examples/solution_lab_03_linreg.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 03. Lab exercises, Linear regression\n",
    "\n",
    "----\n",
    "\n",
    "1 Implement linear regression using SVD. (use np.linalg.svd). Write a class for linear regression, using the following template\n",
    "\n",
    "\n",
    "    ```\n",
    "    class LinReg():\n",
    "    \"\"\"Linear regression class.\"\"\"\n",
    "    \n",
    "    def __init__(self):\n",
    "        \"\"\"Intialize linear regression.\"\"\"\n",
    "        self.coefficients = None\n",
    "    \n",
    "    def fit(self,x_train, y_train):\n",
    "        \"\"\"Fit linear regression.\"\"\"\n",
    "        return self\n",
    "    \n",
    "    def predict(self,x_test):\n",
    "        \"\"\"Predict with linear regression.\"\"\"\n",
    "        return y_test\n",
    "    ```\n",
    "    \n",
    "    \n",
    "2 Application:\n",
    "- A, Apply the linear regressor on photometric redshift estimation using the provided photoz_mini.csv file. Use a 80-20% train test split. Calculate the mean squared error (MSE) of predicctions and plot the true and the predicted values on a scatterplot for both the training set and the test set. \n",
    "- B, Repeat the same with the linear regression class of scikit-learn.\n",
    "- C, Compare the coefficients of the 2 implementations\n",
    "- D, Apply the linear regressor on photometric redshift estimation using the provided photoz_mini.csv file. Use 5 fold cross validation. Estimate the mean and standard deviation of the MSE of the predictions. \n",
    "- E, Compare it to the result of a KNN regression.\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "3 Statsmodels\n",
    "- A Apply the linear regression in the statsmodels package on the whole dataset. Asses the significance of each color.\n",
    "- B Iteratvely omit the least significant colors. Compare the $R^2$ of the 5 fits.\n",
    "- C Validate each 5 combinations of colors using cross validation on 5 folds using your linear regression class or the scikit-learn linear regression class. How does the MSE change after omitting the color? Which is best combination of inputs?\n",
    "- D, Repeat execise C using a KNN regressor, do you see similar behaviour?\n",
    "\n",
    "\n",
    "4 Inspection \n",
    "- A, Select the best combination of inputs found in 3/C, fit the whole dataset, and inspect the residuals of the fit, on a residual plot, is the a clear trend? \n",
    "- B, Inspect the residuals of the fit, on a residual plot, identify and color outliers, where residual are larger than 3 $\n",
    "\\sigma$.\n",
    "- C, Identify high levarage points.\n",
    "\n",
    "\n",
    "5 Interactions, quadratic\n",
    "\n",
    "- A, Select the best combination of inputs found in 3/C and add interaction to the data and inspect its siginifcance using the whole dataset.\n",
    "- B, Validate the added interaction using cross validation on 5 folds using your linear regression class or the scikit-learn linear regression class. How does the MSE change after adding interactions?\n",
    "- C, Add quadratic form of the colors as predictive variable. Asses the significance of the quadratic terms. Which quadratic term is significant?\n",
    "- D, Create the final model by adding the siginificant quadratic term. Validate this model Using cross validation on 5 folds using your linear regression class or the scikit-learn linear regression class. Inspect the final MSE, and compare it to the original, the one with the best colors, and the one with interactions. \n",
    "---\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Populating the interactive namespace from numpy and matplotlib\n"
     ]
    }
   ],
   "source": [
    "%pylab inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1 Implement linear regression using SVD. (use np.linalg.svd). Write a class for linear regression, using the following template\n",
    "\n",
    "\n",
    "    ```\n",
    "    class LinReg():\n",
    "    \"\"\"Linear regression class.\"\"\"\n",
    "    \n",
    "    def __init__(self):\n",
    "        \"\"\"Intialize linear regression.\"\"\"\n",
    "        self.coefficients = None\n",
    "    \n",
    "    def fit(self,x_train, y_train):\n",
    "        \"\"\"Fit linear regression.\"\"\"\n",
    "        return self\n",
    "    \n",
    "    def predict(self,x_test):\n",
    "        \"\"\"Predict with linear regression.\"\"\"\n",
    "        return y_test\n",
    "    ```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "class LinReg():\n",
    "    \"\"\"Linear regression class.\"\"\"\n",
    "    \n",
    "    def __init__(self):\n",
    "        \"\"\"Intialize linear regression.\"\"\"\n",
    "        self.coefficients = None\n",
    "    \n",
    "    def fit(self,x_train, y_train):\n",
    "        \"\"\"Fit linear regression.\"\"\"\n",
    "        # make matrices\n",
    "        A = np.column_stack((np.ones(len(x_train)),x_train))\n",
    "        b = y_train\n",
    "        \n",
    "        # perform SVD\n",
    "        U, w ,VT = np.linalg.svd(A, full_matrices=False)\n",
    "        \n",
    "        # just write the formula\n",
    "        self.coefficients = np.sum([(np.dot(U[:,i], b)/wi) * VT[i,:] \n",
    "                                    for i,wi in enumerate(w)], axis=0)\n",
    "\n",
    "        return self\n",
    "    \n",
    "    def predict(self,x_test):\n",
    "        \"\"\"Predict with linear regression.\"\"\"\n",
    "        y_test = np.column_stack((np.ones(len(x_test))\n",
    "                                  ,x_test)).dot(self.coefficients)\n",
    "        return y_test"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2 Application:\n",
    "- A, Apply the linear regressor on photometric redshift estimation using the provided photoz_mini.csv file. Use a 80-20% train test split. Calculate the mean squared error (MSE) of predicctions and plot the true and the predicted values on a scatterplot for both the training set and the test set. \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "from sklearn.model_selection import train_test_split"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Load data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "df = pd.read_csv('../data/photoz_mini.csv')  # load train data\n",
    "x = df[['u','g','r','i','z']].values  # format x as scipy expects it\n",
    "y = df['redshift'].values  # format y as scipy expects it"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "x_train, x_test, y_train, y_test  = train_test_split(x, y, test_size= 0.2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Apply the class"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 190 ms, sys: 6.55 ms, total: 197 ms\n",
      "Wall time: 189 ms\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "mylr = LinReg()\n",
    "mylr.fit(x_train, y_train)\n",
    "myyp_train = mylr.predict(x_train)\n",
    "myyp_test = mylr.predict(x_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Plot it"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0, 1)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 864x432 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "figsize(12,6)\n",
    "plt.subplot(1,2,1)\n",
    "plot(y_train, myyp_train,'o')\n",
    "xlabel('z true')\n",
    "ylabel('z predicted')\n",
    "ttl = 'TRAIN mae = %.4f' % np.mean(np.abs(y_train-myyp_train))\n",
    "ttl += '\\n         mse = %.4f' % np.linalg.norm(y_train-myyp_train,2) \n",
    "title(ttl)\n",
    "xlim(0,1)\n",
    "ylim(0,1)\n",
    "\n",
    "plt.subplot(1,2,2)\n",
    "plot(y_test, myyp_test,'o')\n",
    "\n",
    "xlabel('z true')\n",
    "ylabel('z predicted')\n",
    "ttl = 'TEST mae = %.4f' % np.mean(np.abs(y_test-myyp_test))\n",
    "ttl += '\\n         mse = %.4f' % np.linalg.norm(y_test-myyp_test,2) \n",
    "title(ttl)\n",
    "xlim(0,1)\n",
    "ylim(0,1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2 Application:\n",
    "- B, Repeat the same with the linear regression class of scikit-learn."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.linear_model import LinearRegression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 4.55 ms, sys: 419 µs, total: 4.97 ms\n",
      "Wall time: 3.57 ms\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "lreg = LinearRegression()\n",
    "lreg.fit(x_train, y_train)\n",
    "yp_train = lreg.predict(x_train)\n",
    "yp_test = lreg.predict(x_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0, 1)"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x432 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "figsize(12,6)\n",
    "plt.subplot(1,2,1)\n",
    "plot(y_train, yp_train,'o')\n",
    "xlabel('z true')\n",
    "ylabel('z predicted')\n",
    "ttl = 'TRAIN mae = %.4f' % np.mean(np.abs(y_train-yp_train))\n",
    "ttl += '\\n         mse = %.4f' % np.linalg.norm(y_train-yp_train,2) \n",
    "title(ttl)\n",
    "xlim(0,1)\n",
    "ylim(0,1)\n",
    "\n",
    "plt.subplot(1,2,2)\n",
    "plot(y_test, yp_test,'o')\n",
    "\n",
    "xlabel('z true')\n",
    "ylabel('z predicted')\n",
    "ttl = 'TEST mae = %.4f' % np.mean(np.abs(y_test-yp_test))\n",
    "ttl += '\\n         mse = %.4f' % np.linalg.norm(y_test-yp_test,2) \n",
    "title(ttl)\n",
    "xlim(0,1)\n",
    "ylim(0,1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2 Application:\n",
    "- C, Compare the coefficients of the 2 implementations"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Answer: the coefficients are the same"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-1.39683966 -0.01341133  0.03100846  0.31563485 -0.22479868 -0.02563066]\n",
      "-1.39683965577 [-0.01341133  0.03100846  0.31563485 -0.22479868 -0.02563066]\n"
     ]
    }
   ],
   "source": [
    "print mylr.coefficients\n",
    "print lreg.intercept_, lreg.coef_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2 Application:\n",
    "- D, Apply the linear regressor on photometric redshift estimation using the provided photoz_mini.csv file. Use 5 fold cross validation. Estimate the mean and standard deviation of the MSE of the predictions. \n",
    "- E, Compare it to the result of a KNN regression.\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Answer: MSE is = 10.7127 +/- 0.6217 but KNN is more accurate"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.model_selection import KFold\n",
    "from sklearn.neighbors import KNeighborsRegressor"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "mses = 10.7127 +/- 0.6217\n",
      "mses = 9.9352 +/- 0.4864\n",
      "CPU times: user 33.4 ms, sys: 2.39 ms, total: 35.8 ms\n",
      "Wall time: 17.7 ms\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "\n",
    "def my_kfold(model, x, y):\n",
    "    kf = KFold(n_splits=5)\n",
    "    mses = []\n",
    "    for train_index, test_index in kf.split(x):\n",
    "        x_train, x_test = x[train_index], x[test_index]\n",
    "        y_train, y_test = y[train_index], y[test_index]\n",
    "        lreg = model()\n",
    "        lreg.fit(x_train, y_train)\n",
    "        yp = lreg.predict(x_test)\n",
    "        mses.append(np.linalg.norm(y_test-yp,1))\n",
    "    print 'mses = %.4f +/- %.4f' % (np.mean(mses), np.std(mses, ddof=1))  # note ddof!\n",
    "    \n",
    "my_kfold(LinReg, x, y)\n",
    "my_kfold(KNeighborsRegressor, x, y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3 Statsmodels\n",
    "- A Apply the linear regression in the statsmodels package on the whole dataset. Asses the significance of each color. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Answer : Color z does not seem to be too significant"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "import statsmodels.formula.api as smf"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:               redshift   R-squared:                       0.817\n",
      "Model:                            OLS   Adj. R-squared:                  0.817\n",
      "Method:                 Least Squares   F-statistic:                     890.4\n",
      "Date:                Sat, 29 Sep 2018   Prob (F-statistic):               0.00\n",
      "Time:                        17:42:29   Log-Likelihood:                 1099.9\n",
      "No. Observations:                1000   AIC:                            -2188.\n",
      "Df Residuals:                     994   BIC:                            -2158.\n",
      "Df Model:                           5                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "Intercept     -1.3883      0.058    -24.084      0.000      -1.501      -1.275\n",
      "u             -0.0181      0.005     -3.376      0.001      -0.029      -0.008\n",
      "g              0.0368      0.011      3.219      0.001       0.014       0.059\n",
      "r              0.2929      0.024     12.313      0.000       0.246       0.340\n",
      "i             -0.1900      0.028     -6.692      0.000      -0.246      -0.134\n",
      "z             -0.0384      0.018     -2.126      0.034      -0.074      -0.003\n",
      "==============================================================================\n",
      "Omnibus:                      363.949   Durbin-Watson:                   2.006\n",
      "Prob(Omnibus):                  0.000   Jarque-Bera (JB):             4958.977\n",
      "Skew:                           1.276   Prob(JB):                         0.00\n",
      "Kurtosis:                      13.607   Cond. No.                         986.\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    }
   ],
   "source": [
    "results = smf.ols('redshift ~ u + g + r + i + z ', data=df).fit()\n",
    "print(results.summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3 Statsmodels\n",
    "- B Iteratvely omit the least significant colors. Compare the $R^2$ of the 5 fits.\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Anser: I omitted z, u, g, i , \n",
    "\n",
    "The R-square did not drop first, then it dropped from 0.817 to 0.815, then to 0.814 and then to 0.75. Onlyn the last drop is large."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:               redshift   R-squared:                       0.817\n",
      "Model:                            OLS   Adj. R-squared:                  0.816\n",
      "Method:                 Least Squares   F-statistic:                     1108.\n",
      "Date:                Sat, 29 Sep 2018   Prob (F-statistic):               0.00\n",
      "Time:                        17:42:29   Log-Likelihood:                 1097.7\n",
      "No. Observations:                1000   AIC:                            -2185.\n",
      "Df Residuals:                     995   BIC:                            -2161.\n",
      "Df Model:                           4                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "Intercept     -1.3721      0.057    -23.971      0.000      -1.484      -1.260\n",
      "u             -0.0182      0.005     -3.382      0.001      -0.029      -0.008\n",
      "g              0.0420      0.011      3.754      0.000       0.020       0.064\n",
      "r              0.2943      0.024     12.357      0.000       0.248       0.341\n",
      "i             -0.2357      0.019    -12.697      0.000      -0.272      -0.199\n",
      "==============================================================================\n",
      "Omnibus:                      358.105   Durbin-Watson:                   2.001\n",
      "Prob(Omnibus):                  0.000   Jarque-Bera (JB):             4808.008\n",
      "Skew:                           1.253   Prob(JB):                         0.00\n",
      "Kurtosis:                      13.446   Cond. No.                         881.\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    }
   ],
   "source": [
    "results = smf.ols('redshift ~  u + g + r + i  ', data=df).fit()\n",
    "print(results.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:               redshift   R-squared:                       0.815\n",
      "Model:                            OLS   Adj. R-squared:                  0.814\n",
      "Method:                 Least Squares   F-statistic:                     1458.\n",
      "Date:                Sat, 29 Sep 2018   Prob (F-statistic):               0.00\n",
      "Time:                        17:42:29   Log-Likelihood:                 1092.0\n",
      "No. Observations:                1000   AIC:                            -2176.\n",
      "Df Residuals:                     996   BIC:                            -2156.\n",
      "Df Model:                           3                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "Intercept     -1.5034      0.042    -35.557      0.000      -1.586      -1.420\n",
      "g              0.0148      0.008      1.891      0.059      -0.001       0.030\n",
      "r              0.3244      0.022     14.612      0.000       0.281       0.368\n",
      "i             -0.2510      0.018    -13.870      0.000      -0.287      -0.215\n",
      "==============================================================================\n",
      "Omnibus:                      347.661   Durbin-Watson:                   1.991\n",
      "Prob(Omnibus):                  0.000   Jarque-Bera (JB):             4957.935\n",
      "Skew:                           1.185   Prob(JB):                         0.00\n",
      "Kurtosis:                      13.648   Cond. No.                         586.\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    }
   ],
   "source": [
    "results = smf.ols('redshift ~  g + r + i  ', data=df).fit()\n",
    "print(results.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:               redshift   R-squared:                       0.814\n",
      "Model:                            OLS   Adj. R-squared:                  0.814\n",
      "Method:                 Least Squares   F-statistic:                     2180.\n",
      "Date:                Sat, 29 Sep 2018   Prob (F-statistic):               0.00\n",
      "Time:                        17:42:29   Log-Likelihood:                 1090.2\n",
      "No. Observations:                1000   AIC:                            -2174.\n",
      "Df Residuals:                     997   BIC:                            -2160.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "Intercept     -1.4761      0.040    -37.100      0.000      -1.554      -1.398\n",
      "r              0.3582      0.013     27.102      0.000       0.332       0.384\n",
      "i             -0.2711      0.015    -18.497      0.000      -0.300      -0.242\n",
      "==============================================================================\n",
      "Omnibus:                      328.785   Durbin-Watson:                   1.988\n",
      "Prob(Omnibus):                  0.000   Jarque-Bera (JB):             5035.708\n",
      "Skew:                           1.076   Prob(JB):                         0.00\n",
      "Kurtosis:                      13.781   Cond. No.                         414.\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    }
   ],
   "source": [
    "results = smf.ols('redshift ~  r + i  ', data=df).fit()\n",
    "print(results.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:               redshift   R-squared:                       0.750\n",
      "Model:                            OLS   Adj. R-squared:                  0.750\n",
      "Method:                 Least Squares   F-statistic:                     2994.\n",
      "Date:                Sat, 29 Sep 2018   Prob (F-statistic):          1.07e-302\n",
      "Time:                        17:42:29   Log-Likelihood:                 942.65\n",
      "No. Observations:                1000   AIC:                            -1881.\n",
      "Df Residuals:                     998   BIC:                            -1871.\n",
      "Df Model:                           1                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "Intercept     -1.8514      0.040    -46.705      0.000      -1.929      -1.774\n",
      "r              0.1161      0.002     54.718      0.000       0.112       0.120\n",
      "==============================================================================\n",
      "Omnibus:                      200.514   Durbin-Watson:                   2.029\n",
      "Prob(Omnibus):                  0.000   Jarque-Bera (JB):             2057.865\n",
      "Skew:                          -0.597   Prob(JB):                         0.00\n",
      "Kurtosis:                       9.925   Cond. No.                         249.\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    }
   ],
   "source": [
    "results = smf.ols('redshift ~  r   ', data=df).fit()\n",
    "print(results.summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3 Statsmodels\n",
    "- C Validate each 5 combinations of colors using cross validation on 5 folds using your linear regression class of the scikit-learn linear regression class. How does the MSE change after omitting the color?\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Answer : Error drops until R+E ! That seems to be the best combination altough not siginificantly."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "mses = 10.7127 +/- 0.6217\n",
      "mses = 10.6228 +/- 0.5640\n",
      "mses = 10.5756 +/- 0.6706\n",
      "mses = 10.5567 +/- 0.7091\n",
      "mses = 14.6646 +/- 0.9421\n"
     ]
    }
   ],
   "source": [
    "my_kfold(LinReg, df[['u','g','r','i','z']].values, y)\n",
    "my_kfold(LinReg, df[['u','g','r','i']].values, y)\n",
    "my_kfold(LinReg, df[['g','r','i']].values, y)\n",
    "my_kfold(LinReg, df[['r','i']].values, y)\n",
    "my_kfold(LinReg, df[['i']].values, y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3 Statsmodels\n",
    "\n",
    "- D, Repeat execise C using a KNN regressor, do you see similar behaviour?\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Answer: Yes kinda, error siginificantly drops after the first 2 deletions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "mses = 9.9352 +/- 0.4864\n",
      "mses = 9.8629 +/- 0.5624\n",
      "mses = 9.5428 +/- 0.6110\n",
      "mses = 10.3907 +/- 0.3814\n",
      "mses = 14.3840 +/- 0.6655\n"
     ]
    }
   ],
   "source": [
    "my_kfold(KNeighborsRegressor, df[['u','g','r','i','z']].values, y)\n",
    "my_kfold(KNeighborsRegressor, df[['u','g','r','i']].values, y)\n",
    "my_kfold(KNeighborsRegressor, df[['g','r','i']].values, y)\n",
    "my_kfold(KNeighborsRegressor, df[['r','i']].values, y)\n",
    "my_kfold(KNeighborsRegressor, df[['i']].values, y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 4 Inspection \n",
    "- A, Select the best combination of inputs found in 3/C and inspect the residuals of the fit, on a residual plot, is the a clear trend? \n",
    "- B, Inspect the residuals of the fit, on a residual plot, identify and color outliers, where residual are larger than 3 $\n",
    "\\sigma$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Answer: actually there seems to be a trend"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "mylr = LinReg()\n",
    "mylr.fit(df[['r','i']].values,y)\n",
    "yp = mylr.predict(df[['r','i']].values)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1a23309e10>]"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x504 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "figsize(7,5)\n",
    "res =  (y-yp)/(np.sqrt(np.mean((y-yp)**2)))\n",
    "plot(y,res,\"o\", label=\"normal fit\")\n",
    "idx = np.abs(res)>3\n",
    "plot(y[idx],res[idx],\"o\",label=\"outliers\")    \n",
    "legend()\n",
    "xlabel('redshift')\n",
    "ylabel('residual')\n",
    "axhline(0,c='k')\n",
    "show()\n",
    "\n",
    "figsize(7,7)\n",
    "res =  (y-yp)/(np.sqrt(np.mean((y-yp)**2)))\n",
    "plot(y,yp,\"o\", label=\"normal fit\")\n",
    "idx = np.abs(res)>3\n",
    "plot(y[idx],yp[idx],\"o\",label=\"outliers\")    \n",
    "legend()\n",
    "xlabel('redshift')\n",
    "ylabel('residual')\n",
    "plot([0.1,0.7],[0.1,0.7], c='k')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 4 Inspection \n",
    "- C, Identify high levarage points.\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "import statsmodels.api as sm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x864 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "figsize(12,12)\n",
    "results = smf.ols('redshift ~  r + i  ', data=df).fit()\n",
    "sm.graphics.influence_plot(results, criterion=\"cooks\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 5 Interactions, quadratic\n",
    "\n",
    "- A, Select the best combination of inputs found in 3/C and add interaction to the data and inspect its siginifcance using the whole dataset."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Answer: R+I interaction actually helps!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:               redshift   R-squared:                       0.814\n",
      "Model:                            OLS   Adj. R-squared:                  0.814\n",
      "Method:                 Least Squares   F-statistic:                     2180.\n",
      "Date:                Sat, 29 Sep 2018   Prob (F-statistic):               0.00\n",
      "Time:                        17:42:31   Log-Likelihood:                 1090.2\n",
      "No. Observations:                1000   AIC:                            -2174.\n",
      "Df Residuals:                     997   BIC:                            -2160.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "Intercept     -1.4761      0.040    -37.100      0.000      -1.554      -1.398\n",
      "r              0.3582      0.013     27.102      0.000       0.332       0.384\n",
      "i             -0.2711      0.015    -18.497      0.000      -0.300      -0.242\n",
      "==============================================================================\n",
      "Omnibus:                      328.785   Durbin-Watson:                   1.988\n",
      "Prob(Omnibus):                  0.000   Jarque-Bera (JB):             5035.708\n",
      "Skew:                           1.076   Prob(JB):                         0.00\n",
      "Kurtosis:                      13.781   Cond. No.                         414.\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    }
   ],
   "source": [
    "inter = smf.ols('redshift ~ r + i ', data=df).fit()\n",
    "print(inter.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:               redshift   R-squared:                       0.819\n",
      "Model:                            OLS   Adj. R-squared:                  0.818\n",
      "Method:                 Least Squares   F-statistic:                     1498.\n",
      "Date:                Sat, 29 Sep 2018   Prob (F-statistic):               0.00\n",
      "Time:                        17:42:31   Log-Likelihood:                 1103.0\n",
      "No. Observations:                1000   AIC:                            -2198.\n",
      "Df Residuals:                     996   BIC:                            -2178.\n",
      "Df Model:                           3                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "Intercept      1.0583      0.499      2.121      0.034       0.079       2.038\n",
      "r              0.2381      0.027      8.832      0.000       0.185       0.291\n",
      "i             -0.4243      0.033    -12.712      0.000      -0.490      -0.359\n",
      "r:i            0.0073      0.001      5.094      0.000       0.004       0.010\n",
      "==============================================================================\n",
      "Omnibus:                      305.686   Durbin-Watson:                   1.986\n",
      "Prob(Omnibus):                  0.000   Jarque-Bera (JB):             7193.317\n",
      "Skew:                           0.835   Prob(JB):                         0.00\n",
      "Kurtosis:                      16.033   Cond. No.                     6.73e+04\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "[2] The condition number is large, 6.73e+04. This might indicate that there are\n",
      "strong multicollinearity or other numerical problems.\n"
     ]
    }
   ],
   "source": [
    "inter = smf.ols('redshift ~ r + i + r*i ', data=df).fit()\n",
    "print(inter.summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 5 Interactions, quadratic\n",
    "\n",
    "- B, Validate the added interaction using cross validation on 5 folds using your linear regression class or the scikit-learn linear regression class. How does the MSE change after adding interactions?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Answer: Yay, it helps in CV too"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "mses = 10.5567 +/- 0.7091\n",
      "mses = 10.2045 +/- 0.6687\n"
     ]
    }
   ],
   "source": [
    "r, i = df[['r']].values, df[['i']].values\n",
    "xint = np.column_stack([r,i,r*i])\n",
    "my_kfold(LinReg, df[['r','i']].values, y)\n",
    "my_kfold(LinReg, xint, y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 5 Interactions, quadratic\n",
    "\n",
    "- C, Add quadratic form of the colors as predictive variable. Asses the significance of the quadratic terms. Which quadratic term is significant?\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Answer: r^2 quatratic term helps, i^2 is not significant"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:               redshift   R-squared:                       0.823\n",
      "Model:                            OLS   Adj. R-squared:                  0.822\n",
      "Method:                 Least Squares   F-statistic:                     923.4\n",
      "Date:                Sat, 29 Sep 2018   Prob (F-statistic):               0.00\n",
      "Time:                        17:42:31   Log-Likelihood:                 1114.9\n",
      "No. Observations:                1000   AIC:                            -2218.\n",
      "Df Residuals:                     994   BIC:                            -2188.\n",
      "Df Model:                           5                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==================================================================================\n",
      "                     coef    std err          t      P>|t|      [0.025      0.975]\n",
      "----------------------------------------------------------------------------------\n",
      "Intercept          0.9476      0.503      1.885      0.060      -0.039       1.934\n",
      "r                  1.2563      0.237      5.297      0.000       0.791       1.722\n",
      "i                 -1.4566      0.247     -5.895      0.000      -1.942      -0.972\n",
      "np.power(r, 2)     0.0472      0.033      1.421      0.156      -0.018       0.112\n",
      "np.power(i, 2)     0.1037      0.035      2.959      0.003       0.035       0.173\n",
      "r:i               -0.1426      0.067     -2.112      0.035      -0.275      -0.010\n",
      "==============================================================================\n",
      "Omnibus:                      306.570   Durbin-Watson:                   2.017\n",
      "Prob(Omnibus):                  0.000   Jarque-Bera (JB):             8610.507\n",
      "Skew:                           0.782   Prob(JB):                         0.00\n",
      "Kurtosis:                      17.290   Cond. No.                     1.19e+05\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "[2] The condition number is large, 1.19e+05. This might indicate that there are\n",
      "strong multicollinearity or other numerical problems.\n"
     ]
    }
   ],
   "source": [
    "inter = smf.ols('redshift ~ r + i + np.power(r, 2) + np.power(i, 2)+ r*i ', data=df).fit()\n",
    "print(inter.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:               redshift   R-squared:                       0.822\n",
      "Model:                            OLS   Adj. R-squared:                  0.822\n",
      "Method:                 Least Squares   F-statistic:                     1153.\n",
      "Date:                Sat, 29 Sep 2018   Prob (F-statistic):               0.00\n",
      "Time:                        17:42:31   Log-Likelihood:                 1113.9\n",
      "No. Observations:                1000   AIC:                            -2218.\n",
      "Df Residuals:                     995   BIC:                            -2193.\n",
      "Df Model:                           4                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==================================================================================\n",
      "                     coef    std err          t      P>|t|      [0.025      0.975]\n",
      "----------------------------------------------------------------------------------\n",
      "Intercept          1.0815      0.494      2.189      0.029       0.112       2.051\n",
      "r                  1.3187      0.233      5.656      0.000       0.861       1.776\n",
      "i                 -1.5368      0.241     -6.384      0.000      -2.009      -1.064\n",
      "np.power(i, 2)     0.0570      0.012      4.665      0.000       0.033       0.081\n",
      "r:i               -0.0482      0.012     -4.022      0.000      -0.072      -0.025\n",
      "==============================================================================\n",
      "Omnibus:                      319.688   Durbin-Watson:                   2.011\n",
      "Prob(Omnibus):                  0.000   Jarque-Bera (JB):             9584.535\n",
      "Skew:                           0.825   Prob(JB):                         0.00\n",
      "Kurtosis:                      18.077   Cond. No.                     9.35e+04\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "[2] The condition number is large, 9.35e+04. This might indicate that there are\n",
      "strong multicollinearity or other numerical problems.\n"
     ]
    }
   ],
   "source": [
    "inter = smf.ols('redshift ~ r + i + np.power(i, 2)+ r*i ', data=df).fit()\n",
    "print(inter.summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 5 Interactions, quadratic\n",
    "\n",
    "- D, Create the final model by adding the siginificant quadratic term. Validate this model Using cross validation on 5 folds using your linear regression class or the scikit-learn linear regression class. Inspect the final MSE, and compare it to the original, the one with the best colors, and the one with interactions. \n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "mses = 10.7127 +/- 0.6217\n",
      "mses = 10.5567 +/- 0.7091\n",
      "mses = 10.2045 +/- 0.6687\n",
      "mses = 9.9400 +/- 0.7365\n"
     ]
    }
   ],
   "source": [
    "r, i = df[['r']].values, df[['i']].values\n",
    "xfinal = np.column_stack([r,i,r*i,r*r])\n",
    "\n",
    "my_kfold(LinReg, x, y)\n",
    "my_kfold(LinReg, df[['r','i']].values, y)\n",
    "my_kfold(LinReg, xint, y)\n",
    "my_kfold(LinReg, xfinal, y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### The end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### BTW: Interactions or quadratic forms did not fix trend in residuals ..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "mylr = LinReg()\n",
    "mylr.fit(xfinal,y)\n",
    "yp = mylr.predict(xfinal)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1c248b2250>]"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x504 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "figsize(7,5)\n",
    "res =  (y-yp)/(np.sqrt(np.mean((y-yp)**2)))\n",
    "plot(y,res,\"o\", label=\"normal fit\")\n",
    "idx = np.abs(res)>3\n",
    "plot(y[idx],res[idx],\"o\",label=\"outliers\")    \n",
    "legend()\n",
    "xlabel('redshift')\n",
    "ylabel('residual')\n",
    "axhline(0,c='k')\n",
    "show()\n",
    "\n",
    "figsize(7,7)\n",
    "res =  (y-yp)/(np.sqrt(np.mean((y-yp)**2)))\n",
    "plot(y,yp,\"o\", label=\"normal fit\")\n",
    "idx = np.abs(res)>3\n",
    "plot(y[idx],yp[idx],\"o\",label=\"outliers\")    \n",
    "legend()\n",
    "xlabel('redshift')\n",
    "ylabel('residual')\n",
    "plot([0.1,0.7],[0.1,0.7], c='k')"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.15"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}