Chapter 5 - ScikitLearn - Modelo lineal - 2.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Comenzando a modelar con Scikit-Learn"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "El más sencillo de los problemas y con el cual siempre se comienza en el mundo del machine learning es la **regresión lineal**.\n",
    "\n",
    "Una regresión lineal es un enfoque lineal para modelar la relación entre una variable escalar dependiente **y** y una o más variables explicativas (o variables independientes)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "heights = [[1.6], [1.65], [1.7], [1.73], [1.8]] # alturas en m\n",
    "\n",
    "weights = [[60], [65], [72.3], [75], [80]] # esos en Kg\n",
    "\n",
    "plt.title(\"Pesos vs alturas\")\n",
    "plt.xlabel(\"Alturas en metros\")\n",
    "plt.ylabel(\"Pesos en kg\")\n",
    "plt.plot(heights,weights,'k.')\n",
    "\n",
    "plt.axis([1.5, 1.85,50, 90]) # rangos de valores: xi,xf , yi,yf\n",
    "plt.grid(True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Se observa una relación lineal entre la talla y el peso de una persona, entonces podemos \"predecir\" o estimar el peso de una persona si tenemos su altura."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Usando la clase regresión lineal para ajustar el modelo\n",
    "\n",
    "Queremos trazar una recta que pase por todos los puntos o almenos que se acerque lo más posible a cada uno de ellos, esto podemos hacerlo con la librería Scikit-Learn en especifico con clase LinearRegression."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.linear_model import LinearRegression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Tenemos primero que definir que modelo queremos , en este caso una regresión lineal ( LinearRegression ) y luego modelamos con los datos que poseemos, en nuestro caso **heights** y **weights**."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None,\n",
       "         normalize=False)"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model = LinearRegression()\n",
    "model.fit(X = heights, y = weights)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Observar como heights tiene dos dimensiones (5,1), y tambien weight!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(5, 1)"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "checkheights = np.array(heights)\n",
    "checkheights.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(5, 1)"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "checkweights = np.array(weights)\n",
    "checkweights.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Esto se debe a que la función fit requiere tanto los argumentos X e Y requiere que sean bidimensionales."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Haciendo predicciones\n",
    "\n",
    "Una vez ya ajustado nuestro modelo con los datos podemos realizar predicciones de la siguiente manera."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "76.04"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "weight = model.predict([[1.75]])[0][0]\n",
    "round(weight,2) # mostramos con una aproximación de 2 digitos"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Como vimos se puede realizar predicciones con la funcion predict y pasandole una variable tipo bidimensional.\n",
    "Aqui se observa como para un tamaño de 1.75 m una persona pesará alrededor de 76.04 kg."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Graficando una linea de regresión lineal\n",
    "\n",
    "Como siempre debemos gráficar nuestro modelo para tener una visión más clara de lo que esta sucediendo."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f8c9f0b76d0>]"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.title(\"Pesos vs Alturas\")\n",
    "plt.xlabel(\"Altura en metros\")\n",
    "plt.ylabel(\"Peso en kg\")\n",
    "plt.grid(True)\n",
    "\n",
    "plt.axis([1.5, 1.85, 50, 90])\n",
    "plt.plot(heights, weights, 'k.')\n",
    "plt.plot(heights, model.predict(heights), color = 'r')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Obteniendo el gradiente e interceptandolo con la linea de Regresión lineal\n",
    "\n",
    "Debido a que si bien la linea muestra como se acerca a los puntos no sabemos exactamente en que valor la recta se intersecta con el eje y, y esto es debido a que nuestro dato comienza desde 1.60 pero podemos solucionarlo de la siguiente manera:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f8c9f0b1550>]"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.title(\"Pesos vs Alturas\")\n",
    "plt.xlabel(\"Altura en metros\")\n",
    "plt.ylabel(\"Peso en kg\")\n",
    "plt.grid(True)\n",
    "\n",
    "plt.plot(heights, weights, 'k.') # k. indica punto con punto (no linea)\n",
    "plt.axis([0,1.85, -200,200])\n",
    "\n",
    "extreme_heights = [[0], [1.8]]\n",
    "plt.plot(extreme_heights, model.predict(extreme_heights), color = 'r') # una linea"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-104.75454545],\n",
       "       [  81.20428816]])"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.predict(extreme_heights) # vemos que es bidimensional , si queremos el valor en si mismo agregamos [0][0] \n",
    "                               # como lo hizimos previamente"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Intersección con el eje y en ..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-104.75"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "round(model.predict([[0]])[0][0],2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "O tambien podemos usar"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-104.75"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "round(model.intercept_[0],2) # de nuevo ponemos 0 para quedarnos con el valor en si mismo y no un array"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Y obtenemos la gradiente de esta manera:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "103.31"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "round(model.coef_[0],2)"
   ]
  }
 ],
 "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": "2.7.12"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}