demo_mvlr.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Introduction\n",
    "\n",
    "This notebook is a demonstration of the *Multivariable Linear Regression*\n",
    "\n",
    "The *Multivariable Linear Regression* package (short: `mvlr`) can be found in the `openergyid.mvlr` module."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Step 1: Importing the libraries"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from openenergyid.mvlr import MultiVariableRegressionInput, find_best_mvlr"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Step 2: Loading Input Data\n",
    "\n",
    "In the `data` folder, a few json samples are stored.\n",
    "\n",
    "The input model is described by the `MultivariableRegressionInput` class. You can find the class definition in the `openergyid.mvlr` module, or you can use `MultiVariableRegressionInput.model_json_schema()` to get the json schema of the input model.\n",
    "\n",
    "By using the `MultiVariableRegressionInput.model_validate_json()` method, you can load the input model from a json file with automatic validation. Regular constructors are also available."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "with open('data/mvlr/sample_solar.json', 'r') as f:\n",
    "    input_data = MultiVariableRegressionInput.model_validate_json(f.read())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'timezone': 'Europe/Brussels',\n",
       " 'independent_variables': [{'name': 'temperatureEquivalent',\n",
       "   'variants': ['HDD_16.5', 'CDD_24', 'HDD_15', 'FDD_0'],\n",
       "   'allow_negative_coefficient': True},\n",
       "  {'name': 'solarRadiation',\n",
       "   'variants': [],\n",
       "   'allow_negative_coefficient': True},\n",
       "  {'name': 'windPower', 'variants': [], 'allow_negative_coefficient': True}],\n",
       " 'dependent_variable': 'energyProduction/solarPhotovoltaic',\n",
       " 'frame': {'columns': ['energyProduction/solarPhotovoltaic',\n",
       "   'temperatureEquivalent',\n",
       "   'solarRadiation',\n",
       "   'windPower'],\n",
       "  'index': [datetime.datetime(2021, 1, 1, 0, 0, tzinfo=TzInfo(+01:00)),\n",
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       "   datetime.datetime(2021, 8, 3, 0, 0, tzinfo=TzInfo(+02:00)),\n",
       "   datetime.datetime(2021, 8, 4, 0, 0, tzinfo=TzInfo(+02:00)),\n",
       "   datetime.datetime(2021, 8, 5, 0, 0, tzinfo=TzInfo(+02:00)),\n",
       "   datetime.datetime(2021, 8, 6, 0, 0, tzinfo=TzInfo(+02:00)),\n",
       "   datetime.datetime(2021, 8, 7, 0, 0, tzinfo=TzInfo(+02:00)),\n",
       "   datetime.datetime(2021, 8, 8, 0, 0, tzinfo=TzInfo(+02:00)),\n",
       "   datetime.datetime(2021, 8, 9, 0, 0, tzinfo=TzInfo(+02:00)),\n",
       "   datetime.datetime(2021, 8, 10, 0, 0, tzinfo=TzInfo(+02:00)),\n",
       "   datetime.datetime(2021, 8, 11, 0, 0, tzinfo=TzInfo(+02:00)),\n",
       "   datetime.datetime(2021, 8, 12, 0, 0, tzinfo=TzInfo(+02:00)),\n",
       "   datetime.datetime(2021, 8, 13, 0, 0, tzinfo=TzInfo(+02:00)),\n",
       "   datetime.datetime(2021, 8, 14, 0, 0, tzinfo=TzInfo(+02:00)),\n",
       "   datetime.datetime(2021, 8, 15, 0, 0, tzinfo=TzInfo(+02:00)),\n",
       "   datetime.datetime(2021, 8, 16, 0, 0, tzinfo=TzInfo(+02:00)),\n",
       "   datetime.datetime(2021, 8, 17, 0, 0, tzinfo=TzInfo(+02:00)),\n",
       "   datetime.datetime(2021, 8, 18, 0, 0, tzinfo=TzInfo(+02:00)),\n",
       "   datetime.datetime(2021, 8, 19, 0, 0, tzinfo=TzInfo(+02:00)),\n",
       "   datetime.datetime(2021, 8, 20, 0, 0, tzinfo=TzInfo(+02:00)),\n",
       "   datetime.datetime(2021, 8, 21, 0, 0, tzinfo=TzInfo(+02:00)),\n",
       "   datetime.datetime(2021, 8, 22, 0, 0, tzinfo=TzInfo(+02:00)),\n",
       "   datetime.datetime(2021, 8, 23, 0, 0, tzinfo=TzInfo(+02:00)),\n",
       "   datetime.datetime(2021, 8, 24, 0, 0, tzinfo=TzInfo(+02:00)),\n",
       "   datetime.datetime(2021, 8, 25, 0, 0, tzinfo=TzInfo(+02:00)),\n",
       "   datetime.datetime(2021, 8, 26, 0, 0, tzinfo=TzInfo(+02:00)),\n",
       "   datetime.datetime(2021, 8, 27, 0, 0, tzinfo=TzInfo(+02:00)),\n",
       "   datetime.datetime(2021, 8, 28, 0, 0, tzinfo=TzInfo(+02:00)),\n",
       "   datetime.datetime(2021, 8, 29, 0, 0, tzinfo=TzInfo(+02:00)),\n",
       "   datetime.datetime(2021, 8, 30, 0, 0, tzinfo=TzInfo(+02:00)),\n",
       "   datetime.datetime(2021, 8, 31, 0, 0, tzinfo=TzInfo(+02:00)),\n",
       "   datetime.datetime(2021, 9, 1, 0, 0, tzinfo=TzInfo(+02:00)),\n",
       "   datetime.datetime(2021, 9, 2, 0, 0, tzinfo=TzInfo(+02:00)),\n",
       "   datetime.datetime(2021, 9, 3, 0, 0, tzinfo=TzInfo(+02:00)),\n",
       "   datetime.datetime(2021, 9, 4, 0, 0, tzinfo=TzInfo(+02:00)),\n",
       "   datetime.datetime(2021, 9, 5, 0, 0, tzinfo=TzInfo(+02:00)),\n",
       "   datetime.datetime(2021, 9, 6, 0, 0, tzinfo=TzInfo(+02:00)),\n",
       "   datetime.datetime(2021, 9, 7, 0, 0, tzinfo=TzInfo(+02:00)),\n",
       "   datetime.datetime(2021, 9, 8, 0, 0, tzinfo=TzInfo(+02:00)),\n",
       "   datetime.datetime(2021, 9, 9, 0, 0, tzinfo=TzInfo(+02:00)),\n",
       "   datetime.datetime(2021, 9, 10, 0, 0, tzinfo=TzInfo(+02:00)),\n",
       "   datetime.datetime(2021, 9, 11, 0, 0, tzinfo=TzInfo(+02:00)),\n",
       "   datetime.datetime(2021, 9, 12, 0, 0, tzinfo=TzInfo(+02:00)),\n",
       "   datetime.datetime(2021, 9, 13, 0, 0, tzinfo=TzInfo(+02:00)),\n",
       "   datetime.datetime(2021, 9, 14, 0, 0, tzinfo=TzInfo(+02:00)),\n",
       "   datetime.datetime(2021, 9, 15, 0, 0, tzinfo=TzInfo(+02:00)),\n",
       "   datetime.datetime(2021, 9, 16, 0, 0, tzinfo=TzInfo(+02:00)),\n",
       "   datetime.datetime(2021, 9, 17, 0, 0, tzinfo=TzInfo(+02:00)),\n",
       "   datetime.datetime(2021, 9, 18, 0, 0, tzinfo=TzInfo(+02:00)),\n",
       "   datetime.datetime(2021, 9, 19, 0, 0, tzinfo=TzInfo(+02:00)),\n",
       "   datetime.datetime(2021, 9, 20, 0, 0, tzinfo=TzInfo(+02:00)),\n",
       "   datetime.datetime(2021, 9, 21, 0, 0, tzinfo=TzInfo(+02:00)),\n",
       "   datetime.datetime(2021, 9, 22, 0, 0, tzinfo=TzInfo(+02:00)),\n",
       "   datetime.datetime(2021, 9, 23, 0, 0, tzinfo=TzInfo(+02:00)),\n",
       "   datetime.datetime(2021, 9, 24, 0, 0, tzinfo=TzInfo(+02:00)),\n",
       "   datetime.datetime(2021, 9, 25, 0, 0, tzinfo=TzInfo(+02:00)),\n",
       "   datetime.datetime(2021, 9, 26, 0, 0, tzinfo=TzInfo(+02:00)),\n",
       "   datetime.datetime(2021, 9, 27, 0, 0, tzinfo=TzInfo(+02:00)),\n",
       "   datetime.datetime(2021, 9, 28, 0, 0, tzinfo=TzInfo(+02:00)),\n",
       "   datetime.datetime(2021, 9, 29, 0, 0, tzinfo=TzInfo(+02:00)),\n",
       "   datetime.datetime(2021, 9, 30, 0, 0, tzinfo=TzInfo(+02:00)),\n",
       "   datetime.datetime(2021, 10, 1, 0, 0, tzinfo=TzInfo(+02:00)),\n",
       "   datetime.datetime(2021, 10, 2, 0, 0, tzinfo=TzInfo(+02:00)),\n",
       "   datetime.datetime(2021, 10, 3, 0, 0, tzinfo=TzInfo(+02:00)),\n",
       "   datetime.datetime(2021, 10, 4, 0, 0, tzinfo=TzInfo(+02:00)),\n",
       "   datetime.datetime(2021, 10, 5, 0, 0, tzinfo=TzInfo(+02:00)),\n",
       "   datetime.datetime(2021, 10, 6, 0, 0, tzinfo=TzInfo(+02:00)),\n",
       "   datetime.datetime(2021, 10, 7, 0, 0, tzinfo=TzInfo(+02:00)),\n",
       "   datetime.datetime(2021, 10, 8, 0, 0, tzinfo=TzInfo(+02:00)),\n",
       "   datetime.datetime(2021, 10, 9, 0, 0, tzinfo=TzInfo(+02:00)),\n",
       "   datetime.datetime(2021, 10, 10, 0, 0, tzinfo=TzInfo(+02:00)),\n",
       "   datetime.datetime(2021, 10, 11, 0, 0, tzinfo=TzInfo(+02:00)),\n",
       "   datetime.datetime(2021, 10, 12, 0, 0, tzinfo=TzInfo(+02:00)),\n",
       "   datetime.datetime(2021, 10, 13, 0, 0, tzinfo=TzInfo(+02:00)),\n",
       "   datetime.datetime(2021, 10, 14, 0, 0, tzinfo=TzInfo(+02:00)),\n",
       "   datetime.datetime(2021, 10, 15, 0, 0, tzinfo=TzInfo(+02:00)),\n",
       "   datetime.datetime(2021, 10, 16, 0, 0, tzinfo=TzInfo(+02:00)),\n",
       "   datetime.datetime(2021, 10, 17, 0, 0, tzinfo=TzInfo(+02:00)),\n",
       "   datetime.datetime(2021, 10, 18, 0, 0, tzinfo=TzInfo(+02:00)),\n",
       "   datetime.datetime(2021, 10, 19, 0, 0, tzinfo=TzInfo(+02:00)),\n",
       "   datetime.datetime(2021, 10, 20, 0, 0, tzinfo=TzInfo(+02:00)),\n",
       "   datetime.datetime(2021, 10, 21, 0, 0, tzinfo=TzInfo(+02:00)),\n",
       "   datetime.datetime(2021, 10, 22, 0, 0, tzinfo=TzInfo(+02:00)),\n",
       "   datetime.datetime(2021, 10, 23, 0, 0, tzinfo=TzInfo(+02:00)),\n",
       "   datetime.datetime(2021, 10, 24, 0, 0, tzinfo=TzInfo(+02:00)),\n",
       "   datetime.datetime(2021, 10, 25, 0, 0, tzinfo=TzInfo(+02:00)),\n",
       "   datetime.datetime(2021, 10, 26, 0, 0, tzinfo=TzInfo(+02:00)),\n",
       "   datetime.datetime(2021, 10, 27, 0, 0, tzinfo=TzInfo(+02:00)),\n",
       "   datetime.datetime(2021, 10, 28, 0, 0, tzinfo=TzInfo(+02:00)),\n",
       "   datetime.datetime(2021, 10, 29, 0, 0, tzinfo=TzInfo(+02:00)),\n",
       "   datetime.datetime(2021, 10, 30, 0, 0, tzinfo=TzInfo(+02:00)),\n",
       "   datetime.datetime(2021, 10, 31, 0, 0, tzinfo=TzInfo(+02:00)),\n",
       "   datetime.datetime(2021, 11, 1, 0, 0, tzinfo=TzInfo(+01:00)),\n",
       "   datetime.datetime(2021, 11, 2, 0, 0, tzinfo=TzInfo(+01:00)),\n",
       "   datetime.datetime(2021, 11, 3, 0, 0, tzinfo=TzInfo(+01:00)),\n",
       "   datetime.datetime(2021, 11, 4, 0, 0, tzinfo=TzInfo(+01:00)),\n",
       "   datetime.datetime(2021, 11, 5, 0, 0, tzinfo=TzInfo(+01:00)),\n",
       "   datetime.datetime(2021, 11, 6, 0, 0, tzinfo=TzInfo(+01:00)),\n",
       "   datetime.datetime(2021, 11, 7, 0, 0, tzinfo=TzInfo(+01:00)),\n",
       "   datetime.datetime(2021, 11, 8, 0, 0, tzinfo=TzInfo(+01:00)),\n",
       "   datetime.datetime(2021, 11, 9, 0, 0, tzinfo=TzInfo(+01:00)),\n",
       "   datetime.datetime(2021, 11, 10, 0, 0, tzinfo=TzInfo(+01:00)),\n",
       "   datetime.datetime(2021, 11, 11, 0, 0, tzinfo=TzInfo(+01:00)),\n",
       "   datetime.datetime(2021, 11, 12, 0, 0, tzinfo=TzInfo(+01:00)),\n",
       "   datetime.datetime(2021, 11, 13, 0, 0, tzinfo=TzInfo(+01:00)),\n",
       "   datetime.datetime(2021, 11, 14, 0, 0, tzinfo=TzInfo(+01:00)),\n",
       "   datetime.datetime(2021, 11, 15, 0, 0, tzinfo=TzInfo(+01:00)),\n",
       "   datetime.datetime(2021, 11, 16, 0, 0, tzinfo=TzInfo(+01:00)),\n",
       "   datetime.datetime(2021, 11, 17, 0, 0, tzinfo=TzInfo(+01:00)),\n",
       "   datetime.datetime(2021, 11, 18, 0, 0, tzinfo=TzInfo(+01:00)),\n",
       "   datetime.datetime(2021, 11, 19, 0, 0, tzinfo=TzInfo(+01:00)),\n",
       "   datetime.datetime(2021, 11, 20, 0, 0, tzinfo=TzInfo(+01:00)),\n",
       "   datetime.datetime(2021, 11, 21, 0, 0, tzinfo=TzInfo(+01:00)),\n",
       "   datetime.datetime(2021, 11, 22, 0, 0, tzinfo=TzInfo(+01:00)),\n",
       "   datetime.datetime(2021, 11, 23, 0, 0, tzinfo=TzInfo(+01:00)),\n",
       "   datetime.datetime(2021, 11, 24, 0, 0, tzinfo=TzInfo(+01:00)),\n",
       "   datetime.datetime(2021, 11, 25, 0, 0, tzinfo=TzInfo(+01:00)),\n",
       "   datetime.datetime(2021, 11, 26, 0, 0, tzinfo=TzInfo(+01:00)),\n",
       "   datetime.datetime(2021, 11, 27, 0, 0, tzinfo=TzInfo(+01:00)),\n",
       "   datetime.datetime(2021, 11, 28, 0, 0, tzinfo=TzInfo(+01:00)),\n",
       "   datetime.datetime(2021, 11, 29, 0, 0, tzinfo=TzInfo(+01:00)),\n",
       "   datetime.datetime(2021, 11, 30, 0, 0, tzinfo=TzInfo(+01:00)),\n",
       "   datetime.datetime(2021, 12, 1, 0, 0, tzinfo=TzInfo(+01:00)),\n",
       "   datetime.datetime(2021, 12, 2, 0, 0, tzinfo=TzInfo(+01:00)),\n",
       "   datetime.datetime(2021, 12, 3, 0, 0, tzinfo=TzInfo(+01:00)),\n",
       "   datetime.datetime(2021, 12, 4, 0, 0, tzinfo=TzInfo(+01:00)),\n",
       "   datetime.datetime(2021, 12, 5, 0, 0, tzinfo=TzInfo(+01:00)),\n",
       "   datetime.datetime(2021, 12, 6, 0, 0, tzinfo=TzInfo(+01:00)),\n",
       "   datetime.datetime(2021, 12, 7, 0, 0, tzinfo=TzInfo(+01:00)),\n",
       "   datetime.datetime(2021, 12, 8, 0, 0, tzinfo=TzInfo(+01:00)),\n",
       "   datetime.datetime(2021, 12, 9, 0, 0, tzinfo=TzInfo(+01:00)),\n",
       "   datetime.datetime(2021, 12, 10, 0, 0, tzinfo=TzInfo(+01:00)),\n",
       "   datetime.datetime(2021, 12, 11, 0, 0, tzinfo=TzInfo(+01:00)),\n",
       "   datetime.datetime(2021, 12, 12, 0, 0, tzinfo=TzInfo(+01:00)),\n",
       "   datetime.datetime(2021, 12, 13, 0, 0, tzinfo=TzInfo(+01:00)),\n",
       "   datetime.datetime(2021, 12, 14, 0, 0, tzinfo=TzInfo(+01:00)),\n",
       "   datetime.datetime(2021, 12, 15, 0, 0, tzinfo=TzInfo(+01:00)),\n",
       "   datetime.datetime(2021, 12, 16, 0, 0, tzinfo=TzInfo(+01:00)),\n",
       "   datetime.datetime(2021, 12, 17, 0, 0, tzinfo=TzInfo(+01:00)),\n",
       "   datetime.datetime(2021, 12, 18, 0, 0, tzinfo=TzInfo(+01:00)),\n",
       "   datetime.datetime(2021, 12, 19, 0, 0, tzinfo=TzInfo(+01:00)),\n",
       "   datetime.datetime(2021, 12, 20, 0, 0, tzinfo=TzInfo(+01:00)),\n",
       "   datetime.datetime(2021, 12, 21, 0, 0, tzinfo=TzInfo(+01:00)),\n",
       "   datetime.datetime(2021, 12, 22, 0, 0, tzinfo=TzInfo(+01:00)),\n",
       "   datetime.datetime(2021, 12, 23, 0, 0, tzinfo=TzInfo(+01:00)),\n",
       "   datetime.datetime(2021, 12, 24, 0, 0, tzinfo=TzInfo(+01:00)),\n",
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       "   datetime.datetime(2021, 12, 31, 0, 0, tzinfo=TzInfo(+01:00))],\n",
       "  'data': [[3.982, 1.95, 583.87, 5.83],\n",
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       "   [17.577, 10.14, 4316.67, 21.95],\n",
       "   [15.945, 12.09, 4316.67, 24.39],\n",
       "   [4.529, 9.36, 4316.67, 39.3],\n",
       "   [8.24, 7.43, 4316.67, 9.26],\n",
       "   [11.391, 6.96, 4712.9, 13.82],\n",
       "   [13.257, 6.99, 4712.9, 12.17],\n",
       "   [14.998, 8.69, 4712.9, 97.34],\n",
       "   [5.86, 9.52, 4712.9, 389.02],\n",
       "   [13.067, 8.42, 4712.9, 54.87],\n",
       "   [12.078, 7.55, 4712.9, 21.95],\n",
       "   [14.887, 7.77, 4712.9, 21.95],\n",
       "   [6.353, 10.65, 4712.9, 175.62],\n",
       "   [12.653, 15.9, 4712.9, 205.38],\n",
       "   [11.3, 16.64, 4712.9, 125.0],\n",
       "   [8.679, 14.61, 4712.9, 6.86],\n",
       "   [13.005, 12.81, 4712.9, 12.17],\n",
       "   [11.173, 11.78, 4712.9, 15.62],\n",
       "   [10.723, 11.65, 4712.9, 13.82],\n",
       "   [6.17, 11.01, 4712.9, 35.94],\n",
       "   [12.0, 11.13, 4712.9, 35.94],\n",
       "   [7.821, 11.05, 4712.9, 85.18],\n",
       "   [13.932, 11.51, 4712.9, 27.0],\n",
       "   [10.391, 10.88, 4712.9, 17.58],\n",
       "   [12.928, 11.38, 4712.9, 85.18],\n",
       "   [11.481, 12.38, 4712.9, 328.51],\n",
       "   [4.348, 11.2, 4712.9, 195.11],\n",
       "   [13.775, 11.56, 4712.9, 125.0],\n",
       "   [8.087, 10.92, 4712.9, 117.65],\n",
       "   [7.623, 10.35, 4712.9, 64.0],\n",
       "   [11.307, 10.77, 4712.9, 35.94],\n",
       "   [5.679, 11.38, 4712.9, 39.3],\n",
       "   [16.522, 12.37, 4712.9, 12.17],\n",
       "   [17.938, 14.58, 4712.9, 29.79],\n",
       "   [19.6, 15.78, 4712.9, 29.79],\n",
       "   [18.676, 17.31, 4712.9, 19.68],\n",
       "   [19.882, 18.51, 5206.67, 21.95],\n",
       "   [19.384, 20.08, 5206.67, 13.82],\n",
       "   [0.233, 20.72, 5206.67, 19.68],\n",
       "   [12.601, 19.76, 5206.67, 8.0],\n",
       "   [3.941, 16.19, 5206.67, 19.68],\n",
       "   [19.415, 15.88, 5206.67, 12.17],\n",
       "   [19.779, 16.91, 5206.67, 13.82],\n",
       "   [14.922, 18.58, 5206.67, 4.1],\n",
       "   [16.949, 19.23, 5206.67, 5.83],\n",
       "   [19.119, 19.82, 5206.67, 10.65],\n",
       "   [18.627, 19.91, 5206.67, 13.82],\n",
       "   [11.461, 18.36, 5206.67, 35.94],\n",
       "   [19.592, 17.68, 5206.67, 5.83],\n",
       "   [19.387, 19.88, 5206.67, 13.82],\n",
       "   [15.95, 20.8, 5206.67, 21.95],\n",
       "   [18.692, 22.61, 5206.67, 8.0],\n",
       "   [14.741, 24.06, 5206.67, 46.66],\n",
       "   [15.524, 24.14, 5206.67, 85.18],\n",
       "   [6.214, 20.99, 5206.67, 27.0],\n",
       "   [13.365, 20.06, 5206.67, 27.0],\n",
       "   [3.943, 17.49, 5206.67, 39.3],\n",
       "   [4.796, 14.84, 5206.67, 64.0],\n",
       "   [7.661, 13.96, 5206.67, 21.95],\n",
       "   [8.117, 15.05, 5206.67, 13.82],\n",
       "   [7.841, 15.28, 5206.67, 17.58],\n",
       "   [10.987, 17.25, 5206.67, 3.38],\n",
       "   [9.203, 18.95, 5206.67, 13.82],\n",
       "   [8.973, 19.43, 5206.67, 5.83],\n",
       "   [10.515, 18.48, 5206.67, 17.58],\n",
       "   [2.625, 15.32, 5206.67, 24.39],\n",
       "   [5.075, 14.26, 4416.13, 15.62],\n",
       "   [11.833, 16.37, 4416.13, 6.86],\n",
       "   [6.917, 17.73, 4416.13, 15.62],\n",
       "   [9.081, 17.52, 4416.13, 4.91],\n",
       "   [8.687, 17.21, 4416.13, 24.39],\n",
       "   [10.78, 17.22, 4416.13, 166.38],\n",
       "   [14.771, 17.64, 4416.13, 29.79],\n",
       "   [11.934, 18.02, 4416.13, 4.1],\n",
       "   [12.367, 17.57, 4416.13, 8.0],\n",
       "   [7.516, 17.18, 4416.13, 3.38],\n",
       "   [14.63, 16.9, 4416.13, 4.91],\n",
       "   [8.459, 18.14, 4416.13, 4.91],\n",
       "   [3.909, 17.64, 4416.13, 29.79],\n",
       "   [1.852, 16.57, 4416.13, 110.59],\n",
       "   [0.998, 16.02, 4416.13, 79.51],\n",
       "   [7.21, 16.08, 4416.13, 27.0],\n",
       "   [17.438, 18.21, 4416.13, 32.77],\n",
       "   [18.423, 20.28, 4416.13, 29.79],\n",
       "   [17.635, 20.29, 4416.13, 10.65],\n",
       "   [17.707, 19.86, 4416.13, 9.26],\n",
       "   [18.308, 19.87, 4416.13, 8.0],\n",
       "   [17.164, 20.02, 4416.13, 13.82],\n",
       "   [18.673, 19.73, 4416.13, 32.77],\n",
       "   [4.226, 19.2, 4416.13, 19.68],\n",
       "   [12.032, 18.96, 4416.13, 15.62],\n",
       "   [8.156, 18.42, 4416.13, 32.77],\n",
       "   [8.638, 18.12, 4416.13, 39.3],\n",
       "   [11.336, 17.95, 4416.13, 85.18],\n",
       "   [14.571, 17.55, 4416.13, 64.0],\n",
       "   [10.709, 17.54, 4416.13, 110.59],\n",
       "   [11.947, 16.67, 4416.13, 39.3],\n",
       "   [6.173, 15.65, 3790.32, 8.0],\n",
       "   [8.968, 15.56, 3790.32, 4.1],\n",
       "   [12.084, 15.94, 3790.32, 4.1],\n",
       "   [10.696, 16.69, 3790.32, 4.1],\n",
       "   [12.848, 18.21, 3790.32, 15.62],\n",
       "   [10.534, 17.88, 3790.32, 74.09],\n",
       "   [12.856, 17.03, 3790.32, 85.18],\n",
       "   [10.948, 16.05, 3790.32, 117.65],\n",
       "   [9.849, 15.99, 3790.32, 50.65],\n",
       "   [7.875, 16.47, 3790.32, 13.82],\n",
       "   [16.017, 17.03, 3790.32, 8.0],\n",
       "   [12.19, 18.75, 3790.32, 3.38],\n",
       "   [11.637, 19.13, 3790.32, 15.62],\n",
       "   [14.761, 18.75, 3790.32, 9.26],\n",
       "   [14.892, 19.43, 3790.32, 21.95],\n",
       "   [5.65, 16.6, 3790.32, 39.3],\n",
       "   [3.462, 14.42, 3790.32, 17.58],\n",
       "   [4.148, 15.44, 3790.32, 19.68],\n",
       "   [6.134, 16.4, 3790.32, 21.95],\n",
       "   [6.86, 17.74, 3790.32, 12.17],\n",
       "   [11.957, 18.72, 3790.32, 9.26],\n",
       "   [6.425, 17.74, 3790.32, 35.94],\n",
       "   [2.67, 17.49, 3790.32, 35.94],\n",
       "   [0.0, 17.2, 3790.32, 50.65],\n",
       "   [0.0, 16.96, 3790.32, 35.94],\n",
       "   [0.0, 16.17, 3790.32, 39.3],\n",
       "   [0.0, 15.51, 3790.32, 39.3],\n",
       "   [0.0, 16.03, 3790.32, 39.3],\n",
       "   [0.0, 15.65, 3790.32, 39.3],\n",
       "   [0.0, 16.56, 3790.32, 54.87],\n",
       "   [0.0, 16.95, 3790.32, 42.88],\n",
       "   [0.0, 16.63, 3480.0, 13.82],\n",
       "   [12.591, 16.86, 3480.0, 24.39],\n",
       "   [15.797, 17.98, 3480.0, 24.39],\n",
       "   [7.974, 17.64, 3480.0, 21.95],\n",
       "   [15.584, 18.61, 3480.0, 8.0],\n",
       "   [13.86, 19.03, 3480.0, 4.91],\n",
       "   [16.132, 19.99, 3480.0, 10.65],\n",
       "   [17.074, 20.49, 3480.0, 15.62],\n",
       "   [13.371, 20.68, 3480.0, 39.3],\n",
       "   [6.374, 19.5, 3480.0, 21.95],\n",
       "   [5.126, 17.88, 3480.0, 17.58],\n",
       "   [9.232, 16.69, 3480.0, 10.65],\n",
       "   [13.953, 16.46, 3480.0, 15.62],\n",
       "   [7.901, 17.37, 3480.0, 21.95],\n",
       "   [4.598, 17.49, 3480.0, 13.82],\n",
       "   [10.663, 16.38, 3480.0, 5.83],\n",
       "   [14.849, 16.08, 3480.0, 4.91],\n",
       "   [13.948, 16.83, 3480.0, 12.17],\n",
       "   [11.153, 16.67, 3480.0, 4.91],\n",
       "   [12.411, 15.54, 3480.0, 19.68],\n",
       "   [14.304, 13.88, 3480.0, 10.65],\n",
       "   [13.469, 13.6, 3480.0, 2.74],\n",
       "   [11.021, 14.41, 3480.0, 19.68],\n",
       "   [7.983, 15.89, 3480.0, 24.39],\n",
       "   [11.76, 16.47, 3480.0, 6.86],\n",
       "   [7.841, 17.27, 3480.0, 32.77],\n",
       "   [3.586, 16.21, 3480.0, 79.51],\n",
       "   [12.913, 14.49, 3480.0, 46.66],\n",
       "   [7.499, 12.79, 3480.0, 68.92],\n",
       "   [5.514, 11.55, 3480.0, 54.87],\n",
       "   [4.238, 12.54, 1806.45, 166.38],\n",
       "   [3.929, 13.7, 1806.45, 226.98],\n",
       "   [1.879, 13.25, 1806.45, 64.0],\n",
       "   [9.631, 13.28, 1806.45, 148.88],\n",
       "   [4.098, 12.73, 1806.45, 175.62],\n",
       "   [2.991, 11.6, 1806.45, 59.32],\n",
       "   [6.885, 11.41, 1806.45, 2.2],\n",
       "   [9.178, 11.62, 1806.45, 12.17],\n",
       "   [10.019, 11.59, 1806.45, 8.0],\n",
       "   [7.863, 11.17, 1806.45, 4.91],\n",
       "   [4.766, 11.14, 1806.45, 9.26],\n",
       "   [3.537, 10.45, 1806.45, 17.58],\n",
       "   [4.669, 9.52, 1806.45, 4.1],\n",
       "   [4.118, 10.18, 1806.45, 17.58],\n",
       "   [3.939, 10.44, 1806.45, 13.82],\n",
       "   [7.577, 9.39, 1806.45, 5.83],\n",
       "   [5.708, 9.81, 1806.45, 9.26],\n",
       "   [6.164, 11.27, 1806.45, 85.18],\n",
       "   [2.164, 14.71, 1806.45, 140.61],\n",
       "   [2.034, 15.89, 1806.45, 262.14],\n",
       "   [4.537, 11.84, 1806.45, 140.61],\n",
       "   [4.459, 9.14, 1806.45, 29.79],\n",
       "   [5.794, 8.78, 1806.45, 10.65],\n",
       "   [5.162, 8.94, 1806.45, 74.09],\n",
       "   [3.371, 9.97, 1806.45, 50.65],\n",
       "   [4.856, 11.1, 1806.45, 54.87],\n",
       "   [4.689, 12.25, 1806.45, 64.0],\n",
       "   [4.195, 12.39, 1806.45, 166.38],\n",
       "   [3.681, 12.77, 1806.45, 226.98],\n",
       "   [1.062, 12.39, 1806.45, 110.59],\n",
       "   [3.01, 12.01, 1806.45, 157.46],\n",
       "   [3.859, 10.39, 796.67, 117.65],\n",
       "   [2.21, 8.14, 796.67, 21.95],\n",
       "   [3.786, 6.85, 796.67, 6.86],\n",
       "   [2.545, 6.27, 796.67, 10.65],\n",
       "   [2.477, 6.91, 796.67, 9.26],\n",
       "   [2.096, 7.33, 796.67, 85.18],\n",
       "   [2.819, 8.63, 796.67, 59.32],\n",
       "   [3.879, 7.53, 796.67, 4.91],\n",
       "   [3.377, 6.82, 796.67, 9.26],\n",
       "   [2.788, 5.73, 796.67, 4.91],\n",
       "   [2.218, 5.87, 796.67, 4.1],\n",
       "   [3.979, 6.55, 796.67, 50.65],\n",
       "   [1.592, 8.95, 796.67, 29.79],\n",
       "   [1.267, 9.22, 796.67, 21.95],\n",
       "   [0.167, 7.4, 796.67, 19.68],\n",
       "   [0.271, 5.79, 796.67, 2.74],\n",
       "   [1.645, 6.1, 796.67, 12.17],\n",
       "   [3.011, 7.05, 796.67, 29.79],\n",
       "   [0.927, 9.12, 796.67, 10.65],\n",
       "   [0.43, 8.95, 796.67, 13.82],\n",
       "   [1.209, 7.72, 796.67, 17.58],\n",
       "   [1.568, 5.62, 796.67, 50.65],\n",
       "   [1.567, 4.44, 796.67, 1.0],\n",
       "   [0.747, 5.25, 796.67, 2.2],\n",
       "   [0.964, 4.6, 796.67, 3.38],\n",
       "   [0.615, 4.02, 796.67, 79.51],\n",
       "   [2.529, 2.77, 796.67, 15.62],\n",
       "   [1.384, 2.68, 796.67, 17.58],\n",
       "   [2.386, 2.49, 796.67, 27.0],\n",
       "   [0.296, 5.44, 796.67, 140.61],\n",
       "   [0.964, 6.84, 435.48, 175.62],\n",
       "   [1.167, 4.07, 435.48, 17.58],\n",
       "   [1.045, 2.92, 435.48, 103.82],\n",
       "   [0.429, 3.64, 435.48, 32.77],\n",
       "   [1.205, 3.75, 435.48, 19.68],\n",
       "   [1.274, 3.02, 435.48, 39.3],\n",
       "   [2.041, 3.57, 435.48, 166.38],\n",
       "   [2.256, 4.48, 435.48, 148.88],\n",
       "   [0.888, 4.01, 435.48, 85.18],\n",
       "   [0.302, 2.57, 435.48, 64.0],\n",
       "   [2.226, 3.44, 435.48, 21.95],\n",
       "   [0.297, 6.32, 435.48, 79.51],\n",
       "   [0.391, 8.02, 435.48, 29.79],\n",
       "   [0.71, 7.89, 435.48, 21.95],\n",
       "   [0.537, 8.15, 435.48, 17.58],\n",
       "   [1.747, 7.83, 435.48, 1.33],\n",
       "   [0.338, 6.6, 435.48, 15.62],\n",
       "   [0.314, 6.04, 435.48, 17.58],\n",
       "   [0.256, 5.71, 435.48, 9.26],\n",
       "   [0.759, 5.27, 435.48, 9.26],\n",
       "   [1.256, 1.82, 435.48, 8.0],\n",
       "   [2.673, -0.1, 435.48, 13.82],\n",
       "   [1.07, 1.64, 435.48, 85.18],\n",
       "   [0.561, 5.44, 435.48, 24.39],\n",
       "   [0.392, 4.46, 435.48, 29.79],\n",
       "   [1.533, 4.27, 435.48, 19.68],\n",
       "   [0.742, 6.76, 435.48, 79.51],\n",
       "   [0.753, 8.71, 435.48, 205.38],\n",
       "   [0.38, 9.83, 435.48, 68.92],\n",
       "   [1.224, 12.11, 435.48, 157.46],\n",
       "   [1.102, 12.63, 435.48, 85.18]]},\n",
       " 'granularities': [<Granularity.P7D: 'P7D'>, <Granularity.P1M: 'P1M'>],\n",
       " 'allow_negative_predictions': False,\n",
       " 'validation_parameters': {'rsquared': 0.75,\n",
       "  'f_pvalue': 0.05,\n",
       "  'pvalues': 0.05},\n",
       " 'single_use_exog_prefixes': None}"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "input_data.model_dump()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Step 4: Running the model\n",
    "\n",
    "The `find_best_mvlr` function is the main function of the `mvlr` module. It takes an input model and returns a `MultivariableRegressionOutput` object."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "result = find_best_mvlr(input_data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'dependent_variable': 'energyProduction/solarPhotovoltaic',\n",
       " 'independent_variables': [{'name': 'solarRadiation',\n",
       "   'coef': 0.0024924735991862625,\n",
       "   't_stat': 12.25091474554284,\n",
       "   'p_value': 2.4042026616615334e-07,\n",
       "   'std_err': 0.0002034520401909646,\n",
       "   'confidence_interval': {'confidence': 0.95,\n",
       "    'lower': 0.002039154203925242,\n",
       "    'upper': 0.002945792994447283}}],\n",
       " 'r2': 0.9375331511967008,\n",
       " 'r2_adj': 0.9312864663163709,\n",
       " 'f_stat': 150.0849121025591,\n",
       " 'prob_f_stat': 2.4042026616615286e-07,\n",
       " 'intercept': {'name': 'Intercept',\n",
       "  'coef': 2.7333024502329124,\n",
       "  't_stat': 0.13401884485997115,\n",
       "  'p_value': 0.896046519829883,\n",
       "  'std_err': 20.39491127601337,\n",
       "  'confidence_interval': {'confidence': 0.95,\n",
       "   'lower': -42.7093917462303,\n",
       "   'upper': 48.17599664669613}},\n",
       " 'granularity': <Granularity.P1M: 'P1M'>,\n",
       " 'frame': {'columns': ['energyProduction/solarPhotovoltaic', 'solarRadiation'],\n",
       "  'index': [Timestamp('2021-01-01 00:00:00+0100', tz='Europe/Brussels'),\n",
       "   Timestamp('2021-02-01 00:00:00+0100', tz='Europe/Brussels'),\n",
       "   Timestamp('2021-03-01 00:00:00+0100', tz='Europe/Brussels'),\n",
       "   Timestamp('2021-04-01 00:00:00+0200', tz='Europe/Brussels'),\n",
       "   Timestamp('2021-05-01 00:00:00+0200', tz='Europe/Brussels'),\n",
       "   Timestamp('2021-06-01 00:00:00+0200', tz='Europe/Brussels'),\n",
       "   Timestamp('2021-07-01 00:00:00+0200', tz='Europe/Brussels'),\n",
       "   Timestamp('2021-08-01 00:00:00+0200', tz='Europe/Brussels'),\n",
       "   Timestamp('2021-09-01 00:00:00+0200', tz='Europe/Brussels'),\n",
       "   Timestamp('2021-10-01 00:00:00+0200', tz='Europe/Brussels'),\n",
       "   Timestamp('2021-11-01 00:00:00+0100', tz='Europe/Brussels'),\n",
       "   Timestamp('2021-12-01 00:00:00+0100', tz='Europe/Brussels')],\n",
       "  'data': [[40.328, 18099.97],\n",
       "   [108.824, 49700.0],\n",
       "   [264.38, 89099.89],\n",
       "   [360.802, 129500.1],\n",
       "   [357.702, 146099.9],\n",
       "   [374.439, 156200.1],\n",
       "   [342.98199999999997, 136900.03],\n",
       "   [219.634, 117499.92],\n",
       "   [318.481, 104400.0],\n",
       "   [150.203, 55999.950000000004],\n",
       "   [58.608, 23900.1],\n",
       "   [30.832, 13499.880000000001]]}}"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "result.model_dump()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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