",
       "        3.36712215e-01, 3.34089054e-01],\n",
       "       [1.00000000e+00, 7.40623516e-01, 8.01174907e-01, 7.45341047e-02,\n",
       "        5.74353051e-01, 5.33536425e-01],\n",
       "       [8.88888889e-01, 5.25241336e-01, 8.96903285e-01, 4.68055899e-01,\n",
       "        6.24309385e-01, 6.96451388e-01],\n",
       "       [7.77777778e-01, 5.19069473e-01, 7.53418917e-01, 4.82109655e-01,\n",
       "        5.25635444e-01, 5.82191322e-01],\n",
       "       [5.55555556e-01, 7.76705175e-01, 4.06844447e-01, 1.76661501e-01,\n",
       "        2.42759819e-01, 2.98763149e-01],\n",
       "       [7.22222222e-01, 1.29450862e-01, 3.60436446e-01, 2.88561556e-01,\n",
       "        2.81028974e-01, 6.35990288e-01]])"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_test_continuous_scaled2 = mm_scaler.transform(X_test_continuous)\n",
    "X_test_continuous_scaled2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "de1f1e92",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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