Auto-mpg.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Load and clean data\n",
    "* drop missing values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 388,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(392, 9)\n",
      "     mpg  cylinders  displacement  horsepower  weight  acceleration  \\\n",
      "0   18.0          8         307.0       130.0  3504.0          12.0   \n",
      "1   15.0          8         350.0       165.0  3693.0          11.5   \n",
      "2   18.0          8         318.0       150.0  3436.0          11.0   \n",
      "3   16.0          8         304.0       150.0  3433.0          12.0   \n",
      "4   17.0          8         302.0       140.0  3449.0          10.5   \n",
      "5   15.0          8         429.0       198.0  4341.0          10.0   \n",
      "6   14.0          8         454.0       220.0  4354.0           9.0   \n",
      "7   14.0          8         440.0       215.0  4312.0           8.5   \n",
      "8   14.0          8         455.0       225.0  4425.0          10.0   \n",
      "9   15.0          8         390.0       190.0  3850.0           8.5   \n",
      "10  15.0          8         383.0       170.0  3563.0          10.0   \n",
      "11  14.0          8         340.0       160.0  3609.0           8.0   \n",
      "12  15.0          8         400.0       150.0  3761.0           9.5   \n",
      "13  14.0          8         455.0       225.0  3086.0          10.0   \n",
      "14  24.0          4         113.0        95.0  2372.0          15.0   \n",
      "15  22.0          6         198.0        95.0  2833.0          15.5   \n",
      "16  18.0          6         199.0        97.0  2774.0          15.5   \n",
      "17  21.0          6         200.0        85.0  2587.0          16.0   \n",
      "18  27.0          4          97.0        88.0  2130.0          14.5   \n",
      "19  26.0          4          97.0        46.0  1835.0          20.5   \n",
      "\n",
      "    model_year  origin                      car_name  \n",
      "0           70       1     chevrolet chevelle malibu  \n",
      "1           70       1             buick skylark 320  \n",
      "2           70       1            plymouth satellite  \n",
      "3           70       1                 amc rebel sst  \n",
      "4           70       1                   ford torino  \n",
      "5           70       1              ford galaxie 500  \n",
      "6           70       1              chevrolet impala  \n",
      "7           70       1             plymouth fury iii  \n",
      "8           70       1              pontiac catalina  \n",
      "9           70       1            amc ambassador dpl  \n",
      "10          70       1           dodge challenger se  \n",
      "11          70       1            plymouth 'cuda 340  \n",
      "12          70       1         chevrolet monte carlo  \n",
      "13          70       1       buick estate wagon (sw)  \n",
      "14          70       3         toyota corona mark ii  \n",
      "15          70       1               plymouth duster  \n",
      "16          70       1                    amc hornet  \n",
      "17          70       1                 ford maverick  \n",
      "18          70       3                  datsun pl510  \n",
      "19          70       2  volkswagen 1131 deluxe sedan  \n"
     ]
    }
   ],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "\n",
    "from sklearn.linear_model import Ridge\n",
    "from sklearn.model_selection import cross_val_score\n",
    "from sklearn.model_selection import KFold\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "from sklearn.pipeline import Pipeline\n",
    "from sklearn.model_selection import GridSearchCV\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "%matplotlib inline\n",
    "\n",
    "\"\"\"The data concerns city-cycle fuel consumption in miles per gallon,\n",
    "    to be predicted in terms of 3 multivalued discrete and 5 continuous\n",
    "    attributes.\" (Quinlan, 1993)\"\"\"\n",
    "\n",
    "df = pd.read_csv(\"http://archive.ics.uci.edu/ml/machine-learning-databases/auto-mpg/auto-mpg.data-original\",\n",
    "                header=None, names = ['mpg', 'cylinders', 'displacement', 'horsepower', 'weight', 'acceleration',\n",
    "                                      'model', 'origin', 'car_name'], sep='\\s+', na_values='?')\n",
    "\n",
    "df = df.dropna().reset_index(drop=True) # drop 6 rows with missing horsepower\n",
    "df['horsepower'] = df['horsepower'].astype(float)\n",
    "\n",
    "# Exclude origin for brevity\n",
    "training_columns = ['cylinders','displacement','horsepower','weight',\n",
    "                    'acceleration','model_year']\n",
    "\n",
    "print(df.shape)\n",
    "print(df.head(20))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Visualize columns with histograms"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 342,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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62CDNzMysNQ2mRmQysA34sqT7JF2Rq//GFjLrzcDYSk/2LWFmZmY2mERkOHA4cHlEHAY8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\naX4BDgW5STSsTLYAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11f90d0d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "_ = df.hist(bins=10,figsize=(9,7),grid=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Evaluate a simple linear model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 351,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "X = df[training_columns]\n",
    "Y = df['mpg']\n",
    "\n",
    "seed = 3294805"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Grid search for best regularization"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 347,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Best: -13.362014 using {'alpha': 16.0}\n",
      "-13.370124 (8.201364) with: {'alpha': 0.25}\n",
      "-13.369974 (8.201273) with: {'alpha': 0.5}\n",
      "-13.369678 (8.201097) with: {'alpha': 1.0}\n",
      "-13.369094 (8.200768) with: {'alpha': 2.0}\n",
      "-13.367962 (8.200206) with: {'alpha': 4.0}\n",
      "-13.365831 (8.199430) with: {'alpha': 8.0}\n",
      "-13.362014 (8.199095) with: {'alpha': 16.0}\n",
      "Raw ridge\n",
      "-13.379404023883612\n"
     ]
    }
   ],
   "source": [
    "lr = Ridge()\n",
    "\n",
    "alpha_values = np.array([0.25,0.5,1,2,4,8,16])\n",
    "param_grid = dict(alpha=alpha_values)\n",
    "kfold = KFold(n_splits=10, random_state=seed)\n",
    "grid = GridSearchCV(estimator=lr, param_grid=param_grid, cv=kfold, scoring='neg_mean_squared_error')\n",
    "grid_result = grid.fit(X, Y)\n",
    "\n",
    "print(\"Best: %f using %s\" % (grid_result.best_score_, grid_result.best_params_))\n",
    "means = grid_result.cv_results_['mean_test_score']\n",
    "stds = grid_result.cv_results_['std_test_score']\n",
    "params = grid_result.cv_results_['params']\n",
    "for mean, stdev, param in zip(means, stds, params):\n",
    "    print(\"%f (%f) with: %r\" % (mean, stdev, param))\n",
    "\n",
    "lr = Ridge(**grid_result.best_params_)\n",
    "\n",
    "kfold = KFold(n_splits=10, random_state=seed)\n",
    "scores = cross_val_score(lr, X, Y, cv=kfold, scoring='neg_mean_squared_error')\n",
    "print('Raw ridge')\n",
    "print(scores.mean())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Scale inputs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 348,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Scaled ridge\n",
      "-13.775824354309814\n"
     ]
    }
   ],
   "source": [
    "scaled_lr = Pipeline([('Scaler', StandardScaler()),('LR', lr)])\n",
    "scores = cross_val_score(scaled_lr, X, Y, cv=kfold, scoring='neg_mean_squared_error')\n",
    "print('Scaled ridge')\n",
    "print(scores.mean())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Evaluation results\n",
    "\n",
    "The cross-validated mean squared error for linear regression is approximately **13.4**. This will be the baseline."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Linear model insights"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 396,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "weight: -4.137636\n",
      "model_year: 2.564799\n",
      "cylinders: -0.624572\n",
      "horsepower: -0.622318\n",
      "displacement: -0.356307\n",
      "acceleration: -0.103126\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x11ed58c90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def print_coefs(coefs, training_columns):\n",
    "    sorted_idx = np.argsort(-abs(coefs)) # negative for descending\n",
    "    for (name, coef) in zip(np.array(training_columns)[sorted_idx], coefs[sorted_idx]):\n",
    "        print(\"%s: %f\" % (name, coef))\n",
    "\n",
    "def plot_coefs(coefs, training_columns, title_suffix=''):\n",
    "    sorted_idx = np.argsort(abs(coefs))\n",
    "    pos = np.arange(len(coefs)) + .5\n",
    "    plt.subplot(1, 2, 2)\n",
    "    plt.barh(pos, coefs[sorted_idx], align='center')\n",
    "    plt.yticks(pos, np.array(training_columns)[sorted_idx])\n",
    "    plt.xlabel('Coef value')\n",
    "    plt.title('Coefficents' + title_suffix)\n",
    "    plt.xlim(-5.5, 5.5)\n",
    "    plt.show()\n",
    "\n",
    "# use scaled model\n",
    "scaled_lr.fit(X, Y)\n",
    "print_coefs(lr.coef_, training_columns)\n",
    "plot_coefs(lr.coef_, training_columns)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Insights\n",
    "\n",
    "We can see that weight has the most significant impact (heavier means worse mpg). model_year has a positive impact, and the other features, which represent the size and power of the engine, are slightly negative."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Simple decision tree"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 352,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Best: -11.974432 using {'max_depth': 10, 'min_samples_leaf': 10}\n",
      "CART\n",
      "-12.010052711251006\n",
      "Wrote output to ./auto_mpg.graphviz\n"
     ]
    }
   ],
   "source": [
    "from sklearn.tree import DecisionTreeRegressor\n",
    "from sklearn.tree import export_graphviz\n",
    "\n",
    "dt = DecisionTreeRegressor()\n",
    "\n",
    "# Grid search meta parameters\n",
    "param_grid = dict(min_samples_leaf=np.array([1,5,10,50,100,200]), max_depth=np.array([2,4,6,8,10]))\n",
    "kfold = KFold(n_splits=10, random_state=seed)\n",
    "grid = GridSearchCV(estimator=dt, param_grid=param_grid, cv=kfold, scoring='neg_mean_squared_error')\n",
    "grid_result = grid.fit(X, Y)\n",
    "\n",
    "# Evaluate best model\n",
    "print(\"Best: %f using %s\" % (grid_result.best_score_, grid_result.best_params_))\n",
    "dt = DecisionTreeRegressor(**grid_result.best_params_)\n",
    "scores = cross_val_score(dt, X, Y, cv=kfold, scoring='neg_mean_squared_error')\n",
    "print('CART')\n",
    "print(scores.mean())\n",
    "\n",
    "# Serialize tree structure for investigation\n",
    "dt.fit(X, Y)\n",
    "output_file = './auto_mpg.graphviz'\n",
    "export_graphviz(dt, out_file=output_file, feature_names = X.columns)\n",
    "print(\"Wrote output to \" + output_file)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Evaluation results\n",
    "\n",
    "The cross-validated mean squared error is for our CART tree is approximately **12.0**. This is better than the linear model."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Insights\n",
    "\n",
    "The structure of the decision tree suggests that displacement and horsepower are the most important features. This does not agree with what we found from the linear model. \n",
    "\n",
    "We can see inefficiencies in the tree model in the fact that the two nodes below the root each split on horsepower, and that the nodes in the layer below that all split on model year. Furthermore, all four second-layer nodes split on almost the same value of model year. This suggests that a model that can use those attributes from the entire dataset (rather than the subpopulation that the tree uses at each node) may have better predictive performance.\n",
    "\n",
    "However, the fact that the tree model's predictive performance is better than the linear model suggests that there is a significant nonlinear effect."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Gradient Boosting Trees\n",
    "\n",
    "Let's also try out a gradient boosting tree model, which often has better predictive performance than any other model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 404,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "GBT\n",
      "-8.736805616265736\n"
     ]
    },
    {
     "data": {
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zCvtqlaSxkm7Jz/0ulPRZSV/M206VNLCw/x8WeiGjcvnAvP3cvP5OufwsSb+U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\nAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11dd72510>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.ensemble import GradientBoostingRegressor\n",
    "\n",
    "scores = cross_val_score(GradientBoostingRegressor(), X, Y, cv=kfold, scoring='neg_mean_squared_error')\n",
    "print('GBT')\n",
    "print(scores.mean())\n",
    "\n",
    "clf = GradientBoostingRegressor()\n",
    "clf.fit(X, Y)\n",
    "\n",
    "feature_importance = clf.feature_importances_\n",
    "# make importances relative to max importance\n",
    "feature_importance = 100.0 * (feature_importance / feature_importance.max())\n",
    "\n",
    "sorted_idx = np.argsort(feature_importance)\n",
    "pos = np.arange(sorted_idx.shape[0]) + .5\n",
    "plt.subplot(1, 2, 2)\n",
    "plt.barh(pos, feature_importance[sorted_idx], align='center')\n",
    "plt.yticks(pos, X.columns[sorted_idx])\n",
    "plt.xlabel('Relative Importance')\n",
    "plt.title('GBT Variable Importance')\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Evaluation results and insights\n",
    "\n",
    "The cross-validated mean squared error from GBT is approximately **8.8**. This is much better than linear regression or our simple decision tree. \n",
    "\n",
    "GBT's variable importance attribute tells us that weight is the most important feature, followed by acceleration, horsepower, displacement, and model_year, which are all similar. Unfortunately, GBT does not tell us anything about the numerical magnitude or sign of their impact, nor relationship of these features."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Linear model tree"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 392,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "8.943056984982718\n"
     ]
    }
   ],
   "source": [
    "import sys\n",
    "sys.path.append('/Users/logan/ws/price-modeling/python/')\n",
    "\n",
    "from lmt import LinearModelTree\n",
    "from sklearn.metrics import mean_squared_error\n",
    "\n",
    "X = df[training_columns]\n",
    "\n",
    "shared_scaler = StandardScaler()\n",
    "shared_scaler.fit(X)\n",
    "\n",
    "def fit_linear_model(x, y):\n",
    "    lr = Ridge()\n",
    "    lr.fit(shared_scaler.transform(x), y)\n",
    "    return SharedScalerModel(shared_scaler, lr)\n",
    "\n",
    "class SharedScalerModel:\n",
    "    \n",
    "    def __init__(self, scaler, lm):\n",
    "        self.scaler = scaler\n",
    "        self.lm = lm\n",
    "        self.coef_ = lm.coef_\n",
    "        self.intercept_ = lm.intercept_\n",
    "        \n",
    "    def predict(self, X):\n",
    "        return self.lm.predict(self.scaler.transform(X))\n",
    "\n",
    "\n",
    "MIN_NODE_SIZE = 100\n",
    "MIN_SPLIT_IMPROVEMENT = 10\n",
    "lmt = LinearModelTree(MIN_NODE_SIZE, fit_linear_model, min_split_improvement=MIN_SPLIT_IMPROVEMENT)\n",
    "\n",
    "kfold = KFold(n_splits=10, random_state=seed)\n",
    "scores = []\n",
    "for train_index, test_index in kfold.split(X):\n",
    "    X_train, X_test = X.iloc[train_index], X.iloc[test_index]\n",
    "    y_train, y_test = Y[train_index], Y[test_index]\n",
    "    \n",
    "    lmt.build_tree(X_train.values, X_train, y_train.values)\n",
    "    y_pred = lmt.predict(X_test.values, X_test)\n",
    "    mse = mean_squared_error(y_test, y_pred)\n",
    "    scores.append(mse)\n",
    "\n",
    "print(np.array(scores).mean())\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Evaluation results\n",
    "\n",
    "[Optimal meta parameters found via grid search, not shown]\n",
    "\n",
    "The LMT gives a cross-validated mean squared error of approximately **8.9**, which is nearly as good as GBT, and much better than our linear regression and simple decision tree models."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Insights"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 369,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "T,rc:392,f:2,v:78.0\n",
      "TL,rc:104,f:_,v:_ \n",
      "TR,rc:288,f:2,v:97.0\n",
      "TRL,rc:110,f:_,v:_ \n",
      "TRR,rc:178,f:_,v:_ \n"
     ]
    }
   ],
   "source": [
    "# Build a tree on the full dataset, and serialize it to see the feature splits\n",
    "lmt = LinearModelTree(MIN_NODE_SIZE, fit_linear_model, MIN_SPLIT_IMPROVEMENT)\n",
    "lmt.build_tree(X.values, X, Y.values)\n",
    "print(lmt.serialize())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 357,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "horsepower\n"
     ]
    }
   ],
   "source": [
    "print(X.columns[2])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Tree structure\n",
    "\n",
    "The linear model tree produces just 2 splits, for a total of 3 leaf nodes. It splits first at horsepower = 78, and for horsepower >= 78 it splits at horsepower = 97. We will call the three subpopulations low power, medium power, and high power."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 397,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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DwNbARzu1lWY9THf+vNhpwCWS5gJvAEfl5acDV+VLiPuAvwFExAOSTgEm5Gv7JcDXgafa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\nbZE0Gtgf2DvyBWc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      "text/plain": [
       "<matplotlib.figure.Figure at 0x11df8aa10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x11e316550>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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DQyPijXxe6Hpgww5qSrfvbweGpRARY6rJJ+kC4MYKSc8B6xbm18nLat4WSWOB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\nYGYl/x8PzKX1AAAABElEQVSEWJ6E76BZzgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11e213410>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "displacement: -5.186292\n",
      "model_year: 4.287827\n",
      "weight: -4.287711\n",
      "horsepower: -1.605432\n",
      "cylinders: 0.685287\n",
      "acceleration: 0.608814\n",
      "\n",
      "weight: -5.522914\n",
      "model_year: 2.410542\n",
      "horsepower: -1.416881\n",
      "acceleration: -0.805342\n",
      "cylinders: -0.311572\n",
      "displacement: -0.156405\n",
      "\n",
      "weight: -2.154847\n",
      "model_year: 1.428982\n",
      "horsepower: -1.089580\n",
      "displacement: 1.041145\n",
      "cylinders: -0.867039\n",
      "acceleration: -0.200428\n"
     ]
    }
   ],
   "source": [
    "root_lm = lmt.root.lm\n",
    "node_1_coef = root_lm.coef_ + lmt.root.left.lm.coef_\n",
    "plot_coefs(node_1_coef, training_columns, ' (horsepower < 78)')\n",
    "\n",
    "right_coef = lmt.root.right.lm.coef_\n",
    "node_2_coef = root_lm.coef_ + right_coef + lmt.root.right.left.lm.coef_\n",
    "plot_coefs(node_2_coef, training_columns, ' (horsepower >= 78 & horsepower < 97)')\n",
    "\n",
    "\n",
    "node_3_coef = root_lm.coef_ + right_coef + lmt.root.right.right.lm.coef_\n",
    "plot_coefs(node_3_coef, training_columns, ' (horsepower >= 97)')\n",
    "\n",
    "\n",
    "print_coefs(node_1_coef, training_columns)\n",
    "print('')\n",
    "print_coefs(node_2_coef, training_columns)\n",
    "print('')\n",
    "print_coefs(node_3_coef, training_columns)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 430,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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582g4QmWHzGazxo4dqyFDhihfvny2HkeS1KdPH3Xr1k3S7XPx582b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\nZolMAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11f371850>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "rows = 1\n",
    "cols = 3\n",
    "coefs = [\n",
    "    node_1_coef,\n",
    "    node_2_coef,\n",
    "    node_3_coef,\n",
    "]\n",
    "titles = ['Low power', 'Medium power', 'High power']\n",
    "f, axs = plt.subplots(rows, cols, sharex='col', figsize=(12, 4))\n",
    "for col in range(cols):\n",
    "    pos = np.arange(len(coefs[col])) + .5\n",
    "    axs[col].barh(pos, coefs[col], align='center')\n",
    "    axs[col].set_yticks(pos)\n",
    "    axs[col].set_yticklabels(np.array(training_columns))\n",
    "    axs[col].set_xlabel('Coef value')\n",
    "    axs[col].set_title(titles[col])\n",
    "    axs[col].set_xlim(-5.5, 5.5)\n",
    "\n",
    "f.tight_layout()\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 434,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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4IhERERERkQ5JSsq6d++OM2fOYO3atahRowY6dOgAb29veHh4wNTUVN8xEhER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\nERERERERKej/AfyIvcPm5kRdAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x12061dc10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "\n",
    "sns.set_style(\"white\")\n",
    "\n",
    "def gen(n=40):\n",
    "    return np.random.normal(size=n)\n",
    "\n",
    "rows, cols = 3, 5\n",
    "\n",
    "fsize = 15\n",
    "\n",
    "rownames = ['low power', 'medium power', 'high power']\n",
    "subpop_data = [\n",
    "    df.query('horsepower < 78'),\n",
    "    df.query('horsepower >= 78 & horsepower < 97'),\n",
    "    df.query('horsepower >= 97'),\n",
    "]\n",
    "\n",
    "cmap = sns.color_palette(\"Set2\", cols)\n",
    "\n",
    "f, axs = plt.subplots(rows, cols, sharex='col', figsize=(15, 6))\n",
    "\n",
    "for i in range(rows):\n",
    "    for j in range(cols):\n",
    "        _ = axs[i,j].hist(subpop_data[i][training_columns[j]], histtype='step', color=cmap[j])\n",
    "        axs[i,j].set_xticks([])\n",
    "        axs[i,j].set_yticks([])\n",
    "        left, right = _[1][0], _[1][-1]\n",
    "        \n",
    "        # black dots\n",
    "        axs[i,j].scatter(left, 0, c='black', s=15)\n",
    "        axs[i,j].scatter(right, 0, c='black', s=15)\n",
    "        \n",
    "        # min,max annotations\n",
    "        axs[i,j].annotate(str(int(left)), \n",
    "                          xy=(left, 0), \n",
    "                          xytext=(-5, -20),\n",
    "                          textcoords='offset points')\n",
    "        \n",
    "        axs[i,j].annotate(str(int(right)), \n",
    "                          xy=(right, 0), \n",
    "                          xytext=(-5, -20),\n",
    "                          textcoords='offset points')\n",
    "        \n",
    "        if i == 0:\n",
    "            axs[i,j].set_xlabel(training_columns[j], labelpad=15, size=fsize)\n",
    "            axs[i,j].xaxis.set_label_position('top')\n",
    "            \n",
    "        if j == 0:\n",
    "            axs[i,j].set_ylabel(rownames[i], size=fsize)\n",
    "\n",
    "f.subplots_adjust(hspace=1.5)\n",
    "sns.despine(left=True, bottom=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Inspecting the weights from the linear model tree gives us a very different understanding of what affects fuel efficiency than we got from the other models. While there are some commonalities across the different subpopulations that our LMT has identified, we also see some significant differences.\n",
    "\n",
    "For all vehicles, weight has a large negative impact, which makes sense because fuel economy should get worse with the more mass the vehicle has to move. Model year has a large positive impact for all vehicles; presumably engine technology improved significantly in this period. These are similar to what we see in the single linear model. However, the magnitude of those impacts changes across the subpopulations that our LMT has identified, and engine size and power have different magnitudes of effect in different subpopulations.\n",
    "\n",
    "For low-power vehicles, model year has a huge positive impact, and we see that in this population fuel economy is very sensitive to engine displacement.\n",
    "\n",
    "In the medium-power category, weight again has a huge negative impact but fuel economy only increases moderately with model year.\n",
    "\n",
    "For vehicles with high-power, weight has as much less significant impact, and the same can be said for model year. The engine size and power features are more relevant in this population by comparison to weight and model year. In this population the engine sizes are far more variable than in the other populations, so engine size ends up having a larger impact on the prediction than even what the coefficients tell us."
   ]
  }
 ],
 "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": "2.7.13"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}