{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "Working with Notebooks:\n", "* Press `Shift + Enter` to evaluate a cell.\n", "* Only the return value of the last line of each cell is shown in the `Out` cells. If you want to see the result of an intermediate step, insert a new cell (with the `+` symbol in the toolbar) and paste that intermediate step to that cell.\n", "\n", "New R commands:\n", "* `regsubsets`: used for subset selection, `method` can be e.g. `\"exhaustive\"` (best subset), `\"forward\"`, `\"backward\"`\n", "\n", "Useful R commands to remember:\n", "* `which.min` and `which.max` return the index that contains the smallest or largest element in a list.\n", "* `sample(range, number_of_samples, replace = True/False)`\n", "* `apply(data, i, function)` where `i = 1` if the function should be applied to all rows and `i=2` if the function should be applied to all columns." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# The Contrived High-Dimensional Example " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Data Set\n", "First we create an artifical data set with n = 50 points of p = 1000 random predictors and one response that does not depend on the predictors." ] }, { "cell_type": "code", "execution_count": 87, "metadata": { "ExecuteTime": { "end_time": "2019-10-14T15:18:03.937719Z", "start_time": "2019-10-14T15:18:03.836Z" } }, "outputs": [], "source": [ "set.seed(932)\n", "data = data.frame(matrix(rnorm(50*1000), 50, 1000))\n", "data$y = rnorm(50)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Forward Selection with Adjusted Training Loss\n", "Now we load the `leaps` package and use the `regsubsets` function to do forward selection up to at most `nvmax = 30` predictors.\n", "We use the formula `y ~ .` to indicate that the response `y` should be regressed on all other columns of `data`." ] }, { "cell_type": "code", "execution_count": 88, "metadata": { "ExecuteTime": { "end_time": "2019-10-14T15:27:04.754554Z", "start_time": "2019-10-14T15:27:04.295Z" } }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "Warning message in leaps.setup(x, y, wt = wt, nbest = nbest, nvmax = nvmax, force.in = force.in, :\n", "“951 linear dependencies found”\n" ] } ], "source": [ "library(leaps)\n", "regfit.fwd = regsubsets(y ~ .,data = data, method = \"forward\", nvmax = 30)\n", "regfit.fwd.summary = summary(regfit.fwd)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let us plot the adjusted R^2 and mark in red the optimal (maximal) R^2." ] }, { "cell_type": "code", "execution_count": 89, "metadata": { "ExecuteTime": { "end_time": "2019-10-14T16:21:36.439367Z", "start_time": "2019-10-14T16:21:36.356Z" } }, "outputs": [ { "data": { "image/png": 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6+/9u7d28LCQnYoAFAsih2A7Je+fcnc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"text/plain": [ "plot without title" ] }, "metadata": { "image/png": { "height": 420, "width": 420 }, "text/plain": { "height": 420, "width": 420 } }, "output_type": "display_data" } ], "source": [ "plot(regfit.fwd.summary$adjr2, type = \"l\", xlab = \"Number of Variables\", ylab = \"adjusted R^2\")\n", "adjr2.max = which.max(regfit.fwd.summary$adjr2)\n", "points(adjr2.max, regfit.fwd.summary$adjr2[adjr2.max], col = \"red\", cex = 2, pch = 20)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Plot now the BIC-curve and mark the optimal BIC point in red. Write your answer in the following cell.\n", "\n", "Hints: \n", "1. Use `names(regfit.fwd.summary)` to see how BIC is called in the `regfit.fwd.summary`.\n", "2. What does optimal mean for the BIC?" ] }, { "cell_type": "code", "execution_count": 90, "metadata": {}, "outputs": [ { "data": { "image/png": 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HR0QkJCtm3btnr1amdn5wsXLoheBADA\neyPsgL+0bt362LFj5ubmdnZ2y5cvFz0HAID3Q9gB//DJJ59s2rRp8uTJ/fv3V6vVT58+Fb0I\nAIB3RdgB/6ZSqQIDAxMTE/fv3//ZZ58dOHBA9CIAAN4JYQcUzMHB4fDhw87Ozq6uriEhIXl5\neaIXAQDwFoQd8FpGRkbLli1buHDhjz/+2LZt29u3b4teBADAmxB2wFuo1erjx49nZGTY2NjE\nxMSIngMAwGsRdsDbVa9efe/evYMHD+7QoQMPugMAaCzCDngnurq6ISEhW7dujY6OdnFxuXjx\nouhFAAD8G2EHvAcPD49jx46VL1/ezs5uxYoVoucAAPAPhB3wfszNzbds2TJp0qR+/fqp1epn\nz56JXgQAwJ8IO+C9vXrQ3Z49e+Lj4xs3bpyamip6EQAAkkTYAR+sadOmR48ebdCgQdOmTRct\nWiR6DgAAhB3wEYyNjdesWTNr1qwhQ4bwtiwAQDjCDvhY/v7++/bt27dvn4ODA2/LAgAEIuyA\nQmBnZ3f48GFra2tHR8eFCxeKngMAKKEIO6BwlC1bdtWqVdOmTRs6dKharc7MzBS9CABQ4hB2\nQKF5dbdsYmJiQkKCg4PDyZMnRS8CAJQshB1QyBwcHI4cOfLqblkeYgwAKE6EHVD4jI2NV69e\nPWXKlL59+/K2LACg2BB2QJF49bZsQkJCfHy8i4vLhQsXRC8CACgfYQcUoSZNmiQlJVlYWNjZ\n2a1cuVL0HACAwhF2QNEyMzPbvHnz5MmT1Wq1Wq1+/vy56EUAAMUi7IAi9+pt2R07duzcudPF\nxeXixYuiFwEAlImwA4qJq6vr0aNHP/nkEzs7u9WrV4ueAwBQIMIOKD6ffPLJ1q1bx44d+/nn\nnw8cODA7O1v0IgCAohB2QLFSqVRBQUE7duzYuHGjs7PzpUuXRC8CACgHYQcI0LJly6NHj5qa\nmtrZ2a1Zs0b0HACAQhB2gBjm5uZbt24dPnx4jx49/P3909PTRS8CAMgeYQcIo62tPXny5Li4\nuD179jRs2HDjxo2iFwEA5I2wAwRr3rz5sWPHBgwY4OPj4+fnd+/ePdGLAAByRdgB4hkYGISE\nhCQlJV28eLFu3brz588XvQgAIEuEHaApbGxsDh48GBQUFBAQ0L59+2vXroleBACQGcIO0CA6\nOjpBQUEpKSkPHjywtrYOCwvLy8sTPQoAIBuEHaBxGjZsuG/fvhkzZowfP75ly5bnzp0TvQgA\nIA+EHaCJtLS0/P39jx8/rq+v36hRo9DQ0NzcXNGjAACajrADNFf16tVjY2PnzZs3Y8YMFxeX\nU6dOiV4EANBohB2g0VQqlVqtPnHiRMWKFRs1ahQcHMwJswCA1yHsABmoWLHi77//HhkZuWjR\nIgcHh6SkJNGLAACaiLADZMPX1/fs2bNOTk7NmjULDAx89uyZ6EUAAM1C2AFyYmpqGh4e/scf\nf6xbt87GxiYuLk70IgCABiHsAPnx8vJKTU1t3bq1u7v7wIEDMzIyRC8CAGgEwg6QJWNj4/Dw\n8G3btm3fvt3a2vrkyZOiFwEAxCPsABlzd3dPTU21t7dv06bNlStXRM8BAAhG2AHyVrp06aio\nKCsrK3d39zt37oieAwAQibADZE9PT2/16tXGxsbe3t5Pnz4VPQcAIAxhByiBkZFRTEzMkydP\nOnXq9OLFC9FzAABiEHaAQpiZmW3duvX06dN9+/bNy8sTPQcAIABhByjHq7Nlt23bNnz4cNFb\nAAAC6IgeAKAwWVlZbd682d3d3dLScuzYsaLnAACKlVzDLu9lTr62rrZK9A5A8zg5Oa1cudLH\nx8fc3HzAgAGi5wAAio983op9cTMxYspgn5Y2NSoY6Wlr6+rpaOuUMrWs4+DeY/j3yxOv8XFx\n4P/z9vb+73//O3jw4DVr1ojeAgAoPvK4YpdzLrJ/l4HLTr068lylY2BkZlbWQMrJevbwYsrO\n8yk7V/06eUL7b5cuG+tiKngqoCF69+597dq1Xr16mZiYuLu7i54DACgOcrhi9zJpnHffZWeN\nXAaFLtuadCU9O+d5+r2b167dvH0v/XnWk+vHdyz9rkvVW5vHtevw0znRYwHNMXbs2KFDh/r4\n+Bw5ckT0FgBAcZDBFbucmDnzzqma/bB399e1tf/nu7pGltat1datOzcfZOsR/v2snSN+ay2H\nWgWKxY8//vjw4cO2bdsmJCTUrl1b9BwAQNGSQQNdP306Q6rfoVMBVfc3Zd39u1eXHhw7dr24\ndgEyoFKpFixYYG9v365du9u3b4ueAwAoWjIIOyMjI0m6ff36yze/7OX9++mSpK+vXzyrALnQ\n1dVds2ZNhQoV2rRp8/jxY9FzAABFSAZhZ+bmbqN9d1FgwIa01975mnN964jRyx5KDVu3qlCc\n2wBZMDQ03LBhQ05OTpcuXbKyskTPAQAUFRl8xk6qGzB33No2k37rVHetrWcHdyebutUqmRkZ\n6qpePH3y5OH1M0cO7t68+cCNF3rWo+YG1he9FtBI5cuXj42NdXZ27tGjx9q1a7W13/jRBgCA\nPMkh7CTDZhN376szMXjSvC2bFh3ZVMArDD51GTxh9vQBtkbFPg6Qi08//XTLli2urq5Dhw6d\nN2+e6DkAgMIni7CTJKm0da8Zm3tOvH3iQPy+5FNX7z589PhZjpZBmXIW1epYO7i2bFrTmAsQ\nwNs0bNhwy5YtrVu3rlix4oQJE0TPAQAUMrmEnSRJkqQqZWHt5mvtJnGkGPChHB0dV61a1blz\nZ1NT04CAANFzAACFSQY3T/yJI8WAQtK+ffslS5aMGjUqOjpa9BYAQGGSxxU7jhQDClevXr1u\n3rzZu3dvExMTT09P0XMAAIVDDlfsOFIMKAKjR48OCAjo1q1bSkqK6C0AgMIhgyt2HCkGFJEZ\nM2Y8ePCgXbt28fHxdevWFT0HAPCxZNBAHCkGFBGVShUeHt64cWMvL69Lly6JngMA+FgyCDuO\nFAOKjq6u7urVq2vXrm1tbf3TTz/l5uaKXgQA+HAyCDuOFAOKlKGh4datW3/77bfvv//ewcHh\n8OHDohcBAD6QDD5jV6RHimVlZS1YsCAzM/MNrzl48OBH7Qc0nkqlUqvVnp6ew4cPd3R0HDVq\n1MSJE7n+DQCyo8rPzxe94V08S42cGDxp3pZzGQV+2+BTl34TZk8fYFv2PX/vjRs3fHx8Xr58\n0/u89+7du3r1akZGRpkyZd7z1wPys3HjxsGDB5cqVWrBggUtW7YUPQcANE52dra+vn5iYmKz\nZs1Eb/k3uYSdJEmSlP9cyJFi4eHhgwYNIuxQcjx+/DgoKGjhwoUDBgyYOXOmkRGHMAPAXzQ5\n7OTwVuz/97cjxQAUHRMTk/Dw8F69en311Vf16tWbM2dO586dRY8CALydDG6eACCEq6vr0aNH\ne/fu3a1bNz8/v3v37oleBAB4C8IOwGuVKlVq+vTpSUlJFy9erFev3vz580UvAgC8CWEH4C1s\nbW0PHDjwzTffBAQEtG/f/urVq6IXAQAKJoPP2F2Y26Xz3PPv+OLaQ9avG1KrSPcAJZCurm5Q\nUJCPj89XX33VoEGDb7/9dvTo0Vpa/M0QADSLDMKudKXqZi927b3w5J1u372bVdR7gBKrVq1a\nu3btWrBgwddff71x48YFCxbUr/+ej44EABQlGfyFu2Lnn3afu5I43tFAkqT6Y1Iy3iRpbAPR\newElU6lU/v7+Z86cMTMzs7OzCwkJyc7OFj0KAPAnGYSdJEmSysTp2/E+RpKkpWdY5k1K6cnk\n3wiQs0qVKq1fvz4iImLOnDmNGzdOSkoSvQgAIEmyCTtJkvScnOxFbwDwN76+vidPnmzQoEGz\nZs2CgoKeP38uehEAlHTyCTupfJfQtatn+VmK3gHg/zM3N4+Kivr9999XrFhhZ2fHpTsAEEtG\nYSdVatK1m0cDzjYCNI23t/eJEydcXV2bNWsWHBzMp+4AQBQ5hR0AjWVsbBweHv7HH39EREQ4\nODgcO3ZM9CIAKIlkHHb5p9ZOmTJl/l6OOQI0hZeX19GjR2vVqtW0adPQ0NDc3FzRiwCgZJFx\n2OUej/r2229n77ojegiAv5ibm//+++8RERGhoaHNmzc/f/5dny4OAPh4Mg47ABrL19f36NGj\npUqVatSoUVhYWH7+Oz1fHADwkQg7AEWiSpUqO3bsmDVr1rhx49q1a3fjxg3RiwBA+Qg7AEXl\n1TEVx48ff/bsmZWV1bJly0QvAgCFk3HYadsP+OWXX8Z5VRI9BMCb1KhRIy4uLjg4eMCAAX5+\nfg8ePBC9CAAUS8Zhp6rddtiwYZ83KSd6CIC30NHRCQoKSk5OPn/+fMOGDTds2CB6EQAok4zD\nDoC8WFtbHzhwoG/fvl27dlWr1RkZGaIXAYDSEHYAio++vv706dPj4+MPHDjw2Wef7d69W/Qi\nAFAUwg5AcXNycjp69GjHjh1bt249cODAzMxM0YsAQCEIOwACGBoahoWFbd26dcuWLY0bN05J\nSRG9CACUgLADIIynp2dqaqqLi0vTpk2Dg4NzcnJELwIAeSPsAIhkYmISHh4eGRm5cOFCFxeX\nM2fOiF4EADJG2AEQz8/P7+TJkxUrVrS1tQ0NDc3NzRW9CABkibADoBEqVKiwfv36iIiI0NBQ\nV1fXCxcuiF4EAPJD2AHQIL6+vkeOHDEwMLCxsQkLC8vPzxe9CADkhLADoFmqVq26Y8eOWbNm\njRs3rm3bttevXxe9CABkg7ADoHFUKpW/v//x48efP39uZWU1f/580YsAQB4IOwAaqkaNGnFx\ncWPGjAkICPD19b1//77oRQCg6Qg7AJpLW1s7KCgoOTn50qVLDRs2XLdunehFAKDRCDsAms7K\nyurAgQMjR47s3r27n5/fw4cPRS8CAA1F2AGQAV1d3aCgoISEhNTUVCsrq82bN4teBACaiLAD\nIBtNmjQ5cuSIWq3u1KnTwIEDnz59KnoRAGgWwg6AnBgYGEyfPn3Pnj27du367LPP9u7dK3oR\nAGgQwg6A/Dg7O6ekpHh4eLi5uQUGBr548UL0IgDQCIQdAFkqW7ZseHj4li1b1q5da29vn5KS\nInoRAIhH2AGQsTZt2pw4ccLZ2blp06bBwcE5OTmiFwGASIQdAHkzMTEJDw9fvnz5woULXV1d\nL126JHoRAAhD2AFQgu7dux8/frxMmTK2traRkZGi5wCAGIQdAIWoVKlSbGzspEmTvvzySz8/\nv8ePH4teBADFjbADoBwqlSowMHDfvn3Hjh1r1KhRYmKi6EUAUKwIOwBKY29vf/To0U6dOrVs\n2TIkJCQ3N1f0IgAoJoQdAAUqVapUWFjYypUrf/nlF3d39+vXr4teBADFgbADoFg+Pj5HjhzJ\ny8uzsrJauXKl6DkAUOQIOwBKVqVKlV27do0ZM0atVqvV6mfPnoleBABFiLADoHDa2tpBQUHx\n8fH79u1zcHA4cuSI6EUAUFQIOwAlgqOj4+HDh+3t7Z2cnEJDQ/Py8kQvAoDCR9gBKCnKli27\nfPny+fPnT5kypU2bNrdu3RK9CAAKGWEHoGRRq9XHjx9/9uyZjY3N5s2bRc8BgMJE2AEocapX\nr753794hQ4Z06tQpMDDwxYsXohcBQOEg7ACURDo6OiEhIbGxsWvXrrW3t09NTRW9CAAKAWEH\noORq1arV0aNHa9as6ejoGBYWJnoOAHwswg5AiWZmZrZ+/foffvghODjYx8fn4cOHohcBwIcj\n7ACUdCqVaujQoUlJSWfPnnVzc3v06JHoRQDwgQg7AJAkSbKyskpMTNTW1m7Xrt3Tp09FzwGA\nD0HYAcCfjI2NY2JiHj9+3LlzZ26VBSBHhB0A/MXc3Hz79u3nz5/v0aPHy5cvRc8BgPdD2AHA\nP1SuXHn79u379u3r379/fn6+6DkA8B4IOwD4tzp16mzatGndunUjRowQvQUA3oOO6AEAoIka\nN278xx9/eHl5VahQYezYsaLnAMA7IewAoGBubm6rVq3y8fExNDTk0h0AWeCtWAB4rY4dOy5e\nvHj06NFRUVGitwDA23HFDgDe5IsvvkhPT+/Tp0/ZsmXbt28veg4AvAlhBwBvMXTo0Lt37/r6\n+sbExLi6uoqeAwCvRdgBwNtNnDjx6dOn3t7eu3btsre3Fz0HAApG2AHAO5k5c1Q2RMUAACAA\nSURBVObjx4/btWu3Z8+e+vXri54DAAXg5gkAeCcqlWr+/Pmurq6enp5XrlwRPQcACkDYAcC7\n0tbWXrFiRYMGDTw8PO7cuSN6DgD8G2EHAO9BT09vzZo1xsbGnp6ejx49Ej0HAP6BsAOA92Nk\nZLR169aXL1+2b9/+2bNnoucAwF8IOwB4b2ZmZrGxsbdv3+7SpUt2drboOQDwJ8IOAD6EpaXl\n9u3bU1NT+/Xrl5eXJ3oOAEgSYQcAH6xmzZqxsbExMTHDhg0TvQUAJInn2AHAx7C2tt68ebOH\nh0f58uUnT54seg6Ako6wA4CP0rRp03Xr1nXo0KFs2bKjR48WPQdAiUbYAcDHcnd3j4qK8vPz\nMzU1HTBggOg5AEouPmMHAIWgS5cuc+bMGTx48LJly0RvAVByccUOAAqHv79/VlZW//79169f\n/+uvv1asWFH0IgAlDlfsAKDQBAQEpKSkXL9+vX79+vPnz8/Pzxe9CEDJQtgBQGGytrbev3//\njBkzRo0a1aJFi3PnzoleBKAEIewAoJBpaWn5+/sfP35cX1+/UaNGoaGhubm5okcBKBEIOwAo\nEtWrV4+NjZ03b94PP/zg4OCQkpIiehEA5SPsAKCoqFQqtVp94sSJWrVqNW3aNDg4OCsrS/Qo\nAEpG2AFA0bKwsFi9evXvv/8eGRlpbW0dFxcnehEAxSLsAKA4eHt7p6amtmrVyt3dfeDAgRkZ\nGaIXAVAgwg4AiomJiUl4eHhcXNzu3bvr1au3fv160YsAKA1hBwDFytXV9ejRo7179+7WrZuf\nn9+9e/dELwKgHIQdABS3UqVKTZ8+PTk5+eLFi3Xr1p0/f77oRQAUgrADADEaNWp08ODBoKCg\ngIAALy+vq1evil4EQPYIOwAQRkdHJygo6MSJE8+fP69fv35oaGheXp7oUQBkjLADAMFq1aq1\nc+fO0NDQqVOntmjR4uzZs6IXAZArwg4AxNPS0ho2bNiJEyfKlCnj6OjIs+4AfBjCDgA0RZUq\nVbZs2TJixIi2bdtGRUWJngNAfnREDwAA/EWlUoWEhJiamvbu3fvq1atBQUGiFwGQE8IOADRO\nYGDgp59++sUXX9y8eXPWrFlaWry7AuCdEHYAoIl8fHzKlSvXpUuXGzduLF++3MDAQPQiADLA\n3wIBQEO5ubklJCQcPHjQy8srPT1d9BwAMkDYAYDmsrKySkhIuHXrlouLy/Xr10XPAaDpCDsA\n0GhVq1bdt2+fqampi4vLmTNnRM8BoNEIOwDQdKamptu3b2/SpEmzZs0SEhJEzwGguQg7AJAB\nfX39qKioHj16uLu7r1mzRvQcABqKu2IBQB60tbXnzp1btWrVzz///P79+4MGDRK9CIDGIewA\nQE6CgoIsLCy++uqrtLS0adOmqVQq0YsAaBDCDgBkpk+fPpUqVfLx8bl9+/aCBQt0dXVFLwKg\nKfiMHQDIj4eHx86dO7du3dq+ffuMjAzRcwBoCsIOAGSpcePG+/fvT0tLa9269d27d0XPAaAR\nCDsAkKsaNWrEx8fn5eU5OTmdP39e9BwA4hF2ACBjFSpU2LNnT926dZs3b56SkiJ6DgDBCDsA\nkLfSpUtv2LDB29u7ZcuWW7duFT0HgEiEHQDIno6Ozvz580eNGtWxY8f//ve/oucAEIbHnQCA\nEqhUqpCQkPLlyw8cOPD+/ftBQUGiFwEQgLADAOUYPnx4xYoV1Wr1+fPnf/vtNx5xB5Q0vBUL\nAIrSrVu3uLi4zZs3t2rV6v79+6LnAChWhB0AKI2jo2NycvKzZ8+cnJzOnj0reg6A4kPYAYAC\nWVpa7t27t169es2aNduzZ4/oOQCKCWEHAMpUpkyZ9evXf/HFF56enhEREaLnACgO3DwBAIql\nra0dFhbWsGHD/v37p6SkzJo1S0uLv88DSkbYAYDC+fv7V61atXv37jdv3oyIiChVqpToRQCK\nCn91AwDla9OmTXx8fFJSkpub2507d0TPAVBU5HTF7llawqaNO/YdOX3p+r0nmS/ydAzKmFpU\nrlnfzqmVVzunKoYq0QMBQHNZW1vv37+/U6dODg4OGzdubNSokehFAAqfTMLu6YlFI9QjFx9J\nzyvw29+qylp9/u2vP41sUYFLkADwGhUrVty7d++XX37ZvHnzqKioDh06iF4EoJDJIuyuL/3c\nrf+mByYN2vX3buXazLZGhXKmpmUNpJysZ49uX7906tDONUujVoz2SLm8cf+cNqai5wKAxjIw\nMIiMjJw4cWKXLl1++umn4cOHi14EoDDJIOzyD4Z9t+l+VfX6g0s6Vfift1sb2jq19u41PDhw\nupfrmLkjwgadDrEWsRIAZOLVqbJVq1YdNGjQiRMn5syZo6Mjg/8XAHgXMnjn8uaBA1elOn2+\nLqDq/lLa5ptJanPpzN74u8W3DABkq1+/frt27Vq3bl2HDh2ePHkieg6AwiGDsMvPz5ek3Nzc\nt7xMy9DQQJKysrKKZRQAyJ6zs/P+/fuvXLni4uJy5coV0XMAFAIZhJ2lvX0F6eKiqcuvvXz9\ni3KvR85YdlWqYG9vWXzLAEDmatasmZiYWL58eScnp6SkJNFzAHwsGYSdqvno773K3VrT29qm\n88gfl23Zd/zizfvpGZmZTx/dvXnlzKFtUb+M6W5v03vNLZPWE/7TQlv0XgCQk3Llym3btq1N\nmzaurq5RUVGi5wD4KLL4wOynX65NUA3vE7Tkj1lf/zGrwJeoyjTs9euyOYNrFPM0AJA/PT29\nxYsXN2rUqHfv3mfPng0JCRG9CMAHkkXYSZJB/X4LDnUfn7Bhw/b4fcmnrt59+OjxsxwtgzLl\nLKrVsXZwbevTzbOeMU8oBoAPFhgY+Omnn6rV6qtXr86bN09PT0/0IgDvTSZhJ0mSJBlWdekx\n3KUHD10CgKLh4+NTuXLlTp06dezYcdOmTTwGBZAdOf1Hy5FiAFDUmjRpsm/fPkdHx+Dg4Jkz\nZ4qeA+D9yCTsOFIMAIpL9erVV61a5enp6ejo6OvrK3oOgPcgi7DjSDEAKFZubm6TJk368ssv\nGzZs2KBBA9FzALwrVX5+/nu8PPfFi3x9/eKtwfyDo6s1nal6zZFif3p2bLqX65i9lSYcL/wj\nxcLDwwcNGpSRkVGmTJlC/tUAoKny8/O7det28uTJQ4cOlS1bVvQcQINkZ2fr6+snJiY2a9ZM\n9JZ/e/07lznXt//k7/mZ85Qjf/vitV+al6lg037Yr3tu5BT9uFc4UgwAip9KpVqyZIlKperT\np8/7XQIAIM5rwi7j4KRWNp6jFmxPvZX59/+c9UxNde8f3zJneEur5sE7HhTLRI4UAwAhjIyM\noqOjt2/fHhYWJnoLgHdSYNilbxjaeULCQ5OmgZFJ+yfa/e07lfpve3AnJWqcx6cZB0O7dvv1\nfDFM5EgxABDF2tp6wYIF33zzzd69e0VvAfB2BX1c7uqSaZG3pRrDN+362bnU/3xXz8yux5St\nLnW7NFJv/C5kY79I79JFO1HVfPT3Xsv7r+ltfWrNl1/6uDvZ1K1WyczIUFf14umTJw+vnzly\ncPf6/85ffeyhSeu5H3Ck2JMnT958PTAzM/Mj5gOAvH3++ecJCQl+fn6HDx+uVKmS6DkA3qSA\nmyeeLutkrN7Q9Kerif+p/IafPD3ZpsF3l/ttfrjIq+hvpsg6vXh4n6AlSfded9FOVaZhz+nL\n5gy1NX6/X3zx4sXatWu/y8dHuHkCQImVk5Pj5uaWl5e3e/duTqQANPnmiQKa7PaNG3mSYb16\nb6o6SZLqN2lSRjp+7txtyevTotn2N0V2pFjNmjXT0tJevnzDu7xSVFTU+PHjP3g7AMidrq7u\n6tWr7e3tx4wZ8+OPP4qeA+C1Cgg7XV3dd/rRvLy84r1ZoYiOFKtSpcqbX2BmZlbIfyQAyE3F\nihUjIyNfPbXYz89P9BwABSvg5omK1arpS5kHDqS++ScvHDuWKWlbWloUzbB/y7qyc8436g4t\nnZ1bdlAHzdtzI/vfrzi/uE/btoOWXymePQBQ0ri5uU2ePLl///4nT54UvQVAwQoIOz33Dh76\n0qm5E9fce/3PPd0147cUSdvJs1UxfOws/9aGofYN3If9sGzznn379mxeNmNwS+sWkxKf/ONV\n6Wf3bNuWcCGj6PcAQAkVFBTUpk2brl27Pnny5O2vBlDsCnrciXH3CSMbaN1f29djUPTZAm4I\nfZG2JahNtwVXpUrqMX2K4ekij1YP7T331IuKbqPCN+1NOhS3ZkZv6zKPDkzo0nfV7aL/0wEA\n/0elUi1evFhbW5unFgOaqcAbWnUcJq777UTLQRvDuzdcFdLau00zm9qVypXWfZlxJy11f8z6\nrYfvZkvGTcZH/+xVDNfrMmNWbXoiNRyzadv3drqSJEkOjVu2dbF0aTF93ZDBkW7repkX/QYA\nwCuvnlrctGnTn3/++T//+Y/oOQD+4TVPKtGt478upcb04cNnrDsdu+x07LJ/fLdUtTYjp86a\n0rP+/z7lrgjcSEvLkT5t18nub/d0lHaavGx8rP2E9aOCt3gv8uIQQwAoPlZWVgsWLOjTp4+9\nvb2rq6voOQD+8vpH0GlXdB+35lTg5cRt2xMOn71+/0m2ThlTs4q1bZ3dWjrWNCn6Z9f9H0ND\nQ0nKfvHin1/VsRozf/Qqx6lLAsZ/2XK2i2GxzQEASJ9//nliYqKfn19KSoqlJUf+AJriLX2m\nKlPdxcffxad4xhSsoq2thZQQ/euq8c27m//tUXW69uPDA1e3+OnXLwa22L/Up6K4hQBQAs2a\nNevYsWO+vr48tRjQHAWeFatZtJoPG9XU8M7qXo1c+oXMiVwXf/H/bugwcJkaOc7O4Mpyv8bt\nxkYl333TuWAAgEKlq6sbHR2dlpYWHBwseguAPxVwxe7hoagVhx6848+Xb9Lz8yblCnXS/1DV\nGbVu45M+fUJjl0zct0RqOOH0iZB6r75l4DApZnNutx6hsdN6xkqSJL3niWIAgA/3/59a3LRp\nU55aDGiCAsLu5papwye+68MnG05oWeRhJ0kqi1aTtqWNPLt3W/yJtFzrfxwE8Ynb1N0X+sWt\nW7UuZl/qBX0z3g4AgOLj5uY2ZcqU/v37N2zYsGHDhqLnACVdAWH3icuAoKB3fUCchcsnhbrn\nDbRN6rp1r+tWwHdURrVaqce1UhfXEgDAX7755pukpKSuXbsmJSWVLctjCgCRCgi7Cu4jprsX\n/5L3d/9Mwpn7pavY2VbhnlgAEObVU4sdHR3VavW6detUKtXbfwZA0fiAmydyczXjJoWXO8Y3\nb96896JLoocAQEn36qnFO3bsmDVrlugtQIn2+rDLvnti79YNm3cfvprx6tSY5+fXBXX47FPj\nUrqGptWafv79lksvXvvDAICSxcrKauHChUFBQXv27BG9BSi5Cn6O3eN933f3mxR744UkSZJW\n+SbDF63/Vhrl2jXqtqRlULasdsaVgyvHtd+xNzxxq38drrkDACRJ6tGjR2JiYvfu3XlqMSBK\nQVfsMrYM7zIu9kZ+pSad1P2+6GCreySsV7vWI6Num7Wduf9ORvrjzCcXNo1xKnt/26jRKx8V\n+2QAgKb66aefateu7evrm52dLXoLUBIVEHbPY5auvitVUq85eXD90kXLNiafXNvH5Nixi5Jj\n0PxRTc10JEkyrNn++4gxDtLTmPU7sop985+0Kjv5+Ph4NuDRdQCgKXR1dVeuXHnx4sWgoCDR\nW4CSqIC3Ym9cvPhCMu2o7mDy5xfKefv7Vlw6S9vJqfLfXlbLuZm5lJyWdkuSqhfH0v+h5Txq\njbOQPxkA8FqWlpZRUVGenp6urq5dunQRPQcoWQq4YpeVlSVJFSws/vbZOUtLS0kyNv7ntbFS\npUpJ0rNnz4p4IQBAZlq1ajVu3Lgvv/wyLS1N9BagZHndXbHa2tqv/ScAAN5swoQJdnZ23bt3\nz8nJEb0FKEE+4Dl2AAC8hZaWVkRExKVLlyZMmCB6C1CCEHYAgCJhaWkZERExY8aM2NhY0VuA\nkqLg59hJ0rkfW1dbqPt//5T75JYk5f/cptoS3b9ekv3ouiTVK+J9AAD5ateuXWBgYO/evY8e\nPVqxYkXRcwDle13Y5Ty+eeXxv76WfvNKelHvAQAoyvTp0/ft29ezZ88dO3bwgW2gqBUQdg3H\nH34enPeOP6+lo1+oewAAiqKrqxsZGWlnZzdjxowxY8aIngMoXAFhp9LRM3jdhTwAAN5TjRo1\nFixY0LNnT1dXV2dnHkAKFCFungAAFDlfX99+/fr16NHjwYMHorcASkbYAQCKw+zZs8uXL9+n\nT5/8/HzRWwDFIuwAAMXBwMBgxYoVcXFxv/76q+gtgGIRdgCAYtKgQYOwsLDRo0cfPnxY9BZA\nmQg7AEDxGTBgQLdu3bp37/7kyRPRWwAFIuwAAMVq3rx52tra/v7+oocACkTYAQCKVZkyZSIj\nI9evX79kyRLRWwClIewAAMXN3t5++vTpw4YNO336tOgtgKIQdgAAAQIDA93d3f38/J4/fy56\nC6AchB0AQACVSrV48eKMjIyRI0eK3gIoB2EHABDD1NR02bJlCxcujIqKEr0FUAjCDgAgTPPm\nzb/77rshQ4ZcvnxZ9BZACQg7AIBI48aNc3Bw6N69e3Z2tugtgOwRdgAAkbS0tJYvX37t2rXx\n48eL3gLIHmEHABCsQoUKS5Ys+fHHHzdu3Ch6CyBvhB0AQLw2bdp8/fXX/fv3v3nzpugtgIwR\ndgAAjTB16tTatWv37NkzNzdX9BZArgg7AIBG0NHRWblyZWpq6tSpU0VvAeSKsAMAaIrKlSvP\nnz9/0qRJu3btEr0FkCXCDgCgQXx8fPz9/dVq9f3790VvAeSHsAMAaJaffvrJzMysb9++fNgO\neF+EHQBAsxgYGERHRx84cKBnz545OTmi5wByQtgBADROnTp14uPj4+Pju3TpkpWVJXoOIBuE\nHQBAE9WvXz8uLu7o0aNdu3Z9/vy56DmAPBB2AAANVbdu3fj4+DNnznh5eT19+lT0HEAGCDsA\ngOaqXr16XFzctWvXvLy8MjIyRM8BNB1hBwDQaFWrVo2Li7t9+3a7du2ePHkieg6g0Qg7AICm\nq1y58t69ex8/ftyqVasHDx6IngNoLsIOACADFhYWu3btys7O9vDw4NnFwOsQdgAAeTA3N9+z\nZ4+Ojo6rq+utW7dEzwE0EWEHAJANU1PT2NjYsmXLurm53bhxQ/QcQOMQdgAAOTExMdm2bVv5\n8uWbN2+elpYmeg6gWQg7AIDMGBsbx8bGVq9evWXLlhcvXhQ9B9AghB0AQH5Kly69cePGOnXq\nuLm5XbhwQfQcQFMQdgAAWTI0NNy4caOtrW3z5s1Pnjwpeg6gEQg7AIBc6evrr1692snJqVWr\nVqmpqaLnAOIRdgAAGdPT04uOjvbw8GjRokVSUpLoOYBghB0AQN50dHSWLl3q7e3t6el58OBB\n0XMAkQg7AIDsaWtrL1q0qEuXLm3atNm/f7/oOYAwOqIHAABQCLS1tf/73/+WLl3aw8Njw4YN\nrVq1Er0IEICwAwAohEqlmj17tra2tre39/r16z08PEQvAoobYQcAUA6VSvXzzz+XKVPG29s7\nOjq6Y8eOohcBxYqwAwAozZQpU/Lz8/38/DZu3Mh1O5QohB0AQIGmTp2am5vbuXPnmJiY5s2b\ni54DFBPCDgCgTNOmTXv8+LG3t/euXbvs7OxEzwGKA487AQAok0qlmjt3rpeXV9u2bc+cOSN6\nDlAcCDsAgGJpaWktXbrU0dHRw8MjLS1N9BygyBF2AAAl09XVjY6OrlWrloeHx+3bt0XPAYoW\nYQcAULhSpUpt2rTJ3Nzc09Pz4cOHoucARYiwAwAoX+nSpTdv3qytrd2+ffunT5+KngMUFcIO\nAFAimJiYbNu27dGjR507d87KyhI9BygShB0AoKQwNzePjY09f/58jx49Xr58KXoOUPgIOwBA\nCVKlSpXt27cfOHCgX79+eXl5oucAhYywAwCULHXq1ImJidm0aVNAQIDoLUAh4+QJAECJ06hR\no82bN3t6epYrV27SpEmi5wCFhrADAJREzZo1W7dunbe3t5GR0ejRo0XPAQoHYQcAKKE8PDxW\nrFjRvXt3Y2Njf39/0XOAQsBn7AAAJVfXrl0XLlw4dOjQlStXit4CFAKu2AEASrQ+ffqkp6er\n1WojI6P27duLngN8FMIOAFDSBQQE3Lt3z9fXd+vWrS1atBA9B/hwhB0AANLkyZMzMzM7duy4\nc+dOBwcH0XOAD0TYAQAgSZI0c+bM9PT0du3a7dmzp0GDBqLnAB+CmycAAJAkSVKpVOHh4W5u\nbp6enpcvXxY9B/gQhB0AAH/S1tZevnz5Z5995uHhcfPmTdFzgPdG2AEA8Bc9Pb01a9ZUqlSp\nTZs2Dx48ED0HeD+EHQAA/2BoaPjHH39oa2t7eXllZmaKngO8B8IOAIB/MzU13bZt261bt4KD\ng0VvAd4DYQcAQAEqVKiwePHiOXPmxMTEiN4CvCvCDgCAgrVu3XrYsGEDBgx4+PCh6C3AOyHs\nAAB4rdDQUBMTk8DAQNFDgHdC2AEA8FoGBgYRERGrVq2Kjo4WvQV4O8IOAIA3sbOzGzt27JAh\nQ27duiV6C/AWhB0AAG8xfvz4mjVr9u3bNz8/X/QW4E0IOwAA3kJHR2fp0qXx8fELFiwQvQV4\nE8IOAIC3q1ev3rRp00aOHHn+/HnRW4DXIuwAAHgnAQEBzZs379u3b25urugtQMEIOwAA3olK\npVq4cOHp06dnzpwpegtQMMIOAIB3ZWlpGRYW9t133x07dkz0FqAAhB0AAO+hd+/enTp16tmz\nZ1ZWlugtwL8RdgAAvJ+5c+c+fPgwJCRE9BDg3wg7AADej5mZ2ZIlS2bOnLlnzx7RW4B/IOwA\nAHhvbdq06devX79+/TIyMkRvAf5C2AEA8CF+/vlnbW3tUaNGiR4C/IWwAwDgQ5QuXXrJkiWL\nFi3atGmT6C3Anwg7AAA+kLOz86hRo/r373/37l3RWwBJIuwAAPgYkyZNsrCwGDhwoOghgCQR\ndgAAfAx9ff0VK1bExMQsX75c9BaAsAMA4OM0bNhwwoQJw4YNu3r1qugtKOkIOwAAPtY333xj\nY2Pz5Zdf5ufni96CEo2wAwDgY2lpaS1ZsuTQoUO//PKL6C0o0Qg7AAAKQfXq1X/44YegoKCT\nJ0+K3oKSi7ADAKBwDBw4sHXr1mq1OicnR/QWlFCEHQAAhWbRokXXr1///vvvRQ9BCUXYAQBQ\naMzNzefNmzdlypRDhw6J3oKSSEf0gPeRn3X7xIH9R05fun7vSeaLPB2DMqYWlWvWt3NsXO8T\nfdHjAACQJEnq0qVL9+7d+/Tpc/jw4VKlSomeg5JFLmH37OTy8SMmLNxx6WkB39QyqtWq9zdT\nJ/ZvYsYVSACAcHPmzPnss8/GjBnz888/i96CkkUWYff80IQWLSalZOmY1HRs79rMtkaFcqam\nZQ2knKxnj25fv3TqUNyOnXP9d66PWbx3VZ+asvhXAgAomLGx8aJFizw9Pdu2bdu2bVvRc1CC\nyKGCLs8dOiVFp8nobWsne35a4Fuu+elH5/ftOPj3QYOWtt3ev0JxDwQA4F9at249ZMgQf3//\n48ePm5iYiJ6DkkIGb10+iI1Jzqv45czpr6k6SZJUxo0GLp/VvUzWjrWbnxTrOAAAXiM0NNTI\nyKhv374cR4FiI4OwS09PlySzChXeMrV0rVoWknTv3r3iWQUAwJsZGhquW7cuLi7uxx9/FL0F\nJYUMwq5ynToG0qm1Ucez3/Sql6l/bLksGdSqZVlcuwAAeIs6derMnz9/zJgx8fHxoregRJBB\n2Om2DxhaK+/wxFauA3/ekHLtae4/v5337Gbqtt+GtWwVcji/6oDBHQzErAQAoCDdu3f/6quv\n/Pz8bt26JXoLlE8ON0/oNpm2bcX99v2Xzv9Pp/n/0TIwrVS5kpmRoa7qxdMnTx7eunbnaa4k\nSQa1fOevn+nK8+wAABpm1qxZSUlJvXr12r59u7a2tug5UDIZXLGTJEm3Ro8lqWmHlk8e2NW1\nnsmLm+dPHj2clJRy/PT5K490LBu5fxE8b8eZ49H9G5J1AACNo6+vv3bt2uPHj0+aNEn0Fiic\nHK7YvaLzSeNe4xv3Gi9JUl7Os/RHj5/laBmUMS1nbCCPOAUAlGBVqlRZunRpp06dnJyceLId\nio58wk7iSDEAgIy1b9/+66+/7tWrV0pKSrVq1UTPgTLJJew4UgwAIHtTp05NTk7u3r17fHy8\nnp6e6DlQIFmEHUeKAQCUQFtbOzIy0tbWNigoaNasWaLnQIHkUEEcKQYAUIoKFSqsWLHCw8PD\n2dm5W7duoudAaWTw1iVHigEAlKRly5YhISH9+vU7c+aM6C1QGhmEHUeKAQAUZuzYsa1bt/bz\n88vMzBS9BYoig7DjSDEAgMKoVKrFixc/ffrU399f9BYoigzCjiPFAADKY2pqumrVqjVr1ixe\nvFj0FiiHKj8/X/SGt8u5tPKr9v2XnsmUJOkNR4r9un7Z+x4+cevWrX79+uXm5r7hNTdu3Dh9\n+nRGRkaZMmU+5t8CAIB/+eWXX7755pt9+/bZ2tqK3oJ3lZ2dra+vn5iY2KxZM9Fb/k0eYSdJ\nkvTyXtKq8P/+vj1+X/KZ25l5f35VpWdSuYGDa9tufQepW1ct9d6/NTMz87fffnv58uUbXnPw\n4MF169YRdgCAotC7d+8DBw4kJycbGxuL3oJ3QtgVsmI+Uiw8PHzQoEGEHQCgKDx9+rRJkyZ1\n6tRZt26dSqUSPQdvp8lhJ4fn2P0PLd3SpualTaUXVxP+WHPo0mNV+TqObdo1q/L+F+wAABCs\nTJky0dHRjo6Os2fPDgwMFD0H8iaTsHtxYe2ksT9E7zlzL79c9SadR4dO7WH0R2839YpLOX++\nQreSx7erV33bzFToTgAA3p+VldWCBQv69u3r4ODg7Owseg5kTBZhdyeqPDH/BwAAIABJREFU\np3PP3+9KKv3yFcs9OLl51hep9xJtNq64pKrhObSXR60yD5JXz4/c/l2H3pVPbupbUfRcAADe\nV8+ePePi4nr06HHkyBEzMzPRcyBXMnjciXTs1wm/39VpMGDD5Sf3b9x8ePvQNLeM5XM3ppft\ntPTQtl8nfT3im2nL9x/6qYXho83T5h0XvRYAgA/yyy+/mJub9+jR483PagDeQAZhdych4bxk\n1OP7X7yr6kmSpF2ucfCMgdUlydC7r2/5/3uRTs2A0X6lpXOJ++4LnAoAwAczMDCIjo5OTk7+\n/vvvRW+BXMkg7B4/fixJlrVq/e3Jw3Xr1pEkyypVtP/2Mu1q1SpL0sOHD4t9IAAAhaNmzZrL\nli2bOHFibGys6C2QJRmEnXmFCpKUduxY+l9f0nMY8MMPYztU/fvLXl69ekuSeAgQAEDWvL29\nAwMDe/fufePGDdFbID8yCDvTdh2b62St/+aLsPgbWa++pGfV7euv+zYr/9eLniRPmbQyXarp\n7FxBzEoAAApJaGho3bp1u3Xrlp39xmPSgf8hg7CTLP3nhbX95NamEa6VTctX/WLFg39899TS\nr7q41q7sOPFAZoVuU4Y3EjQSAIBCoqOjEx0dnZaWNm7cONFbIDNyCDtJp8GQzan7l3zbx9Pa\nQifnxT/vFboaH7U+/kJu1TZfr0pY1oPrdQAABbCwsIiMjPz5559///130VsgJ/+vvfuOq6r+\n4zj+uZe9RXBiIi4wB+ZOUXLkNg0cOVJzr9Q0R6k5Mu2nGaU5MFeuzBR3Wi7U3DNRNAc4caCC\nDAEZ5/cHDlAUMOBwD6/nf55z7uHN1/M4vO+ZBvEcOxHRF6zRbVKNbpNenlNj5PajI0pXKFvA\nnNewAAC0o0GDBmPGjOnZs6e7u3upUqXUjgPDYBBH7F4rf9l3q7nS6gAA2vPVV1/VqlWrTZs2\nUVFRameBYTDgYpe4uoOxsXHlSWfVDgIAQLbQ6/UrV66Mi4vr0qWLoihqx4EBMOBipyQlJiYm\nJiSxoQMANMve3n7jxo3+/v6TJ09WOwsMgKFcYwcAQB7l5ub2yy+/eHt7lytXrm3btmrHQa5m\nwEfsAADII1q3bj127NgePXqcPcsFSHgdAy52OjNbBwcHe0sOOgIAtG/8+PFNmzb18vIKDw9X\nOwtyLwMudkYfLrp3796+kW5qBwEAINvpdLpFixaZmpp26NAhMTEx/Q8gTzLgYgcAQJ5ibW29\ncePGEydOjB07Vu0syKUodgAAGAwXF5eVK1d+9913q1atUjsLciOKHQAAhuT999//5ptvevTo\ncfz4cbWzINeh2AEAYGBGjhzZpk0bb2/v0NBQtbMgd6HYAQBgeBYuXFigQAEvL6/Hjx+rnQW5\nCMUOAADDY2FhsXbt2gsXLowcOVLtLMhFKHYAABik4sWLr127du7cuQsXLlQ7C3ILih0AAIbK\nw8NjxowZgwYNOnz4sNpZkCtQ7AAAMGCDBg3q0qXLhx9+ePPmTbWzQH0UOwAADNucOXNKly7d\nrl27uLg4tbNAZRQ7AAAMm4mJyerVq69du9a3b1+1s0BlFDsAAAxe4cKF16xZs2rVqrlz56qd\nBWqi2AEAoAW1atWaP3/+kCFD/P391c4C1VDsAADQiK5du/bp06dt27bBwcFqZ4E6KHYAAGjH\nDz/8UKlSJS8vr0ePHqmdBSqg2AEAoB3Gxsa///57REREnz591M4CFVDsAADQFAcHBz8/v3Xr\n1s2YMUPtLMhpFDsAALTG3d196dKlo0aN2rp1q9pZkKModgAAaJC3t/ewYcM6d+586dIltbMg\n51DsAADQpqlTp9aoUcPLyysqKkrtLMghFDsAALTJyMjo119/jYqKGj16tNpZkEModgAAaJa9\nvf28efPmzp178OBBtbMgJ1DsAADQssaNG3fo0KFfv37x8fFqZ0G2o9gBAKBxPj4+169fnzVr\nltpBkO0odgAAaFyhQoWmTJkybty4K1euqJ0F2YtiBwCA9vXp06dy5coDBw5UOwiyF8UOAADt\n0+v1vr6+27dvX79+vdpZkI0odgAA5AkVKlQYOnTo4MGDIyMj1c6C7EKxAwAgr5gwYYKJicn4\n8ePVDoLsQrEDACCvsLS0nD179syZM0+cOKF2FmQLih0AAHlI06ZN27Rp07dv38TERLWzIOtR\n7AAAyFtmzZp16dKlOXPmqB0EWY9iBwBA3lKkSJFJkyaNGTPm5s2bamdBFqPYAQCQ5wwcOLB8\n+fJDhw5VOwiyGMUOAIA8J/mxduvXr9+0aZPaWZCVKHYAAORFlSpVGjRo0KBBg6KiotTOgixD\nsQMAII+aPHmyXq//+uuv1Q6CLEOxAwAgj7KysvLx8fn+++9PnTqldhZkDYodAAB5V5s2bVq0\naNG3b9+kpCS1syALUOwAAMjTZs2aFRgYOH/+fLWDIAtQ7AAAyNPeeuutiRMnjho1KiQkRO0s\n+K8odgAA5HVDhgwpVarU559/rnYQ/FcUOwAA8jojIyNfX9/Vq1dv2bJF7Sz4Tyh2AABAqlev\n3q9fv0GDBkVHR6udBW+OYgcAAEREpkyZEh8fP3XqVLWD4M1R7AAAgIiIra2tj4/P9OnTAwMD\n1c6CN0SxAwAAT7Rr165x48Z9+/ZVFEXtLHgTFDsAAPDcTz/9dPLkycWLF6sdBG+CYgcAAJ5z\ndnYeN27ciBEj7t69q3YWZBrFDgAApDJ8+PC33nprxIgRagdBplHsAABAKsbGxr6+vitWrNi5\nc6faWZA5FDsAAPCimjVr9uzZs3///rGxsWpnQSZQ7AAAQBqmTZsWFRX1v//9T+0gyASKHQAA\nSIOdnd306dOnTp167tw5tbMgoyh2AAAgbZ07d65Xr17//v15rJ2hoNgBAIBXmjNnzuHDh7/7\n7ju1gyBDjNUOAAAAcq/SpUsvWbLk448/fvTo0fjx49WOg3RQ7AAAwOt06NDB2tq6Xbt2oaGh\nM2fO1Os53Zd78X8DAADS0aJFi23bti1fvrxbt24JCQlqx8ErUewAAED66tWrt2vXrj///NPL\ny4uH2+VaFDsAAJAhVapU2bt376lTp5o1axYZGal2HKSBYgcAADLKzc1t3759ISEhDRo0uHfv\nntpx8CKKHQAAyARnZ+e9e/cmJCR4enrevHlT7ThIhWIHAAAyp1ChQrt377a3t/fw8Lh06ZLa\ncfAcxQ4AAGRavnz5/vrrLzc3t7p1654+fVrtOHiCYgcAAN6EpaXlhg0b6tat+9577x08eFDt\nOBCh2AEAgDdmamr666+/tm3b9v3339++fbvacUCxAwAA/4GRkZGvr++AAQNatWrl5+endpy8\njleKAQCA/0Sn002bNs3BwaFDhw7z58//5JNP1E6Ud1HsAABAFhg1apStrW3v3r3Dw8M/++wz\ntePkURQ7AACQNfr3729nZ9e9e/c7d+58++23asfJiyh2AAAgy3Tq1MnW1rZ9+/bR0dE//vij\nXs/V/DmK4QYAAFmpZcuWW7duXbp0abdu3RISEtSOk7dQ7AAAQBbz9PTctWvXn3/+6e3tHRsb\nq3acPIRiBwAAsl7VqlX37Nlz4sSJ5s2bR0ZGqh0nr6DYAQCAbFGuXLm9e/dev369SZMmYWFh\nasfJEyh2AAAgu7i4uOzbty8iIqJbt25qZ8kTKHYAACAbFS5ceM2aNdu3b1+6dKnaWbSPYgcA\nALKXm5vbhAkTBg8efP36dbWzaBzFDgAAZLsRI0ZUrFixZ8+eiqKonUXLKHYAACDb6fX6BQsW\n/P3330uWLFE7i5ZR7AAAQE5wdXWdNGnSZ599xgnZ7EOxAwAAOWTYsGEVK1bs0aMHJ2SzCcUO\nAADkkOQTsvv371+0aJHaWbSJYgcAAHKOq6vr5MmThw0bdu3aNbWzaBDFDgAA5KihQ4dWrlyZ\nE7LZgWIHAABylF6vX7x48eHDh3/++We1s2gNxQ4AAOS0kiVLfv3118OGDQsKClI7i6ZQ7AAA\ngAoGDx5crVq13r17c0I2C1HsAACACpJPyB45csTX11ftLNpBsQMAAOpwcXGZMmXK559/fvny\nZbWzaATFDgAAqGbgwIHVq1fnhGxWodgBAADVJJ+QPXbs2Jw5c9TOogUUOwAAoKYSJUpMnTp1\n5MiRly5dUjuLwaPYAQAAlQ0YMMDDw6N79+5JSUlqZzFsFDsAAKAynU7n6+t7+vTp2bNnq53F\nsFHsAACA+kqUKDFt2rTRo0dfvHhR7SwGjGIHAAByhb59+9atW7d79+6JiYlqZzFUFDsAAJAr\n6HS6hQsXBgYG/vTTT2pnMVQUOwAAkFs4OTn973//+/LLLy9cuKB2FoNEsQMAALlI796969Wr\nxwnZN0OxAwAAuYhOp1uwYMH58+d//PFHtbMYHkMtdkkJ8Ym8egQAAC1ycnKaPn36l19+GRgY\nqHYWA2M4xS4uZP/Syf2933MvWcjG1MjIxNTYyNjC3qlstUYffTpl+f7rcWoHBAAAWaVnz54N\nGjTo2bMnJ2QzxTCKXfyFFV2rlPXoNm6e357TwaGxRtaORYoVK+xonfTg8vGdv/005mOPsm+3\nnPJ3mNpBAQBAFlmwYMG///7r4+OjdhBDYgjFLuHomFbdl/1r49Hvf8u2Hr368HF8zMPQkOvX\nQ26HPoyJjbhxescvX33ofGvLmGYtv+cWGgAAtKFo0aIzZswYO3bs2bNn1c5iMAyg2MVvmz3v\ngq72t3v9547s0rRacVvjlHNNbJwqNuw60e/Ixr4low5M8dnJO+YAANCITz75pFmzZpyQzTgD\nKHY3zp2LlHItW5cxet1Sto36dHCR+//8cyOncgEAgGw3e/bsixcvfvfdd2oHMQwGUOxsbGxE\nbt+4kfD6xRLu3XsoYmZmljOpAABADihatKiPj8+ECRO4QzYjDKDYOdZv5G50d9GQwRuvvPLO\n1/gbW4eOWPZAyjdsUCgnswEAgOzWtWvXJk2atG3bNjw8XO0suZ1x+ouoznXwnDFrm0ya29p1\n7TuNWzZ61921RFFHG0sTXVxURMSDG+dPHvbfsuXQzTjTisPnDCmndloAAJDVli1bVrt27Q4d\nOmzZssXY2BDai0oMYmgsa0/0P1B24uhJ8/7YvOjk5jSWMC/m0X/8zG97vWOT4+EAAEB2s7Gx\n2bhxY82aNYcNGzZz5ky14+ReBlHsRMSqYudpWzpNvH3m0L4DxwKv3X0QFh4drze3zl+4RNmK\n1eq9V6uU3WvvrQAAAAbNxcXFz8+vUaNGbm5uAwYMUDtOLmUoxU5ERHQWhSvWb1exvogkJcQr\nRiZGOrUjAQCAnOLh4TFv3rw+ffqULVu2UaNGasfJjQzg5okneKUYAAB5Xvfu3QcPHuzt7c1T\ni9NkGEfs4i+s6Plh32WB0SIiojM2t3F0tDWX+NjoB5eP77x4fOdvP309vsW4X5Z96WGvclQA\nAJCtpk2bdvHixQ8++ODw4cOOjo5qx8ldDOGIHa8UAwAAT+n1+hUrVlhbW3t5eT1+/FjtOLmL\nARQ7XikGAABSsra23rhx44ULF/r37692ltzFAIodrxQDAAAvcHZ29vPzW7FixQ8//KB2llzE\nAIodrxQDAAAvq1279tKlSz///PPNm9N6yG2eZADFjleKAQCANLVv337UqFGdOnUKCAhQO0uu\nYAh3xWbnK8Xi4uKWL1+emJj4mmX27dv3n/IDAIBsM3ny5MuXLyffJFuwYEG146hMpyiK2hky\nIjpgxcTRk+b9cSEyzdnmxTw+GT/z217v2GZyvTdv3vT29k5IeN153vDw8MuXL8fGxnKeFwCA\nXCgmJsbT09PU1HTnzp058Mf68ePHZmZm+/fvr127dnb/rMwylGInIiJKjCqvFDtw4ECdOnXi\n4uJMTU2z62cAAID/ICQkpGbNmg0aNPjll1+y+2fl5mJnCKdin0nxSrFnYkPOnglJjFcrEgAA\nyAWKFi26YcOGunXrli9ffuTIkWrHUY0B3Dzxepfmd6hefcD6tM/QAgCAvKJKlSpLly798ssv\nN2zYoHYW1RjAEbvH94KD7r3yftjge49FHt2+eP68jYiImWNJF0dOmAIAkBd5e3uPGzeuS5cu\nf//9t7u7u9pxVGAAxe7CT60qTnz9i34vjqtRbpyIiJQfH3BmQoWciAUAAHKfr7766sKFC82b\nNz9y5IiTk5PacXKaARS7YvXb1Z13ft+dRL3DOy2bvm2Teu7D05s3B1h5fNzM1VRExKlKfjUy\nAgCAXEGn0y1cuLB+/fqtW7feu3evpaWl2olylAEUu3ye4/cENps9pMcXy8+cDG0+13dcixLP\n72Q+M6HC5oDC3WYu6JVPxYwAACC3MDc3X7duXY0aNbp37/7bokW6+fPFz08uXxYRKVVKvL2l\nTx+xslI7ZrYwjJsndPlrDFp24syWL9wCp7Ws4N7R5+/QJLUzAQCA3Kpw4cIbN268s3lzpJOT\nDB8u+/fL7dty+7bs3y/Dhkm5cnL0qNoZs4VhFDsRETF1bj7xr7PHFna23ja8Xrl3BywNiFA7\nEgAAyKUqGxvv1OlsI9JqC9evS6NGcvb1V/AbJAMqdiIiYluph+/hszum1Lm3uFvVt5uMfc37\nYwEAQF6lKNKzp/GjR69cICJCevYUA3pNQ8YYWrETETEq2mD0hoBTvw4scWJq6zbTz6udBwAA\n5DL798uRI+ksc/iwHDiQI2lyjiEWOxERsXT9yGdv4N8zP2n6XsOGVZxM1M4DAAByjx07MrTY\nzp3ZnCOnGcBdsa+mL/Dupz9v/lTtGAAAIJe5dStDi4WEZHOOnGawR+xElMC1kydPnr83VO0g\nAAAgl7G1zcrFDIcBF7vE07+OGzdu5q47agcBAAC5TPXqWbmY4TDgYgcAAJC2Fi2kYMF0lilY\nUJo3z5E0OYdiBwAANMfKSqZPT2eZ777T3vsnKHYAAECLunaVr79+5dzJk+Xjj3MwTQ4x4GJn\nVLXXrFmzxjQvqnYQAACQK40dKzt2SO3aotM9maLTSe3asnOnjBmjarLsYsCPO9GVaTqojNoh\nAABAbtawoTRsKLduyaVLIiKlS0uRImpnykYGXOwAAAAypEgRbfe5Zwz4VCwAAABSotgBAABo\nBMUOAABAIyh2AAAAGkGxAwAA0AiKHQAAgEZQ7AAAADSCYgcAAKARFDsAAACNoNgBAABoBMUO\nAABAIyh2AAAAGkGxAwAA0AiKHQAAgEYYqx3AAJiamoqImZmZ2kEAAEBukVwPchudoihqZzAA\n//zzT0JCgogMHjzYzs6uU6dOaicyeAcPHly5cuWsWbPUDmLwFEXp2rXrmDFj3Nzc1M5i8GbP\nnm1lZdW9e3e1gxi8Y8eOLViwYN68eWoH0YIePXoMHTq0UqVKagcxeD///LOlpeXkyZOzZG3G\nxsbu7u5ZsqqsxRG7DHn2n+fo6Fi6dOkuXbqom0cDjIyM1q1bx0j+d8nF7v333/f09FQ7i8Hb\nvHlz/vz52Sz/Oysrq6VLlzKSWaJ3794NGjRo2rSp2kEM3s6dO0WkatWqagfJXlxjBwAAoBEU\nOwAAAI2g2AEAAGgExQ4AAEAjKHYAAAAaQbEDAADQCIodAACARlDsAAAANIJiBwAAoBG8eSJz\nTE1Nc+e74QwOI5mFGMyswkhmFUYyCzGYWSWPDCPvis2c0NBQc3NzGxsbtYMYvISEhJCQkOLF\ni6sdRAuCg4NLlCih0+nUDmLw7t+/b2xsbGdnp3YQg5eYmHjjxg1nZ2e1g2hBcHCws7OzXs8Z\ntv8qLCxMROzt7dUOkr0odgAAABrBNwAAAACNoNgBAABoBMUOAABAIyh2AAAAGkGxAwAA0AiK\nHQAAgEZQ7AAAADSCYgcAAKARFDsAAACNoNgBAABoBMUOAABAIyh2AAAAGkGxAwAA0AhjtQMY\nkqSY0OALwfd1DiXLlnI0VzsN8q7o4CNHb9lXrl0m38vz2EozRbl7dm9gfJk6lYuaqB3FkMU9\nuHIx6Fakzvatsm7FbIxemq/EPbh28fKdBDvnsmUKWepUSGgwkqJuXbx07X6cecGSbqULmKkd\nx4DFh1+9cCnkoWLjVMbNOV9aXSf+4Y1LF2/GWBcrU8Ypja3WgCnIkAf7prV1s3kyaEb2b7ef\ncTBM7UwG6dZP9Yxe5jTsb7WDGZCIFa3MpNDA3S/NYCvNtONflBXxnBv6wuSAcW+nsZlW/ea8\nKiFzs8S7e7/xejvfs7+Kxo7Veyw88yjFEtGnfLtVzf/k5JDOulSz8X/dSlQtb24Wc275QA8n\ni6dDqbMq1WzCX7eSns1n55lR0QELe1Yt8Oy7mt7+7bbf7rmbconHF1cP8ijytO2ZF6s3ZE3Q\nY7XiZjmO2GWEcv7HNs1H7o0v3WrkxFalja7umD9z9fCGt3Qn/D9z5WR25ly+dCFRV8i9TuqD\nTfldbNUKZHCij0z9bmucOLw4na000xJvrvx6wQWRIi/OUC5fvJxoVqxa9RJWKSeXfsvixSXz\nuPgzU5o3HncsoVjdngM/KG/78N8/ly7atahnwyjrM7+1dxQRCVnRuUnf9feKNfh0VPtK1ncO\nLp65aGLzRvEHjn1TnePJqYSu71W/y4rbtm97D+1U5y25eXjNgtVbJ7Rsqj98dFxlExF2nhn1\nYFP/xj2X3nao0mV0h5pF5dq+Fb6/rxnd9LrJyYPDXHUiIuF/DWjcccEV+1q9vu5as8DDU6tm\nzvux3XuR204vbGyndvosoXazNAQP17bLJ+Lo/fuzxh+2/qMCIlatfw1XM5cherSstU7KfnVa\n7RwGKGTf/G9G9mr1TqHk76EvHrFjK8242EC/7776tGP9UjbJJwVfOmJ33aemSL2ZIerEMxyP\n/DpZizh6rbj97LDSg80fFxWRkl8cVxRFidvzaTERq/qzgp8eo3v099CSIsZ1fK6rkjj3ujip\nkohxpXHHYp5OeXz2f7XNRCxb/ZJ83J2dZ8ZcnVZDJ6Y1pp2Lfzol7sS4ykYixYcdSP73mYnu\nOjF+Z/zJuCcLxJ+dXM1IxG3MSRXyZgOKXfoiln5gJFJ69LEU05K293UUMW69LEK1WIbp7MSK\nIs2XRqudwwDtHlgo5VeyF4odW2kmhM71TPX19qVit+fTAmLZ4w910hmQbb3yiRQZ+ndSyonH\nRpcWkWrfXlKUxD965BPJ32tbypNcAWNcRaQmzS6VGz/UEjFqNO9+yomPlrfUi1h02awoCjvP\nDIpY1FhE3vdN9X327MRyItJ62WNFUZQTI0uKmLVcnnKJW7PqiEipUdpodpyiSZdycN/+RLGr\nX79Kiom62vXqGkvCoUPHVctlmIKCgqVIqVKWaucwQHX+FxiabMVHL11SzVaaGQ7dNzwZyhPj\n3NOYHxUUFCqlSpXK8WAGJuratXCR8hUqpLobwt7eXkQiIyNFzuzbFy5GderXTXlnSvl69fKL\nHD90KCFn0+Zu165dEylSoUL+lBPN7e3NRWIiI+NF2Hlm0CP7St7e3b1rpjqn+vBhhIido6OJ\niNzaty9IpEr9+imXKFyvXhmRy4cO3cvZtNmDa+zSde/ff++LVClTJtXOy9LZ2VHk9pUrMSJc\nd5Nhd4OCosTZ4urMT6ev3X/xXoL1W5Uath/8WfcajnzFSI+JVX7H5Cu+bF++VY6tNDN05nZP\nbhiOskxrFxgUFCRGzhLwba9hm44Fh4u9S7UmXT4b/FF5bVx/k2UsP14d+mG8mW2qYbm5bVuA\niLGra0lJ+vPfSyJvlSmTqovonJ2Li5y6cuWGSIkczZubVZsYEPqF3tI+5bSYfdv2PBIp6epq\nIuw8M6pQm+lr2qSckBR2fPrYxTelSL+OniIi5//9V8SyTJmiqT7m7OwscvHKlSsijjkXNpuw\nRaQrLCxMRPLnz596cvLX0oiISDUyGaygoCCRQ9M6ffbL8XBTS334uZ0rpvR8t1KrOefi1Y5m\n2NhKs5ASFHRFEreNaTvWLzDG3FK5e2rbwq86VqnSefX1JLWz5Sp6cztHR0cb0+dTwvdP+OiL\n3bFS+OMBXrYSHhamvGarjMjRsLmciXV+R8d8ls+fufE4aFXPT+ZcE9N3B/Z6R4SdZ+Y93vRZ\njeqVyxYuWm30bou2i/19GlqIiBIW9jCNrdLW3t5IM1slxS5d0dHRImJi8sJjrszMzEREURQ1\nMhmquODgEDEp02XZmVvX/jl0JODarcA1vSsa3/rj0w7fnOZv5n/AVpqFbgcHx4hl5SEbL90O\nOnHoaGDIzRPz25eMD1rZ/eM519UOl2vFXdky9v0K7038O8Ku5oS1PzSxYqt8U0rYUd8e1Sp3\n/DVIV6LDwpVDy4iw83wTJuYWpkbG5uYmooSsH9XX53CkiMRGRyemsVXqzMxMNLNVUuzSZWFh\nIU+uGEkpJiZGRGxtbdL6DNJm6r3iQdiDgKVdyj15ioRlGe85S0e4SlLA4l+4EOw/YCvNQoX6\nbwsLu3vkh1YlnhyLsqvUe7FvjyISs2fxqmB1s+VKibd3T2tXsXzLb3bcsq89dO3xPeNr24qk\nu1XylI40RAWuHFzXrVa/xQEJZdp9v+f4r11KJP+VZueZaaZNp+7Zfzzw2p1r+75tbHvX/8vO\nE48mirmFhS6NrVKJiYnTzFZJsUuXk5OTiNy798I1lbdu3RJxLF6cK1kzQWdqnS+ftVmq68CM\nK3vWsRO5duUK3zrfHFtpFtKb2+TLZ5X6C72lh2d1vciVK1fUyZRrKfd2j/Gs0HDUmsuWNfrN\nP3T+bx+vUk+vAXVwcjJ/1VapL17cKcfD5nJx5xd3qly186z9kSVbT9h89vTqz2rnf7azZOeZ\nMUrC49jYuPiUA2Ja2GPU3OHviFz+Y+u/onNyKiLy8N691Dfv3L51SxEpXrx4zsbNHhS7dNm4\nu7uIXDh+PFXBvx4QECG6atWqvOpjeFn4xQP+/gcuPUw9NSk29rGIjZ0dG+ObYyvNOqGBe/z9\nj119lHpqfGxskoidHfdPpBR3ckKTFlP2R7h4+Rw8f2hu7+r5UxaIHpIGAAARsklEQVQPnbt7\nRZF7x49fS/mZRwEBwSKVqlUzFaRw6/du9Xv8etm85jC/gID141u4pHqAMzvPDLo4rZaFhXnL\nhWGpJxcrXvzpcbry7u5GEn/8+OmU85MCAgJFnKpVKyQawOaQvqrNmxeUpF1r1j14Pu3Kb6uP\niFHdD5rbv/pzeNHt3wbUr+/Re/mtlBOj/9qwI0bM6tatoVYsTWArzTL/zu9Qv379zzdFp5wY\numHDAZF8detWVCtWbnRz4fCpJ2KKeC/Zu2ZoDYeXXwFbvHnz8iIn1qxJcQL7vt/qnfHy9gcf\n8DSZlBL3fj3kt9vmlb/6c9eMD0u9/FIOdp4Z5FK+vKXIkb17Y1NOjd2/75giRuXKlRWxbdzc\nw1iC16058fyw3qO/Vm8OlyKtP6iW44GzhZoP0TMY/35b3UykYMsfj4clKUrs9a0ja1qJFOv9\nJ4+KzJxzUysbiRR4f/r+O/GKoihJkeeWdy5lJFJ80O5H6X0YT23qZvbymyfYSt9E8NSq8uID\nihMODnEW0Rdv//PJ8ERFUZTEB8d/bFlExLjShJO85DSF2zPr6cWk4c+3X71IyJKmNiK2dcbv\nvZ2gKPF3909t5Chi9+GKu6/+TF6UuGtAQZHiQ/YlvGoJdp4ZFLOjVxER49IfLz5xP15RlKSY\na7u/a+2sE3Hs5PdQURRFebi5e0ERs0oDN1+NVZTEsFPzvYrrxaz2j5fVjZ5lKHYZEn9uftPC\nehExts5vb6EXEeuqI/c8UDuW4YkNmNO6mKmIGNs6lS7rkvwwsXx1Jx+KUjuZIUm72LGVvoG0\nip2iPDwwuV4BIxExsy9epkxxe1MR0RdtOfdc3CtWk0dt6mwhojOxsEpD3RlP/kheX/2xi4mI\n6C3t81sZiYipa891vKztBRenVhURI7O0htKh51ZFYeeZcfe2Dy1vLiJiZGFfIHlXKGJf88s9\nYc8WefDX0EqWIqIzy+dgYyIieievxRfiX7NSg8IDijPE2K335lOVls1ZtPXE1Sizwm97dhzQ\nq4kLj3zNNLMK/ddfbLZ9wXy/Q4HBoQlW77ap0bRTj/bVCnBNQCY4uNXz9LRO/SZwYSt9E+bF\nq3p6WlcumvpOCdt3x+y53Hbd/AVbj52/GiaV631Uu2XXHq3L2758sjEve5jkWMPT8xUzXQs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AGkGxAwAA0Ij/A1SrcGvpuIl6AAAAAElF\nTkSuQmCC", "text/plain": [ "plot without title" ] }, "metadata": { "image/png": { "height": 420, "width": 420 }, "text/plain": { "height": 420, "width": 420 } }, "output_type": "display_data" } ], "source": [ "plot(regfit.fwd.summary$bic, type = \"l\", xlab = \"Number of Variables\", ylab = \"BIC\")\n", "bic.min = which.min(regfit.fwd.summary$bic)\n", "points(bic.min, regfit.fwd.summary$bic[bic.min], col = \"red\", cex = 2, pch = 20)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Forward Selection with Cross-Validation (the Wrong Way)\n", "Now we do model selection with cross-validation. But we still use the full data set for training (which is wrong!!!).\n", "\n", "Since there is no predict function for regsubsets, we define our own one.\n", "You don't need to fully understand this code now. If you are motivated to dive in deeper you can have a look at the bottom of this notebook." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "ExecuteTime": { "end_time": "2019-10-14T15:42:10.442196Z", "start_time": "2019-10-14T15:42:10.427Z" } }, "outputs": [], "source": [ "predict.regsubsets = function(object, newdata, id, ...) {\n", " form = as.formula(object$call[[2]])\n", " mat = model.matrix(form, newdata)\n", " coefi = coef(object, id = id)\n", " xvars = names(coefi)\n", " mat[,xvars] %*% coefi\n", "}" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we do 5-fold cross-validation. The variable `folds` will be an array of indices telling us in which of the `k` folds data-point `i` should lie. We will then loop over all folds and all models with 0 to 29 predictors (plus one variable for the intercept) and save the validation errors in the matrix `cv.errors.wrong` where we indicate in the variable name that these are the errors for the wrong cv approach.\n", "\n", "The next cell will take some time to run. The star in `[*]` on the left indicates that the cell is still running or in the bottom pane you can see that R is busy." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "k = 5\n", "folds = sample(1:k, nrow(data), replace = T)\n", "cv.errors.wrong = matrix(NA, k, 30)\n", "for (j in 1:k) {\n", " for (i in 1:30) {\n", " pred = predict(regfit.fwd, data[folds==j,], id = i)\n", " cv.errors.wrong[j,i] = mean( (data$y[folds==j] - pred)^2 )\n", " }\n", "}" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we average over all columns (folds) to get the mean cv-error for each number of predictors. The `2` in the `apply` function tells that the `mean` should be taken over each column.\n", "\n", "Then we plot and include in the plot as a dashed line also the standard deviation of the reponse, which should be a lower bound for our estimated test error." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "mean.cv.errors.wrong = apply(cv.errors.wrong, 2, mean)\n", "plot(mean.cv.errors.wrong, type = \"l\", ylim = c(0, 1.3), xlab = \"Number of Variables\", ylab = \"5-fold CV wrong\")\n", "cv.wrong.min = which.min(mean.cv.errors.wrong)\n", "points(cv.wrong.min, mean.cv.errors.wrong[cv.wrong.min], col = \"red\", cex = 2, pch = 20)\n", "abline(sd(data$y), 0, lty = \"dashed\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Forward Selection with Cross-Validation (the Right Way)\n", "The right way is almost the same as the wrong way, except that the training sets in the forward selection are the complements of the validation sets. Compare line 3 in the following cell to the for loop in the above section." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "cv.errors = matrix(NA, k, 30)\n", "for (j in 1:k) {\n", " regfit.fwd = regsubsets(y ~ ., data = data[folds!=j,], method = \"forward\", nvmax = 30)\n", " for (i in 1:30) {\n", " pred = predict(regfit.fwd, data[folds==j,], id = i)\n", " cv.errors[j,i] = mean( (data$y[folds==j] - pred)^2 )\n", " }\n", "}\n", "mean.cv.errors = apply(cv.errors, 2, mean)\n", "plot(mean.cv.errors, type = \"l\", ylim = c(1, 3),\n", " xlab = \"Number of Variables\", ylab = \"5-fold CV right\")\n", "cv.min = which.min(mean.cv.errors)\n", "points(cv.min, mean.cv.errors[cv.min], col = \"red\", cex = 2, pch = 20)\n", "abline(sd(data$y), 0, lty = \"dashed\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Model Selection Applied to the Hitters Data\n", "Here we will apply model section approaches to the Hitters data. We\n", "wish to predict a baseball player’s Salary on the basis of various statistics\n", "associated with performance in the previous year. This section follows the Lab 1 in chapter 6 from the textbook.\n", "\n", "First of all, we note that the Salary variable is missing for some of the\n", "players. The `is.na()` function can be used to identify the missing observations. It returns a vector of the same length as the input vector, with a TRUE\n", "for any elements that are missing, and a FALSE for non-missing elements.\n", "The `sum()` function can then be used to count all of the missing elements." ] }, { "cell_type": "code", "execution_count": 108, "metadata": { "ExecuteTime": { "end_time": "2019-10-14T16:15:16.280613Z", "start_time": "2019-10-14T16:15:16.258Z" } }, "outputs": [ { "data": { "text/html": [ "