{
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   "metadata": {},
   "source": [
    "# Analyzing Linear Regression Model in Python"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Analyze a Simple Linear Model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Goal: Obtaining statistical summary about the linear regression line the topsoil lead concentration (`lead` column, as y-axis) and the topsoil cadmium concentration (`cadmium` column, as x-axis). "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
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    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/lizhoufan/anaconda3/lib/python3.6/site-packages/ipykernel_launcher.py:10: FutureWarning: reshape is deprecated and will raise in a subsequent release. Please use .values.reshape(...) instead\n",
      "  # Remove the CWD from sys.path while we load stuff.\n"
     ]
    }
   ],
   "source": [
    "### Previous steps necessary\n",
    "# import packages\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "from sklearn.linear_model import LinearRegression\n",
    "# import dataset\n",
    "data = pd.read_csv(\"meuse.csv\")\n",
    "# build the model\n",
    "regression_model = LinearRegression()\n",
    "lr = LinearRegression().fit(data.cadmium.reshape((-1, 1)), data.lead)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### R^2\n",
    "R-squared measures how close the data are fitted to the regression line."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
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     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.6383156080918473\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/lizhoufan/anaconda3/lib/python3.6/site-packages/ipykernel_launcher.py:1: FutureWarning: reshape is deprecated and will raise in a subsequent release. Please use .values.reshape(...) instead\n",
      "  \"\"\"Entry point for launching an IPython kernel.\n"
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   ],
   "source": [
    "print(lr.score(data.cadmium.reshape((-1, 1)), data.lead))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "R-squared measures how close the data are fitted to the regression line. In here, we can conclude that about 63% of the variance of the prediction of `lead` based on `cadmium` can be explained by the linear model `m1`."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For other more advanced, please refer to our later posts regarding advanced topics in Linear Regression Modeling."
   ]
  }
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