exercises/python_regression_exercise.ipynb

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    "### Simple Linear Regression using numpy (with pandas and pyplot)\n",
    "\n",
    "In the following, we'll take a closer look at the relationships between following variables:\n",
    "- temperature (y) versus latitude (x)\n",
    "- temperature (y) versus longitude (x)\n",
    "\n",
    "![title](images/latitude_longitude.jpg)"
   ]
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   "source": [
    "import csv\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Reading CSV file into dataframe\n",
    "Let's begin by reading Cities.csv into a dataframe."
   ]
  },
  {
   "cell_type": "code",
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   "source": [
    "f = open('../datasets/Cities.csv','r')\n",
    "cities = pd.read_csv(f)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Plotting a line\n",
    "Suppose we want to plot a line that passes through points (1,2) and (3,7). \n",
    "\n",
    "The way to do this would be as follows:"
   ]
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   "source": [
    "plt.plot([1,3], [2,7], color='green')\n",
    "plt.show()"
   ]
  },
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   "source": [
    "### Temperature versus latitude scatterplot\n",
    "A <b>scatterplot</b> is a type of plot that displays values for typically two variables for a set of data. \n",
    "\n",
    "In the following plot, each point represents a <b>city</b> with its corresponding <b>latitude</b> (x) and <b>temperature</b> (y) values."
   ]
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   "cell_type": "code",
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   "source": [
    "cities.plot.scatter(x='latitude', y='temperature')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Try changing 'latitude' to 'longitude'. What differences do you observe? "
   ]
  },
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   "source": [
    "### Add linear regression\n",
    "We want to calculate a simple <b>linear regression line</b> that <b>passes through the data</b> such that the distance of each data point from the line is minimized. \n",
    "\n",
    "Luckily, the Numpy package comes with a function called <b>ployfit()</b> that automatically calculates the linear regression model for us. "
   ]
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   "source": [
    "cities.plot.scatter(x='latitude', y='temperature')\n",
    "a,b = np.polyfit(cities.latitude, cities.temperature, 1) # Regression line is y = ax + b\n",
    "x1 = min(cities.latitude)\n",
    "x2 = max(cities.latitude)\n",
    "plt.plot([x1,x2], [a*x1 + b, a*x2 + b], color='red')\n",
    "plt.xlim(x1,x2)\n",
    "plt.show()"
   ]
  },
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   "source": [
    "Here, we see that temperature appears to be <b>negatively correlated</b> with latitude. "
   ]
  },
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   "source": [
    "### Correlation coefficients (r values)\n",
    "Recall that the value of <b>r</b> is between -1 and 1. \n",
    "- 1: maximum positive correlation \n",
    "- 0: no correlation\n",
    "- -1: maximum negative correlation\n",
    "\n",
    "In order to get the correlation coefficient of the linear regression model, we can use Numpy's <b>corrcoef()</b> function. "
   ]
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   "source": [
    "cc = np.corrcoef(cities.latitude, cities.temperature)[1,0]\n",
    "print('Correlation coefficient for temperature versus latitude:', cc)\n",
    "cc = np.corrcoef(cities.longitude, cities.temperature)[1,0]\n",
    "print('Correlation coefficient for temperature versus longitude:', cc)"
   ]
  },
  {
   "cell_type": "markdown",
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   "source": [
    "Thus, we confirm that temperature is <b>negatively correlated</b> to latitude as its correlation coeffiticent is closer to -1. \n",
    "\n",
    "Meanwhile, temperature does not seem to be correlated with longitude. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Linear regression for interactive temperature predictor\n",
    "We'll now compute latitude-temperature regression from cities in Norway, France, and Turkey."
   ]
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  {
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   "source": [
    "train = cities[(cities.country=='Norway') | (cities.country=='France') | (cities.country=='Turkey')]\n",
    "# Compute and show regression\n",
    "plt.scatter(train.latitude, train.temperature)\n",
    "a,b = np.polyfit(train.latitude, train.temperature, 1)\n",
    "x1 = min(train.latitude)\n",
    "x2 = max(train.latitude)\n",
    "plt.plot([x1,x2], [a*x1 + b, a*x2 + b], color='red')\n",
    "plt.xlim(x1,x2)\n",
    "plt.show()\n",
    "# Loop asking user for city name, compute predicted + actual temperature\n",
    "while True:\n",
    "    name = input('Enter city name (or \"quit\" to quit): ')\n",
    "    if name == 'quit': break\n",
    "    city = cities[cities.city == name]\n",
    "    if len(city) == 0:\n",
    "        print('City not in dataset')\n",
    "    else:\n",
    "        # Use float() to convert dataframe element to value\n",
    "        print('Predicted temperature:', a * float(city.latitude) + b)\n",
    "        print('Actual temperature:', float(city.temperature))"
   ]
  },
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   "cell_type": "markdown",
   "metadata": {
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   "source": [
    "### <font color=\"green\">Your Turn: World Cup Data</font>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
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   "source": [
    "# Read Players.csv into dataframe\n",
    "f = open('../datasets/Players.csv','r')\n",
    "players = pd.read_csv(f)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Q1: From the players data, compute and plot a linear regression for passes made (y-axis) versus minutes played (x-axis).\n",
    "Reminder: copy-paste-modify approach to programming!"
   ]
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   "source": [
    "Q2: Show the correlation coefficient for the passes-minutes regression. Also show correlation coefficients for tackles versus minutes, shots versus minutes, and saves versus minutes."
   ]
  },
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   "source": [
    "Q3: Use linear regression for an interactive number-of-passes predictor. \n",
    "\n",
    "Training data: compute minutes-passes regression for players from Greece, USA, and Portugal"
   ]
  },
  {
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   "source": [
    "<b>SUPER BONUS!!</b> Repeat the previous exercise but use separate predictor for the four different positions (goalkeeper,defender,midfielder,forward). \n",
    "\n",
    "Does it do better? Try comparing correlation coefficients against one regression for all players. \n",
    "\n",
    "Note: To extract a string value from a dataframe element use df.iloc[0].element, e.g., if \"player\" is a one-row dataframe, then player.iloc[0].position returns the player's position as a string"
   ]
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