{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "42a329dc",
   "metadata": {},
   "source": [
    "## Create a trend line with a confidence band for given dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "d86f1219",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from sklearn.linear_model import LinearRegression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "1832fa4d",
   "metadata": {},
   "outputs": [],
   "source": [
    "x=np.array([1,2,3,4,5,6,7,8,9,10])\n",
    "y=np.array([1.2,2.4,2.6,4.2,4.4,5.5,6.8,8.1,8.5,10.1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "23b3be8b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression()"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lr=LinearRegression()\n",
    "lr.fit(x.reshape(-1,1),y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "7b706cb8",
   "metadata": {},
   "outputs": [],
   "source": [
    "x_fit=np.linspace(min(x),max(x),100)\n",
    "y_fit=lr.predict(x_fit.reshape(-1,1))\n",
    "y_ci=lr.predict(x_fit.reshape(-1,1))\n",
    "y_ci_lw,y_ci_up=lr.predict(x_fit.reshape(-1,1)),lr.predict(x_fit.reshape(-1,1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "89890c1e",
   "metadata": {},
   "outputs": [],
   "source": [
    "for i in range(len(x_fit)):\n",
    "    prd=lr.predict(x_fit[i].reshape(-1,1))[0]\n",
    "    t_val=1.96\n",
    "    std_err=np.sqrt(np.sum((y-lr.predict(x.reshape(-1,1)))**2)/(len(x)-2))/np.sqrt(len(x))\n",
    "    intr=t_val*std_err\n",
    "    y_ci_lw[i]=prd-intr\n",
    "    y_ci_up[i]=prd+intr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "3fde4f5b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(x,y,color='blue',label='Data')\n",
    "plt.plot(x_fit,y_fit,color='red',label='Trend Line')\n",
    "plt.fill_between(x_fit,y_ci_lw,y_ci_up,color='gray')\n",
    "plt.legend()\n",
    "plt.title(\"Trend with 95% Confidence Band\")\n",
    "plt.xlabel('X')\n",
    "plt.ylabel('Y')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "0e7446ea",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.13"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
