6_sgd_vs_gd.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "024c9b6b-8250-49d2-b954-7f15d90392b2",
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "from matplotlib import pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "8319a721-099b-46ba-b9fd-a867549bd7fa",
   "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>area</th>\n",
       "      <th>bedrooms</th>\n",
       "      <th>price</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>3300</td>\n",
       "      <td>4</td>\n",
       "      <td>155.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>1540</td>\n",
       "      <td>3</td>\n",
       "      <td>60.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1521</td>\n",
       "      <td>3</td>\n",
       "      <td>75.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1200</td>\n",
       "      <td>2</td>\n",
       "      <td>51.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>1180</td>\n",
       "      <td>3</td>\n",
       "      <td>48.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    area  bedrooms  price\n",
       "7   3300         4  155.0\n",
       "17  1540         3   60.0\n",
       "3   1521         3   75.0\n",
       "4   1200         2   51.0\n",
       "16  1180         3   48.0"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = pd.read_csv(\"homeprices_banglore.csv\")\n",
    "df.sample(5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "2aa65e17-993e-480f-a948-bb2559a75c18",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.08827586, 0.25      ],\n",
       "       [0.62068966, 0.75      ],\n",
       "       [0.22068966, 0.5       ],\n",
       "       [0.24862069, 0.5       ],\n",
       "       [0.13793103, 0.25      ],\n",
       "       [0.12758621, 0.25      ],\n",
       "       [0.6662069 , 0.75      ],\n",
       "       [0.86206897, 0.75      ],\n",
       "       [0.17586207, 0.5       ],\n",
       "       [1.        , 1.        ],\n",
       "       [0.34482759, 0.5       ],\n",
       "       [0.68448276, 0.75      ],\n",
       "       [0.06896552, 0.25      ],\n",
       "       [0.10344828, 0.25      ],\n",
       "       [0.5       , 0.5       ],\n",
       "       [0.12931034, 0.25      ],\n",
       "       [0.13103448, 0.5       ],\n",
       "       [0.25517241, 0.5       ],\n",
       "       [0.67931034, 0.5       ],\n",
       "       [0.        , 0.        ]])"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn import preprocessing\n",
    "sx = preprocessing.MinMaxScaler()\n",
    "sy = preprocessing.MinMaxScaler()\n",
    "\n",
    "scaled_X = sx.fit_transform(df.drop(\"price\", axis=\"columns\"))\n",
    "scaled_y = sy.fit_transform(df[\"price\"].values.reshape(df.shape[0],1))\n",
    "\n",
    "scaled_X"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "756a6c70-d6b0-40e2-a6f4-fba2788a3161",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.05237037, 0.65185185, 0.22222222, 0.31851852, 0.14074074,\n",
       "       0.04444444, 0.76296296, 0.91111111, 0.13333333, 1.        ,\n",
       "       0.37037037, 0.8       , 0.04444444, 0.05925926, 0.51111111,\n",
       "       0.07407407, 0.11851852, 0.20740741, 0.51851852, 0.        ])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "scaled_y.reshape(20,)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "bb3289a2-f22d-4178-a92a-3718e8d462d3",
   "metadata": {},
   "outputs": [],
   "source": [
    "def batch_gradient_descent(X, y_true, epochs, learning_rate=0.01):\n",
    "    \n",
    "    number_of_features = X.shape[1]\n",
    "    # numpy array with 1 row and columns equal to number of features. In \n",
    "    # our case number_of_features = 2 (area, bedroom)\n",
    "    w = np.ones(shape=(number_of_features))\n",
    "    b = 0\n",
    "    total_samples = X.shape[0] #number of rows in X\n",
    "    \n",
    "    cost_list = []\n",
    "    epoch_list = []\n",
    "    \n",
    "    for i in range(epochs):\n",
    "        y_predicted = np.dot(w, X.T) + b\n",
    "        \n",
    "        w_grad = -(2/total_samples)*(X.T.dot(y_true-y_predicted))\n",
    "        b_grad = -(2/total_samples)*np.sum(y_true-y_predicted)\n",
    "        \n",
    "        w = w - learning_rate * w_grad\n",
    "        b = b - learning_rate * b_grad\n",
    "        \n",
    "        cost = np.mean(np.square(y_true-y_predicted)) # MSE (Mean Squared Error)\n",
    "        \n",
    "        if i%10==0:\n",
    "            cost_list.append(cost)\n",
    "            epoch_list.append(i)\n",
    "            \n",
    "    return w, b, cost, cost_list, epoch_list"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "a0079adc-f1d4-426a-bf36-4108f6ccd525",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([0.70712464, 0.67456527]), -0.23034857438407427, 0.0068641890429808105)"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "w, b, cost, cost_list, epoch_list = batch_gradient_descent(scaled_X, scaled_y.reshape(scaled_y.shape[0],),500)\n",
    "w, b, cost"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "40cbf5f8-991b-463b-abfe-b71c82915120",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1682403d0>]"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.xlabel(\"epoch\")\n",
    "plt.ylabel(\"cost\")\n",
    "plt.plot(epoch_list,cost_list)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "9e20db40-c583-4bfe-a4e7-845777ae7973",
   "metadata": {},
   "outputs": [],
   "source": [
    "def predict(area, bedrooms, w, b):\n",
    "    scaled_X = sx.transform([[area,bedrooms]])[0]\n",
    "    \n",
    "    scaled_price = w[0]*scaled_X[0] + w[1]*scaled_X[1] + b\n",
    "    \n",
    "    return sy.inverse_transform([[scaled_price]])[0][0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "9451c9bd-3ad8-4221-9d39-4228239af54d",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/serhatderya/miniconda3/envs/tfm1_arm64/lib/python3.9/site-packages/sklearn/base.py:450: UserWarning: X does not have valid feature names, but MinMaxScaler was fitted with feature names\n",
      "  warnings.warn(\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "128.45484403267596"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "predict(2600,4,w,b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "4b24d728-7c0c-451b-9688-a9edfd4d44a0",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/serhatderya/miniconda3/envs/tfm1_arm64/lib/python3.9/site-packages/sklearn/base.py:450: UserWarning: X does not have valid feature names, but MinMaxScaler was fitted with feature names\n",
      "  warnings.warn(\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "30.253094462442355"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "predict(1000,2,w,b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "6cbb8d50-3697-47c4-bd3a-173a8827de0b",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/serhatderya/miniconda3/envs/tfm1_arm64/lib/python3.9/site-packages/sklearn/base.py:450: UserWarning: X does not have valid feature names, but MinMaxScaler was fitted with feature names\n",
      "  warnings.warn(\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "69.47860785714694"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "predict(1500,3,w,b)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0187ae4f-86ff-4b73-a036-fca857230a94",
   "metadata": {},
   "source": [
    "# Stochastic Gradient Descent"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "c43ef195-3dc6-4e19-a46a-d9ad83836dff",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import random\n",
    "random.randint(0,6)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "f4585bcd-f4c2-4ebf-84cf-3605e1775ba7",
   "metadata": {},
   "outputs": [],
   "source": [
    "def stochastic_gradient_descent(X, y_true, epochs, learning_rate=0.01):\n",
    "    number_of_features = X.shape[1]\n",
    "    # numpy array with 1 row and columns equal to number of features. In \n",
    "    # our case number_of_features = 3 (area, bedroom and age)\n",
    "    w = np.ones(shape=(number_of_features)) \n",
    "    b = 0\n",
    "    total_samples = X.shape[0]\n",
    "    \n",
    "    cost_list = []\n",
    "    epoch_list = []\n",
    "    \n",
    "    for i in range(epochs):    \n",
    "        random_index = random.randint(0,total_samples-1) # random index from total samples\n",
    "        sample_x = X[random_index]\n",
    "        sample_y = y_true[random_index]\n",
    "        \n",
    "        y_predicted = np.dot(w, sample_x.T) + b\n",
    "    \n",
    "        w_grad = -(2/total_samples)*(sample_x.T.dot(sample_y-y_predicted))\n",
    "        b_grad = -(2/total_samples)*(sample_y-y_predicted)\n",
    "        \n",
    "        w = w - learning_rate * w_grad\n",
    "        b = b - learning_rate * b_grad\n",
    "        \n",
    "        cost = np.square(sample_y-y_predicted)\n",
    "        \n",
    "        if i%100==0: # at every 100th iteration record the cost and epoch value\n",
    "            cost_list.append(cost)\n",
    "            epoch_list.append(i)\n",
    "        \n",
    "    return w, b, cost, cost_list, epoch_list"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "69cbfe1d-6ad6-42ed-be16-f4de4547655e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([0.7068835 , 0.67353282]), -0.23271594063081616, 0.054265185128757935)"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "w_sgd, b_sgd, cost_sgd, cost_list_sgd, epoch_list_sgd = stochastic_gradient_descent(scaled_X, scaled_y.reshape(scaled_y.shape[0],),10000)\n",
    "w_sgd, b_sgd, cost_sgd"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "30b9b757-2295-49e3-9664-f8c6537c2b62",
   "metadata": {},
   "source": [
    "### Compare this with weights and bias that we got using gradient descent. They both of quite similar."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "389d4ad8-fb2e-4548-8bdf-886cf97f95bf",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([0.70712464, 0.67456527]), -0.23034857438407427)"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "w , b "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "c3555818-936e-423d-b4b8-169eb307117b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x168515b80>]"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.xlabel(\"epoch\")\n",
    "plt.ylabel(\"cost\")\n",
    "plt.plot(epoch_list_sgd,cost_list_sgd)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "8653a0b9-258a-4600-9ac8-b0b7791695c2",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/serhatderya/miniconda3/envs/tfm1_arm64/lib/python3.9/site-packages/sklearn/base.py:450: UserWarning: X does not have valid feature names, but MinMaxScaler was fitted with feature names\n",
      "  warnings.warn(\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "128.0105083480264"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "predict(2600,4,w_sgd, b_sgd) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "3081ce49-0ef1-4d31-9236-2c7db5d7f472",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/serhatderya/miniconda3/envs/tfm1_arm64/lib/python3.9/site-packages/sklearn/base.py:450: UserWarning: X does not have valid feature names, but MinMaxScaler was fitted with feature names\n",
      "  warnings.warn(\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "29.89640992775821"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "predict(1000,2,w_sgd, b_sgd)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "a519202d-fd95-4a5a-82b5-5d96ad583c06",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/serhatderya/miniconda3/envs/tfm1_arm64/lib/python3.9/site-packages/sklearn/base.py:450: UserWarning: X does not have valid feature names, but MinMaxScaler was fitted with feature names\n",
      "  warnings.warn(\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "69.08146548928447"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "predict(1500,3,w_sgd, b_sgd)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "96fa83e0-e559-4d4b-b22b-d4370e9392d2",
   "metadata": {},
   "source": [
    "# Mini-Batch Gradient Descent"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "d165c835-0689-4d51-ab2b-278fbabc0ce1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 6,  9, 17, 14, 11, 18, 10, 16,  4,  7,  3,  1,  8,  2, 12, 19, 15,\n",
       "        0,  5, 13])"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.random.permutation(20)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "81f571e1-fec3-44e7-b540-8d249e89064a",
   "metadata": {},
   "outputs": [],
   "source": [
    "def mini_batch_gradient_descent(X, y_true, epochs = 100, batch_size = 5, learning_rate = 0.01):\n",
    "    \n",
    "    number_of_features = X.shape[1]\n",
    "    # numpy array with 1 row and columns equal to number of features. In \n",
    "    # our case number_of_features = 3 (area, bedroom and age)\n",
    "    w = np.ones(shape=(number_of_features)) \n",
    "    b = 0\n",
    "    total_samples = X.shape[0] # number of rows in X\n",
    "    \n",
    "    if batch_size > total_samples: # In this case mini batch becomes same as batch gradient descent\n",
    "        batch_size = total_samples\n",
    "        \n",
    "    cost_list = []\n",
    "    epoch_list = []\n",
    "    \n",
    "    num_batches = int(total_samples/batch_size)\n",
    "    \n",
    "    for i in range(epochs):    \n",
    "        random_indices = np.random.permutation(total_samples)\n",
    "        X_tmp = X[random_indices]\n",
    "        y_tmp = y_true[random_indices]\n",
    "        \n",
    "        for j in range(0,total_samples,batch_size):\n",
    "            Xj = X_tmp[j:j+batch_size]\n",
    "            yj = y_tmp[j:j+batch_size]\n",
    "            y_predicted = np.dot(w, Xj.T) + b\n",
    "            \n",
    "            w_grad = -(2/len(Xj))*(Xj.T.dot(yj-y_predicted))\n",
    "            b_grad = -(2/len(Xj))*np.sum(yj-y_predicted)\n",
    "            \n",
    "            w = w - learning_rate * w_grad\n",
    "            b = b - learning_rate * b_grad\n",
    "                \n",
    "            cost = np.mean(np.square(yj-y_predicted)) # MSE (Mean Squared Error)\n",
    "        \n",
    "        if i%10==0:\n",
    "            cost_list.append(cost)\n",
    "            epoch_list.append(i)\n",
    "        \n",
    "    return w, b, cost, cost_list, epoch_list"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "ef2b8227-1497-4246-9fcb-92baad8f516e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([0.70999299, 0.67804081]), -0.23343522881800174, 0.00710576566010732)"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "w, b, cost, cost_list, epoch_list = mini_batch_gradient_descent(\n",
    "    scaled_X,\n",
    "    scaled_y.reshape(scaled_y.shape[0],),\n",
    "    epochs = 120,\n",
    "    batch_size = 5\n",
    ")\n",
    "w, b, cost"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "836c32d1-d3a6-4df4-ba50-6ccdcf69133b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x168fe51f0>]"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.xlabel(\"epoch\")\n",
    "plt.ylabel(\"cost\")\n",
    "plt.plot(epoch_list,cost_list)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "467a9616-529c-4918-b6f3-8914145c830c",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/serhatderya/miniconda3/envs/tfm1_arm64/lib/python3.9/site-packages/sklearn/base.py:450: UserWarning: X does not have valid feature names, but MinMaxScaler was fitted with feature names\n",
      "  warnings.warn(\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "128.63039263934243"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "predict(2600,4,w,b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "27f7e255-05e9-49b9-9921-5e52b554ff8e",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/serhatderya/miniconda3/envs/tfm1_arm64/lib/python3.9/site-packages/sklearn/base.py:450: UserWarning: X does not have valid feature names, but MinMaxScaler was fitted with feature names\n",
      "  warnings.warn(\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "29.980401158786087"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "predict(1000,2,w,b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "1f8aee8a-9966-4540-a478-9b68ad10d275",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/serhatderya/miniconda3/envs/tfm1_arm64/lib/python3.9/site-packages/sklearn/base.py:450: UserWarning: X does not have valid feature names, but MinMaxScaler was fitted with feature names\n",
      "  warnings.warn(\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "69.38997755353333"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "predict(1500,3,w,b)"
   ]
  },
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   "execution_count": null,
   "id": "85c5a24c-2748-4e87-8647-dca1db1786d5",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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