Paired t-test (Neural Network, Polynomial Regression).ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "7f82ddda",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import numpy\n",
    "import tensorflow as tf\n",
    "from keras.models import Sequential\n",
    "from keras.layers import ReLU\n",
    "from keras.layers import Dense\n",
    "from matplotlib import pyplot\n",
    "from pandas import read_csv\n",
    "from scipy import stats"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "27135226",
   "metadata": {},
   "outputs": [],
   "source": [
    "import warnings\n",
    "warnings.filterwarnings(\"ignore\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "16133642",
   "metadata": {},
   "outputs": [],
   "source": [
    "class ts_preprocessor(object):\n",
    "    \n",
    "    def __init__(self):\n",
    "        self.scaleFactor = 1\n",
    "    \n",
    "    def fit_transform(self, data):\n",
    "        self.scaleFactor = data.max() + 1 if self.scaleFactor == 1.0 else self.scaleFactor\n",
    "        return np.array([(x / self.scaleFactor) for x in data])\n",
    "    \n",
    "    def inverse_transform(self, data):\n",
    "        return [(x * self.scaleFactor) for x in data]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f3fe393a",
   "metadata": {},
   "source": [
    "## Neural Network model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "7484bd31",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>side 1</th>\n",
       "      <th>side 2</th>\n",
       "      <th>side 3</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>3</td>\n",
       "      <td>4</td>\n",
       "      <td>5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>9</td>\n",
       "      <td>12</td>\n",
       "      <td>15</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>12</td>\n",
       "      <td>16</td>\n",
       "      <td>20</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>15</td>\n",
       "      <td>20</td>\n",
       "      <td>25</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>18</td>\n",
       "      <td>24</td>\n",
       "      <td>30</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>994</th>\n",
       "      <td>2988</td>\n",
       "      <td>3984</td>\n",
       "      <td>4980</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>995</th>\n",
       "      <td>2991</td>\n",
       "      <td>3988</td>\n",
       "      <td>4985</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>996</th>\n",
       "      <td>2994</td>\n",
       "      <td>3992</td>\n",
       "      <td>4990</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>997</th>\n",
       "      <td>2997</td>\n",
       "      <td>3996</td>\n",
       "      <td>4995</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>998</th>\n",
       "      <td>3000</td>\n",
       "      <td>4000</td>\n",
       "      <td>5000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>999 rows × 3 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "     side 1  side 2  side 3\n",
       "0         3       4       5\n",
       "1         9      12      15\n",
       "2        12      16      20\n",
       "3        15      20      25\n",
       "4        18      24      30\n",
       "..      ...     ...     ...\n",
       "994    2988    3984    4980\n",
       "995    2991    3988    4985\n",
       "996    2994    3992    4990\n",
       "997    2997    3996    4995\n",
       "998    3000    4000    5000\n",
       "\n",
       "[999 rows x 3 columns]"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data = read_csv('rht_new.csv', header = 0)\n",
    "data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "6d78c5c4",
   "metadata": {},
   "outputs": [],
   "source": [
    "values = data.values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "1ff30f10",
   "metadata": {},
   "outputs": [],
   "source": [
    "# make numeric\n",
    "values = values.astype('float32')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "6c77f43e",
   "metadata": {},
   "outputs": [],
   "source": [
    "#make scaler invariant (remove scale factor)\n",
    "#fit transform over tranform, so I can develop a scaler model from the data\n",
    "#to be used to reverse scale invariance\n",
    "scaler = ts_preprocessor()\n",
    "values = scaler.fit_transform(values)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "1ca90716",
   "metadata": {},
   "outputs": [],
   "source": [
    "# set examples and target\n",
    "examples = values[:,0:2]\n",
    "target = values[:,2:3]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "fdcff3d9",
   "metadata": {},
   "outputs": [],
   "source": [
    "c = len(examples[0])\n",
    "test_s_index = int(len(values) * 0.8)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "1c37a025",
   "metadata": {},
   "outputs": [],
   "source": [
    "# build the neural network model\n",
    "model = Sequential()\n",
    "model.add(Dense(10, input_shape=(c,), activation= tf.nn.sigmoid))\n",
    "model.add(Dense(20, input_shape=(c,), activation= tf.nn.sigmoid))\n",
    "outputlayer = Dense(units = 1, activation= tf.nn.sigmoid)\n",
    "model.add(outputlayer)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "2a22fa79",
   "metadata": {},
   "outputs": [],
   "source": [
    "model.compile(loss=tf.losses.mean_squared_error, optimizer='adam')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "237826ed",
   "metadata": {},
   "outputs": [],
   "source": [
    "validation_ex = examples[test_s_index:,]\n",
    "validation_tgt = target[test_s_index:,]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "b1efff7e",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
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     ]
    },
    {
     "name": "stdout",
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     "text": [
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      "Epoch 1870/2000\n",
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      "Epoch 1875/2000\n",
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      "Epoch 1876/2000\n",
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      "Epoch 1877/2000\n",
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      "Epoch 1878/2000\n",
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      "Epoch 1879/2000\n",
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      "Epoch 1880/2000\n",
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      "Epoch 1883/2000\n",
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      "Epoch 1884/2000\n",
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      "Epoch 1885/2000\n",
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      "Epoch 1886/2000\n",
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      "Epoch 1887/2000\n",
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      "Epoch 1888/2000\n",
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      "Epoch 1889/2000\n",
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      "Epoch 1890/2000\n",
      "20/20 [==============================] - 0s 3ms/step - loss: 1.1443e-05\n",
      "Epoch 1891/2000\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "20/20 [==============================] - 0s 3ms/step - loss: 1.1735e-05\n",
      "Epoch 1892/2000\n",
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      "Epoch 1894/2000\n",
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      "Epoch 1896/2000\n",
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      "Epoch 1897/2000\n",
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      "Epoch 1898/2000\n",
      "20/20 [==============================] - 0s 3ms/step - loss: 1.1206e-05\n",
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      "20/20 [==============================] - 0s 4ms/step - loss: 1.1272e-05\n",
      "Epoch 1900/2000\n",
      "20/20 [==============================] - 0s 3ms/step - loss: 1.1188e-05\n",
      "Epoch 1901/2000\n",
      "20/20 [==============================] - 0s 4ms/step - loss: 1.1495e-05\n",
      "Epoch 1902/2000\n",
      "20/20 [==============================] - 0s 4ms/step - loss: 1.1513e-05\n",
      "Epoch 1903/2000\n",
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      "Epoch 1904/2000\n",
      "20/20 [==============================] - 0s 3ms/step - loss: 1.1191e-05\n",
      "Epoch 1905/2000\n",
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      "Epoch 1906/2000\n",
      "20/20 [==============================] - 0s 3ms/step - loss: 1.1621e-05\n",
      "Epoch 1907/2000\n",
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      "Epoch 1908/2000\n",
      "20/20 [==============================] - 0s 4ms/step - loss: 1.1076e-05\n",
      "Epoch 1909/2000\n",
      "20/20 [==============================] - 0s 5ms/step - loss: 1.1340e-05\n",
      "Epoch 1910/2000\n",
      "20/20 [==============================] - 0s 3ms/step - loss: 1.1721e-05\n",
      "Epoch 1911/2000\n",
      "20/20 [==============================] - 0s 3ms/step - loss: 1.1629e-05\n",
      "Epoch 1912/2000\n",
      "20/20 [==============================] - 0s 3ms/step - loss: 1.1352e-05\n",
      "Epoch 1913/2000\n",
      "20/20 [==============================] - 0s 3ms/step - loss: 1.1465e-05\n",
      "Epoch 1914/2000\n",
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      "Epoch 1915/2000\n",
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      "Epoch 1916/2000\n",
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      "Epoch 1917/2000\n",
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      "Epoch 1919/2000\n",
      "20/20 [==============================] - 0s 3ms/step - loss: 1.1636e-05\n",
      "Epoch 1920/2000\n",
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      "Epoch 1921/2000\n",
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      "Epoch 1922/2000\n",
      "20/20 [==============================] - 0s 3ms/step - loss: 1.1622e-05\n",
      "Epoch 1923/2000\n",
      "20/20 [==============================] - 0s 3ms/step - loss: 1.1115e-05\n",
      "Epoch 1924/2000\n",
      "20/20 [==============================] - 0s 3ms/step - loss: 1.1385e-05\n",
      "Epoch 1925/2000\n",
      "20/20 [==============================] - 0s 4ms/step - loss: 1.1067e-05\n",
      "Epoch 1926/2000\n",
      "20/20 [==============================] - 0s 4ms/step - loss: 1.1301e-05\n",
      "Epoch 1927/2000\n",
      "20/20 [==============================] - 0s 3ms/step - loss: 1.1882e-05\n",
      "Epoch 1928/2000\n",
      "20/20 [==============================] - 0s 3ms/step - loss: 1.1177e-05\n",
      "Epoch 1929/2000\n",
      "20/20 [==============================] - 0s 4ms/step - loss: 1.1191e-05\n",
      "Epoch 1930/2000\n",
      "20/20 [==============================] - 0s 5ms/step - loss: 1.1418e-05\n",
      "Epoch 1931/2000\n",
      "20/20 [==============================] - 0s 4ms/step - loss: 1.1298e-05\n",
      "Epoch 1932/2000\n",
      "20/20 [==============================] - 0s 3ms/step - loss: 1.1366e-05\n",
      "Epoch 1933/2000\n",
      "20/20 [==============================] - 0s 6ms/step - loss: 1.1135e-05\n",
      "Epoch 1934/2000\n",
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      "Epoch 1935/2000\n",
      "20/20 [==============================] - 0s 4ms/step - loss: 1.1219e-05\n",
      "Epoch 1936/2000\n",
      "20/20 [==============================] - 0s 3ms/step - loss: 1.1101e-05\n",
      "Epoch 1937/2000\n",
      "20/20 [==============================] - 0s 4ms/step - loss: 1.1067e-05\n",
      "Epoch 1938/2000\n",
      "20/20 [==============================] - 0s 4ms/step - loss: 1.1056e-05\n",
      "Epoch 1939/2000\n",
      "20/20 [==============================] - 0s 3ms/step - loss: 1.1371e-05\n",
      "Epoch 1940/2000\n",
      "20/20 [==============================] - 0s 3ms/step - loss: 1.1196e-05\n",
      "Epoch 1941/2000\n",
      "20/20 [==============================] - 0s 3ms/step - loss: 1.0902e-05\n",
      "Epoch 1942/2000\n",
      "20/20 [==============================] - 0s 3ms/step - loss: 1.1033e-05\n",
      "Epoch 1943/2000\n",
      "20/20 [==============================] - 0s 5ms/step - loss: 1.0907e-05\n",
      "Epoch 1944/2000\n",
      "20/20 [==============================] - 0s 5ms/step - loss: 1.0856e-05\n",
      "Epoch 1945/2000\n",
      "20/20 [==============================] - 0s 3ms/step - loss: 1.1186e-05\n",
      "Epoch 1946/2000\n",
      "20/20 [==============================] - 0s 3ms/step - loss: 1.1008e-05\n",
      "Epoch 1947/2000\n",
      "20/20 [==============================] - 0s 3ms/step - loss: 1.0793e-05\n",
      "Epoch 1948/2000\n",
      "20/20 [==============================] - 0s 5ms/step - loss: 1.0779e-05\n",
      "Epoch 1949/2000\n",
      "20/20 [==============================] - 0s 3ms/step - loss: 1.1032e-05\n",
      "Epoch 1950/2000\n",
      "20/20 [==============================] - 0s 3ms/step - loss: 1.0827e-05\n",
      "Epoch 1951/2000\n",
      "20/20 [==============================] - 0s 2ms/step - loss: 1.1039e-05\n",
      "Epoch 1952/2000\n",
      "20/20 [==============================] - 0s 4ms/step - loss: 1.1042e-05\n",
      "Epoch 1953/2000\n",
      "20/20 [==============================] - 0s 4ms/step - loss: 1.0751e-05\n",
      "Epoch 1954/2000\n",
      "20/20 [==============================] - 0s 2ms/step - loss: 1.0975e-05\n",
      "Epoch 1955/2000\n",
      "20/20 [==============================] - 0s 3ms/step - loss: 1.1013e-05\n",
      "Epoch 1956/2000\n",
      "20/20 [==============================] - 0s 3ms/step - loss: 1.0988e-05\n",
      "Epoch 1957/2000\n",
      "20/20 [==============================] - 0s 4ms/step - loss: 1.0940e-05\n",
      "Epoch 1958/2000\n",
      "20/20 [==============================] - 0s 4ms/step - loss: 1.1188e-05\n",
      "Epoch 1959/2000\n",
      "20/20 [==============================] - 0s 3ms/step - loss: 1.1087e-05\n",
      "Epoch 1960/2000\n",
      "20/20 [==============================] - 0s 3ms/step - loss: 1.0724e-05\n",
      "Epoch 1961/2000\n",
      "20/20 [==============================] - 0s 3ms/step - loss: 1.1001e-05\n",
      "Epoch 1962/2000\n",
      "20/20 [==============================] - 0s 3ms/step - loss: 1.1396e-05\n",
      "Epoch 1963/2000\n",
      "20/20 [==============================] - 0s 2ms/step - loss: 1.0960e-05\n",
      "Epoch 1964/2000\n",
      "20/20 [==============================] - 0s 4ms/step - loss: 1.1007e-05\n",
      "Epoch 1965/2000\n",
      "20/20 [==============================] - 0s 4ms/step - loss: 1.0610e-05\n",
      "Epoch 1966/2000\n",
      "20/20 [==============================] - 0s 4ms/step - loss: 1.0688e-05\n",
      "Epoch 1967/2000\n",
      "20/20 [==============================] - 0s 3ms/step - loss: 1.0587e-05\n",
      "Epoch 1968/2000\n",
      "20/20 [==============================] - 0s 3ms/step - loss: 1.0903e-05\n",
      "Epoch 1969/2000\n",
      "20/20 [==============================] - 0s 3ms/step - loss: 1.1436e-05\n",
      "Epoch 1970/2000\n",
      "20/20 [==============================] - 0s 3ms/step - loss: 1.0970e-05\n",
      "Epoch 1971/2000\n",
      "20/20 [==============================] - 0s 3ms/step - loss: 1.0784e-05\n",
      "Epoch 1972/2000\n",
      "20/20 [==============================] - 0s 3ms/step - loss: 1.0821e-05\n",
      "Epoch 1973/2000\n",
      "20/20 [==============================] - 0s 3ms/step - loss: 1.0790e-05\n",
      "Epoch 1974/2000\n",
      "20/20 [==============================] - 0s 3ms/step - loss: 1.0699e-05\n",
      "Epoch 1975/2000\n",
      "20/20 [==============================] - 0s 3ms/step - loss: 1.0566e-05\n",
      "Epoch 1976/2000\n",
      "20/20 [==============================] - 0s 3ms/step - loss: 1.0738e-05\n",
      "Epoch 1977/2000\n",
      "20/20 [==============================] - 0s 3ms/step - loss: 1.1060e-05\n",
      "Epoch 1978/2000\n",
      "20/20 [==============================] - 0s 3ms/step - loss: 1.0719e-05\n",
      "Epoch 1979/2000\n",
      "20/20 [==============================] - 0s 3ms/step - loss: 1.0522e-05\n",
      "Epoch 1980/2000\n",
      "20/20 [==============================] - 0s 3ms/step - loss: 1.0620e-05\n",
      "Epoch 1981/2000\n",
      "20/20 [==============================] - 0s 3ms/step - loss: 1.0437e-05\n",
      "Epoch 1982/2000\n",
      "20/20 [==============================] - 0s 3ms/step - loss: 1.0585e-05\n",
      "Epoch 1983/2000\n",
      "20/20 [==============================] - 0s 5ms/step - loss: 1.0658e-05\n",
      "Epoch 1984/2000\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "20/20 [==============================] - 0s 5ms/step - loss: 1.1199e-05\n",
      "Epoch 1985/2000\n",
      "20/20 [==============================] - 0s 4ms/step - loss: 1.1351e-05\n",
      "Epoch 1986/2000\n",
      "20/20 [==============================] - 0s 4ms/step - loss: 1.0839e-05\n",
      "Epoch 1987/2000\n",
      "20/20 [==============================] - 0s 4ms/step - loss: 1.0826e-05\n",
      "Epoch 1988/2000\n",
      "20/20 [==============================] - 0s 4ms/step - loss: 1.0727e-05\n",
      "Epoch 1989/2000\n",
      "20/20 [==============================] - 0s 4ms/step - loss: 1.0496e-05\n",
      "Epoch 1990/2000\n",
      "20/20 [==============================] - 0s 4ms/step - loss: 1.0533e-05\n",
      "Epoch 1991/2000\n",
      "20/20 [==============================] - 0s 3ms/step - loss: 1.0570e-05\n",
      "Epoch 1992/2000\n",
      "20/20 [==============================] - 0s 3ms/step - loss: 1.0597e-05\n",
      "Epoch 1993/2000\n",
      "20/20 [==============================] - 0s 3ms/step - loss: 1.0866e-05\n",
      "Epoch 1994/2000\n",
      "20/20 [==============================] - 0s 4ms/step - loss: 1.0603e-05\n",
      "Epoch 1995/2000\n",
      "20/20 [==============================] - 0s 4ms/step - loss: 1.0770e-05\n",
      "Epoch 1996/2000\n",
      "20/20 [==============================] - 0s 3ms/step - loss: 1.0516e-05\n",
      "Epoch 1997/2000\n",
      "20/20 [==============================] - 0s 3ms/step - loss: 1.0513e-05\n",
      "Epoch 1998/2000\n",
      "20/20 [==============================] - 0s 4ms/step - loss: 1.0718e-05\n",
      "Epoch 1999/2000\n",
      "20/20 [==============================] - 0s 3ms/step - loss: 1.0577e-05\n",
      "Epoch 2000/2000\n",
      "20/20 [==============================] - 0s 3ms/step - loss: 1.0665e-05\n"
     ]
    }
   ],
   "source": [
    "# train\n",
    "ret = model.fit(examples, target, batch_size= 50, epochs = 2000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "3d8e44db",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "7/7 [==============================] - 0s 3ms/step - loss: 3.1332e-05\n",
      "val test loss, val test acc:  3.1331706850323826e-05\n"
     ]
    }
   ],
   "source": [
    "# evaluate model performance\n",
    "vret = model.evaluate(validation_ex, validation_tgt)\n",
    "print(\"val test loss, val test acc: \", vret)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9fe7875c",
   "metadata": {},
   "source": [
    "## Polynomial Regression model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "6b2815ee",
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import matplotlib as mpl\n",
    "\n",
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn import metrics\n",
    "from sklearn.preprocessing import PolynomialFeatures\n",
    "from sklearn.linear_model import LinearRegression\n",
    "from mpl_toolkits.mplot3d import Axes3D"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "7f67333c",
   "metadata": {},
   "outputs": [],
   "source": [
    "df = pd.read_csv('rht_new.csv')\n",
    "X = df[['side 1','side 2']]\n",
    "y = df['side 3']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "137eb8c0",
   "metadata": {},
   "outputs": [],
   "source": [
    "model_linear = LinearRegression()\n",
    "model_linear.fit(X, y)\n",
    "poly_reg = PolynomialFeatures(degree = 3)\n",
    "X_poly = poly_reg.fit_transform(X)\n",
    "model_linear_2 = LinearRegression()\n",
    "# fit the model\n",
    "model_linear_2.fit(X_poly, y)\n",
    "y_poly_pred = model_linear_2.predict(X_poly)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d2469993",
   "metadata": {},
   "source": [
    "## Paired t-test to compare the performance of 2 prediction model"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "afc362aa",
   "metadata": {},
   "source": [
    "### Test 1: The test dataset is not significantly different from the training data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "7a698d77",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "      <th></th>\n",
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       "      <th>side 3</th>\n",
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       "      <th>498</th>\n",
       "      <td>563</td>\n",
       "      <td>75</td>\n",
       "      <td>567.973591</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>499</th>\n",
       "      <td>585</td>\n",
       "      <td>868</td>\n",
       "      <td>1046.732535</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>500 rows × 3 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "     side 1  side 2       side 3\n",
       "0       473     242   531.312526\n",
       "1       596     266   652.665305\n",
       "2       398     519   654.037461\n",
       "3       560     114   571.485783\n",
       "4       295     289   412.972154\n",
       "..      ...     ...          ...\n",
       "495     912     948  1315.464937\n",
       "496     921     834  1242.496278\n",
       "497     206     710   739.280732\n",
       "498     563      75   567.973591\n",
       "499     585     868  1046.732535\n",
       "\n",
       "[500 rows x 3 columns]"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Create a dataset with side 1 and side 2\n",
    "new_data = {\n",
    "    'side 1': np.random.randint(5, 1000, 500),  # Generate random values for side 1\n",
    "    'side 2': np.random.randint(5, 1000, 500)   # Generate random values for side 2\n",
    "}\n",
    "\n",
    "# Calculate side 3 using the Pythagorean theorem\n",
    "new_data['side 3'] = np.sqrt(new_data['side 1']**2 + new_data['side 2']**2)\n",
    "\n",
    "# Create a DataFrame\n",
    "test_df = pd.DataFrame(new_data)\n",
    "test_df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "12775a8a",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
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    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
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      "Done\n"
     ]
    }
   ],
   "source": [
    "# Create empty arrays to store RMSE values\n",
    "rmse_nn_array = []\n",
    "rmse_poly_array = []\n",
    "\n",
    "for i in range(len(test_df)):\n",
    "    # Get the side1, side2, and side3 values for the current row\n",
    "    side1 = test_df.loc[i, 'side 1']\n",
    "    side2 = test_df.loc[i, 'side 2']\n",
    "    side3 = test_df.loc[i, 'side 3']\n",
    "    \n",
    "    # Make predictions for the current row with the Neural Network model\n",
    "    scaled_input_nn = scaler.fit_transform(np.array([[side1, side2]]))\n",
    "    prediction_nn = model.predict(scaled_input_nn)\n",
    "    prediction_nn = scaler.inverse_transform(np.array([[prediction_nn[0][0], 0]]))[0][0]\n",
    "    \n",
    "    # Make predictions for the current row with the Polynomial Regression model\n",
    "    feature_poly = poly_reg.transform(np.array([[side1, side2]]))\n",
    "    prediction_poly = model_linear_2.predict(feature_poly)[0]\n",
    "    \n",
    "    # Calculate RMSE for the current row and store it in the arrays\n",
    "    rmse_nn = np.sqrt(metrics.mean_squared_error([side3], [prediction_nn]))\n",
    "    rmse_poly = np.sqrt(metrics.mean_squared_error([side3], [prediction_poly]))\n",
    "    \n",
    "    rmse_nn_array.append(rmse_nn)\n",
    "    rmse_poly_array.append(rmse_poly)\n",
    "\n",
    "print('Done')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "b6ad0fb9",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-2.2964988913244238 0.02206080983772425\n"
     ]
    }
   ],
   "source": [
    "# Perform t-test\n",
    "t_stat, p_value = stats.ttest_rel(rmse_nn_array, rmse_poly_array)\n",
    "print(t_stat, p_value)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "cb998998",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Reject the null hypothesis. There is a significant difference between the models.\n",
      "The Polynomial Regression model is better (lower RMSE).\n"
     ]
    }
   ],
   "source": [
    "#the significance level (alpha)\n",
    "alpha = 0.05 \n",
    "\n",
    "if p_value < alpha:\n",
    "    print(\"Reject the null hypothesis. There is a significant difference between the models.\")\n",
    "    if np.mean(rmse_nn) < np.mean(rmse_poly):\n",
    "        print(\"The Neural Network model is better (lower RMSE).\")\n",
    "    else:\n",
    "        print(\"The Polynomial Regression model is better (lower RMSE).\")\n",
    "else:\n",
    "    print(\"Fail to reject the null hypothesis. There is no significant difference between the models.\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "31260b47",
   "metadata": {},
   "source": [
    "### Test 2: The test dataset has value which has differ rule from raw dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "3a9a2768",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>side 1</th>\n",
       "      <th>side 2</th>\n",
       "      <th>side 3</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>2144</td>\n",
       "      <td>794</td>\n",
       "      <td>2286.300943</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1105</td>\n",
       "      <td>589</td>\n",
       "      <td>1252.176505</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1837</td>\n",
       "      <td>817</td>\n",
       "      <td>2010.487006</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1247</td>\n",
       "      <td>786</td>\n",
       "      <td>1474.043758</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1750</td>\n",
       "      <td>785</td>\n",
       "      <td>1918.000261</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>495</th>\n",
       "      <td>1741</td>\n",
       "      <td>823</td>\n",
       "      <td>1925.723241</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>496</th>\n",
       "      <td>2108</td>\n",
       "      <td>829</td>\n",
       "      <td>2265.150105</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>497</th>\n",
       "      <td>2543</td>\n",
       "      <td>987</td>\n",
       "      <td>2727.822941</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>498</th>\n",
       "      <td>2958</td>\n",
       "      <td>968</td>\n",
       "      <td>3112.360519</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>499</th>\n",
       "      <td>2959</td>\n",
       "      <td>901</td>\n",
       "      <td>3093.134656</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>500 rows × 3 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "     side 1  side 2       side 3\n",
       "0      2144     794  2286.300943\n",
       "1      1105     589  1252.176505\n",
       "2      1837     817  2010.487006\n",
       "3      1247     786  1474.043758\n",
       "4      1750     785  1918.000261\n",
       "..      ...     ...          ...\n",
       "495    1741     823  1925.723241\n",
       "496    2108     829  2265.150105\n",
       "497    2543     987  2727.822941\n",
       "498    2958     968  3112.360519\n",
       "499    2959     901  3093.134656\n",
       "\n",
       "[500 rows x 3 columns]"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Create a dataset with side 1 and side 2\n",
    "new_data = {\n",
    "    'side 1': np.random.randint(1000, 3000, 500),  # Generate random values for side 1\n",
    "    'side 2': np.random.randint(500, 1000, 500)   # Generate random values for side 2\n",
    "}\n",
    "\n",
    "# Calculate side 3 using the Pythagorean theorem\n",
    "new_data['side 3'] = np.sqrt(new_data['side 1']**2 + new_data['side 2']**2)\n",
    "\n",
    "# Create a DataFrame\n",
    "test_df = pd.DataFrame(new_data)\n",
    "test_df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "fc70d253",
   "metadata": {},
   "outputs": [
    {
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      "Done\n"
     ]
    }
   ],
   "source": [
    "# Create empty arrays to store RMSE values\n",
    "rmse_nn_array = []\n",
    "rmse_poly_array = []\n",
    "\n",
    "for i in range(len(test_df)):\n",
    "    # Get the side1, side2, and side3 values for the current row\n",
    "    side1 = test_df.loc[i, 'side 1']\n",
    "    side2 = test_df.loc[i, 'side 2']\n",
    "    side3 = test_df.loc[i, 'side 3']\n",
    "    \n",
    "    # Make predictions for the current row with the Neural Network model\n",
    "    scaled_input_nn = scaler.fit_transform(np.array([[side1, side2]]))\n",
    "    prediction_nn = model.predict(scaled_input_nn)\n",
    "    prediction_nn = scaler.inverse_transform(np.array([[prediction_nn[0][0], 0]]))[0][0]\n",
    "    \n",
    "    # Make predictions for the current row with the Polynomial Regression model\n",
    "    feature_poly = poly_reg.transform(np.array([[side1, side2]]))\n",
    "    prediction_poly = model_linear_2.predict(feature_poly)[0]\n",
    "    \n",
    "    # Calculate RMSE for the current row and store it in the arrays\n",
    "    rmse_nn = np.sqrt(metrics.mean_squared_error([side3], [prediction_nn]))\n",
    "    rmse_poly = np.sqrt(metrics.mean_squared_error([side3], [prediction_poly]))\n",
    "    \n",
    "    rmse_nn_array.append(rmse_nn)\n",
    "    rmse_poly_array.append(rmse_poly)\n",
    "\n",
    "print('Done')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "fde4e099",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-53.16239916656791 1.172337196049184e-207\n"
     ]
    }
   ],
   "source": [
    "# Perform t-test\n",
    "t_stat, p_value = stats.ttest_rel(rmse_nn_array, rmse_poly_array)\n",
    "print(t_stat, p_value)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "b1796b54",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Reject the null hypothesis. There is a significant difference between the models.\n",
      "The Neural Network model is better (lower RMSE).\n"
     ]
    }
   ],
   "source": [
    "#the significance level (alpha)\n",
    "alpha = 0.05 \n",
    "\n",
    "if p_value < alpha:\n",
    "    print(\"Reject the null hypothesis. There is a significant difference between the models.\")\n",
    "    if np.mean(rmse_nn) < np.mean(rmse_poly):\n",
    "        print(\"The Neural Network model is better (lower RMSE).\")\n",
    "    else:\n",
    "        print(\"The Polynomial Regression model is better (lower RMSE).\")\n",
    "else:\n",
    "    print(\"Fail to reject the null hypothesis. There is no significant difference between the models.\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "71bf8642",
   "metadata": {},
   "source": [
    "<div style=\"border-radius:10px;border:#c3d2bd solid;padding:15px;background-color:#f3f8f1;font-size:110%; color: #565d54;text-align:left\">\n",
    "    \n",
    " <p style=\"display: inline-block; padding: 7px; background-color: #d9ead3; color: #565d54; text-decoration: none; border-radius: 5px 5px; font-size: 150%; text-align: left; border: 1.5px solid #828c7e; font-family: 'New Times Roman', serif;\">-  Notes    -</p>\n",
    "\n",
    "    \n",
    "## The Paired t-test result:    \n",
    "- The performance of the neural network model is **higher** than that of the polynomial regression model when the input data is large.\n",
    "- The performance of the neural network model is **lower** than that of the polynomial regression model when the side 1 is randomly generated in lower range with side 2 (follow the rule of training data: side 1 is smaller than side 2), and when the test range is not significantly different from the training data.\n",
    "\n",
    "*(In my own thought, the reasons are that the dataset is generated based on a fixed rule with a clear linear relationship. So, with the inconsistent input I enter in with the training data can cause the big error for result of polynomial regression)*\n",
    "    \n",
    "## Neural network model:\n",
    "   - The neural network model has low accuracy when input test is low, and its results suggest a trend where **higher input values lead to more accurate predictions**.\n",
    "\n",
    "## Polynomial regression model :\n",
    "   - This makes it easier to identify the linear relationship between the independent and dependent variables, which results in a correlation coefficient of 1 and very low error metrics such as MSQ and RMSE. This indicates that the model has nearly 100% accuracy in predicting the correct answer for inputs that follow the **same rule** as the dataset (*side 1 is a multiple of 3, and side 2 is a multiple of 4,  then side 3 is precisely equal to the square root of the sum of the squares of side 1 and side 2, and side 3 is a multiple of 5 as well , know that they multiplied by the common factor*). Therefore, the **model gets the strongest performance on inputs that follow the same rule as the raw dataset and vice versa**. For example: *in training data, the side 1 is smaller than side 2, so when test values have side 1 values much higher than side 2 values, the results have more error than that of neural network.*\n",
    "\n",
    "\n",
    "- Additionally, when I created a **new dataset with randomly generated values near with raw data** for side 1 and side 2, and calculated side 3 based on the right-angle triangle rule, the **polynomial regression model's performance decreased**, as expected. The RMSE increased (97.36 while it was just 6.3 when applied model with the raw dataset) and the R^2 decreased, but the R^2 score was still high at 0.88 (lower than when applied to the raw dataset – 0.9999). **On the contrary**, RMSE significantly rise and R^2 score reduce (under 0.5) when the input value is much higher than raw data. Therefore, **the higher the input (far with the training data), the more error the result.**\n",
    "    \n",
    "    \n",
    "## Conclusion\n",
    "Therefore, it can be concluded that polynomial regression is a viable alternative to neural networks for tasks where the data is small in specific range, has a clear linear trend and is easy to represent with an equation. Neural networks may be more appropriate for tasks with large input, complex non-linear data, and large datasets.\n"
   ]
  }
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