linear-regression-from-scratch.ipynb

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   "source": [
    "def dot_product(a, b):\n",
    "    if len(a) != len(b):\n",
    "        return -1\n",
    "\n",
    "    result = 0\n",
    "    for each in range(len(a)):\n",
    "        result += a[each] * b[each]\n",
    "\n",
    "    return result"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
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    "collapsed": true
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   "source": [
    "def compute_cost(X, y, theta):\n",
    "    J = 0\n",
    "    predictions = []\n",
    "\n",
    "    for each in X:\n",
    "        predictions.append(dot_product(each, theta))\n",
    "\n",
    "    errors = []\n",
    "    for index, each in enumerate(predictions):\n",
    "        errors.append(each - y[index])\n",
    "\n",
    "    J = (1.0 / 2.0) * dot_product(errors, errors)\n",
    "\n",
    "    return J"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
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   "outputs": [],
   "source": [
    "def run_gradient_descent(X, y, theta, number_of_iterations):\n",
    "    alpha = 0.01\n",
    "    J_history = []\n",
    "\n",
    "    for each_iteration in range(number_of_iterations):\n",
    "        predictions = []\n",
    "        for each_example in X:\n",
    "            predictions.append(dot_product(each_example, theta))\n",
    "\n",
    "        for t_index, each_theta in enumerate(theta):\n",
    "            diff = []\n",
    "            X_col = []\n",
    "            for p_index, each_prediction in enumerate(predictions):\n",
    "                diff.append(each_prediction - y[p_index])\n",
    "                X_col.append(X[t_index][p_index])\n",
    "\n",
    "            error = dot_product(diff, X_col)\n",
    "            result = each_theta - (alpha * error)\n",
    "            theta[t_index] = result\n",
    "\n",
    "        J = compute_cost(X, y, theta)\n",
    "        J_history.append(J)\n",
    "\n",
    "    return (J_history, theta)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "X = [[1, 2], [3, 4]]\n",
    "y = [2, 2.5]\n",
    "theta = [0, 0]\n",
    "number_of_iterations = 10\n",
    "\n",
    "J_history, theta = run_gradient_descent(X, y, theta, number_of_iterations)\n",
    "print(J_history)\n",
    "print(theta)"
   ]
  }
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