{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<figure>\n",
    "  <IMG SRC=\"https://raw.githubusercontent.com/mbakker7/exploratory_computing_with_python/master/tudelft_logo.png\" WIDTH=250 ALIGN=\"right\">\n",
    "</figure>\n",
    "\n",
    "# Exploratory Computing with Python\n",
    "*Developed by Mark Bakker*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Notebook 13: Regression analysis I"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this Notebook, we learn how to fit a model to a set of data. In the first half of this Notebook, we fit several different models to the same data set, also called regression analysis. In the second half of this Notebook, we look under the hood of these regression analyses, we discuss how the best parameters are computed, how the goodness of fit can be quantified, and what these other parameters are that some of the regression functions return. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Root mean square error\n",
    "One way to quantify the fit between data and a model is to compute the root mean square error. The error is defined as the difference between the observed value and the modeled value. Another term for the error is the residual. If the error of data point $i$ is written as $\\varepsilon_i$, and the total number of observations is $N$, then the sum of squared errors $S$ is\n",
    "\n",
    "$$E = \\sum{\\varepsilon_i^2}$$\n",
    "\n",
    "When the total number of observations is $N$, the root mean square error $E$ is computed as\n",
    "\n",
    "$$E_s=\\sqrt{\\frac{1}{N}S}=\\sqrt{\\frac{1}{N}\\sum{\\varepsilon_i^2}}$$\n",
    "\n",
    "The root mean square error is an estimate of the goodness of fit and can be computed for any model and any dataset."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exercise 1. <a name=\"back1\"></a>Fit a straight line\n",
    "Load the $x,y$ values of 20 data points from the file `xydatafit.dat`. Fit a straight line through the data using the `linregress` function of `scipy.stats`. Note that the `linregress` function returns 3 other values beyond the slope and intercept (use `linregress?` to find out); more on these 3 additional values later on in this Notebook. Plot the data and the fitted straight line. Add a legend. Add the root mean square error as a title to the graph. Print the optimal values for the slope and intercept of the straight line to the screen."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a href=\"#ex1answer\">Answers to Exercise 1</a>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exercise 2. <a name=\"back2\"></a>Fit a polynomial\n",
    "Use the $x,y$ values of 20 data points from the file `xydatafit.dat`. Fit a second degree polynomial (a parabola) through the data using the `np.polyfit` function. Plot the data and the fitted parabola. Add a legend. Report the root mean squared error in the title. Did the root mean squared error improve?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a href=\"#ex2answer\">Answers to Exercise 2</a>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Fitting an arbitrary function\n",
    "Python functions to fit a straight line or polynomial are readily available. There are many other functions that you may want to use to fit to your data. The function `curve_fit` can be used to fit an arbitrary function that you define; `curve_fit` is part of the `scipy.optimize` package. The `curve_fit` function requires you to write a function that takes as its first argument the independent variable (in our case above that are the $x$-values) followed by the parameter(s) that you want to fit and returns the value of the function at all the $x$ values for the supplied parameters. For example, to fit a straight line, you need to write a function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def func(x, a, b):\n",
    "    return a * x + b"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The `curve_fit` function needs to be called with three arguments: the function that you want to fit, the values of the independent variable (in our case $x$), and the values of the depenedent variable (in our case $y$). The `curve_fit` funtion than returns an array with the optimal parameters (in a least squares sense) and a second array containing the covariance of the optimal parameters (more on that later). For example, for the case of Exercise 1:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "optimal parameters: [ 6.0774437 42.5824574]\n"
     ]
    }
   ],
   "source": [
    "from scipy.optimize import curve_fit\n",
    "x, y = np.loadtxt('xydatafit.dat')  # in case these were modified in one of the exercises\n",
    "popt, pcov = curve_fit(func, x, y)\n",
    "print('optimal parameters:', popt)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that these optimal parameters are identical to the values you computed in Exercise 1. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exercise 3. <a name=\"back3\"></a>Fit an exponential function with `curve_fit`\n",
    "Use the $x,y$ values of 20 data points from the file `xydatafit.dat`. Fit the function $f(x) = A\\exp(ax) + b$ through the data using the `curve_fit` function of `scipy.optimize`. Plot the data and the fitted function. Report the root mean squared error in the title. Did the root means squared error improve?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a href=\"#ex3answer\">Answers to Exercise 3</a>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Least squares\n",
    "In the exercises above, the *optimal* or *best* parameters were obtained with either the `linregress`, `polyfit` or `curve_fit` methods. But how do these methods do that? Or maybe a more fundamental question: 'What is *optimal*?' or 'What is *best*?' In this Notebook, we define *best* as the parameter set that minimizes the sum of the squared errors (so it also minimizes the root mean square error). Such an optimization approach is also referred to as a *least squares* approach. \n",
    "\n",
    "For example, consider the following three data points: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
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AwCrCCAAAsIowAgAArCKMAAAAqwgjAADAKsIIAACwijACAACsIowAAACrCCMAAMAqwggAALCKMAIAAKwijAAAAKsIIwAAwCrCCAAAsIowAgAArCKMAAAAqwgjAADAKsIIAACwijACAACsIowAAACrCCMAAMAqwggAALAq0nYBAK5cDQ3S3r1SVZXkdksZGVJEhO2qAHS1oM+MVFZWatasWYqLi1P37t01bNgwHTx4sNUxxcXFGjFihKKjo9W3b1+tXLmy3QUDCA+FhVJKinTHHdL99zf9mZLS1A7gyhJUGPn00081ZswYRUVFaevWrTp+/Lh++9vfqmfPni2OKSsrU2ZmpjIyMnT48GEtWbJE2dnZKigo6GjtAEJUYaE0ZYr04YeB7ZWVTe0EEuDK4jDGmLZ2fuyxx/TGG29o7969bd7B4sWLtWnTJpWWlvrbsrKy9M4772jfvn1teg2v1yuXy6Xa2lrFxsa2ed8ALj8NDU1nQL4dRC5wOKRevaSyMi7ZAKGurZ/fQZ0Z2bRpk9LT0zV16lQlJCRo+PDhWrVqVatj9u3bp/Hjxwe0TZgwQSUlJaqvr292jM/nk9frDVgAhIe9e1sOIpJkjFRR0dQPwJUhqDBy+vRprVixQv3799f27duVlZWl7OxsrVu3rsUx1dXVSkxMDGhLTEzU+fPndfbs2WbH5ObmyuVy+RePxxNMmQAuY1VVndsPQOgLKow0Njbqe9/7npYuXarhw4frxz/+sR566CGtWLGi1XEOhyNg/cKVoW+3X5CTk6Pa2lr/UlFREUyZAC5jbnfn9gMQ+oIKI263W4MHDw5oGzRokMrLy1sck5SUpOrq6oC2mpoaRUZGKi4urtkxTqdTsbGxAQuA8JCR0TQnpIX/i8jhkDyepn4ArgxBhZExY8boxIkTAW0nT55Unz59WhwzatQo7dy5M6Btx44dSk9PV1RUVDC7BxAGIiKkZcua/v7tQHJhPS+PyavAlSSoMLJgwQLt379fS5cu1XvvvaeXX35Z+fn5evjhh/19cnJyNGfOHP96VlaWzpw5o4ULF6q0tFRr1qzR6tWrtWjRos57FwBCyqRJ0quvSjfcENjeq1dT+6RJduoCYEdQt/ZK0p///Gfl5OTo1KlTSk1N1cKFC/XQQw/5t//whz/UBx98oKKiIn9bcXGxFixYoGPHjik5OVmLFy9WVlZWm/fJrb1AeOIJrEB4a+vnd9BhxAbCCAAAoec7ec4IAABAZyOMAAAAqwgjAADAKsIIAACwijACAACsIowAAACrCCMAAMAqwggAALCKMAIAAKwijAAAAKsIIwAAwCrCCAAAsIowAgAArCKMAAAAqwgjAADAKsIIAACwijACAACsIowAAACrCCMAAMAqwggAALCKMAIAAKwijAAAAKsIIwAAwCrCCAAAsIowAgAArCKMAAAAqwgjAADAKsIIAACwijACAACsIowAAACrCCMAAMCqoMLIk08+KYfDEbAkJSW12L+oqOii/g6HQ++++26HCwcAAOEhMtgBaWlp2rVrl389IiLikmNOnDih2NhY/3p8fHywuwUAAGEq6DASGRnZ6tmQ5iQkJKhnz57B7goAAFwBgp4zcurUKSUnJys1NVXTp0/X6dOnLzlm+PDhcrvdGjdunHbv3n3J/j6fT16vN2ABAADhKagwcsstt2jdunXavn27Vq1aperqao0ePVqffPJJs/3dbrfy8/NVUFCgwsJCDRgwQOPGjdOePXta3U9ubq5cLpd/8Xg8wZQJAABCiMMYY9o7+Ny5c7rxxhv1s5/9TAsXLmzTmIkTJ8rhcGjTpk0t9vH5fPL5fP51r9crj8ej2tragLknAADg8uX1euVyuS75+d2hW3t79OihIUOG6NSpU20eM3LkyEv2dzqdio2NDVgAAEB46lAY8fl8Ki0tldvtbvOYw4cPB9UfAACEt6Duplm0aJEmTpyo3r17q6amRr/+9a/l9Xo1d+5cSVJOTo4qKyu1bt06SVJeXp5SUlKUlpamuro6rV+/XgUFBSooKOj8dwIAAEJSUGHkww8/1IwZM3T27FnFx8dr5MiR2r9/v/r06SNJqqqqUnl5ub9/XV2dFi1apMrKSsXExCgtLU2bN29WZmZm574LAAAQsjo0gbWrtHUCDAAAuHx0yQRWAACAjiKMAAAAqwgjAADAKsIIAACwijACAACsIowAAACrCCMAAMAqwggAALCKMAIAAKwijAAAAKsIIwAAwCrCCAAAsIowAgAArCKMAAAAqwgjAADAKsIIAACwijACAACsIowAAACrCCMAAMAqwggAALCKMAIAAKwijAAAAKsIIwAAwCrCCAAAsIowAgAArCKMAAAAqwgjAADAKsIIAACwijACAACsIowAAACrCCMAAMCqoMLIk08+KYfDEbAkJSW1Oqa4uFgjRoxQdHS0+vbtq5UrV3aoYAAAEF4igx2QlpamXbt2+dcjIiJa7FtWVqbMzEw99NBDWr9+vd544w390z/9k+Lj4zV58uT2VQwAAMJK0GEkMjLykmdDLli5cqV69+6tvLw8SdKgQYNUUlKi5557jjACAAAktWPOyKlTp5ScnKzU1FRNnz5dp0+fbrHvvn37NH78+IC2CRMmqKSkRPX19S2O8/l88nq9AQsAAAhPQYWRW265RevWrdP27du1atUqVVdXa/To0frkk0+a7V9dXa3ExMSAtsTERJ0/f15nz55tcT+5ublyuVz+xePxBFMmAAAIIUGFkbvvvluTJ0/WkCFDdOedd2rz5s2SpBdffLHFMQ6HI2DdGNNs+zfl5OSotrbWv1RUVARTJgAACCFBzxn5ph49emjIkCE6depUs9uTkpJUXV0d0FZTU6PIyEjFxcW1+LpOp1NOp7MjpQEAgBDRoeeM+Hw+lZaWyu12N7t91KhR2rlzZ0Dbjh07lJ6erqioqI7sGgAAhImgwsiiRYtUXFyssrIyvfXWW5oyZYq8Xq/mzp0rqenyypw5c/z9s7KydObMGS1cuFClpaVas2aNVq9erUWLFnXuuwAAACErqMs0H374oWbMmKGzZ88qPj5eI0eO1P79+9WnTx9JUlVVlcrLy/39U1NTtWXLFi1YsEB/+MMflJycrOeff57begEAgJ/DXJhRehnzer1yuVyqra1VbGys7XIAAEAbtPXzm++mAQAAVhFGAACAVYQRAABgFWEEAABYRRgBAABWEUYAAIBVhBEAAGAVYQQAAFhFGAEAAFYRRgAAgFWEEQAAYBVhBAAAWEUYAQAAVhFGAACAVYQRAABgFWEEAABYRRgBAABWEUYAAIBVhBEAAGAVYQQAAFhFGAEAAFYRRgAAgFWEEQAAYBVhBAAAWEUYAQAAVhFGAACAVYQRAABgFWEEAABYRRgBAABWEUYAAIBVhBEAAGBVh8JIbm6uHA6H5s+f32KfoqIiORyOi5Z33323I7sGAABhIrK9Aw8cOKD8/HwNHTq0Tf1PnDih2NhY/3p8fHx7dw0AAMJIu86MfPHFF5o5c6ZWrVqla6+9tk1jEhISlJSU5F8iIiLas2sAABBm2hVGHn74Yd1zzz2688472zxm+PDhcrvdGjdunHbv3t1qX5/PJ6/XG7AAAIDwFPRlmg0bNujQoUM6cOBAm/q73W7l5+drxIgR8vl8+o//+A+NGzdORUVFuu2225odk5ubq3/5l38JtjQAABCCHMYY09bOFRUVSk9P144dO3TzzTdLkm6//XYNGzZMeXl5bd7pxIkT5XA4tGnTpma3+3w++Xw+/7rX65XH41FtbW3AvBMAAHD58nq9crlcl/z8DuoyzcGDB1VTU6MRI0YoMjJSkZGRKi4u1vPPP6/IyEg1NDS06XVGjhypU6dOtbjd6XQqNjY2YAEAAOEpqMs048aN09GjRwPaHnjgAQ0cOFCLFy9u86TUw4cPy+12B7NrAAAQpoIKI9dcc41uuummgLYePXooLi7O356Tk6PKykqtW7dOkpSXl6eUlBSlpaWprq5O69evV0FBgQoKCjrpLQAAgFDW7ueMtKSqqkrl5eX+9bq6Oi1atEiVlZWKiYlRWlqaNm/erMzMzM7eNQAACEFBTWC1pa0TYAAAwOXjO5nACgAA0NkIIwAAwCrCCAAAsIowAgAArCKMAAAAqwgjAADAKsIIAACwijACAACsIowAAACrCCMAAMAqwggAALCKMAIAAKwijAAAAKsIIwAAwCrCCAAAsIowAgAArCKMAAAAqwgjAADAKsIIAACwijACAACsIowAAACrCCMAAMAqwggAALCKMAIAAKwijAAAAKsIIwAAwCrCCAAAsIowAgAArCKMAAAAqwgjAADAKsIIAACwqkNhJDc3Vw6HQ/Pnz2+1X3FxsUaMGKHo6Gj17dtXK1eu7MhuAQBAGGl3GDlw4IDy8/M1dOjQVvuVlZUpMzNTGRkZOnz4sJYsWaLs7GwVFBS0d9cAACCMtCuMfPHFF5o5c6ZWrVqla6+9ttW+K1euVO/evZWXl6dBgwbpwQcf1Lx58/Tcc8+1q2AAABBe2hVGHn74Yd1zzz268847L9l33759Gj9+fEDbhAkTVFJSovr6+mbH+Hw+eb3egAUAAISnoMPIhg0bdOjQIeXm5rapf3V1tRITEwPaEhMTdf78eZ09e7bZMbm5uXK5XP7F4/EEWyYAAAgRQYWRiooKPfLII1q/fr2io6PbPM7hcASsG2Oabb8gJydHtbW1/qWioiKYMgEAQAiJDKbzwYMHVVNToxEjRvjbGhoatGfPHi1fvlw+n08REREBY5KSklRdXR3QVlNTo8jISMXFxTW7H6fTKafTGUxpAAAgRAUVRsaNG6ejR48GtD3wwAMaOHCgFi9efFEQkaRRo0bp9ddfD2jbsWOH0tPTFRUV1Y6SAQBAOAkqjFxzzTW66aabAtp69OihuLg4f3tOTo4qKyu1bt06SVJWVpaWL1+uhQsX6qGHHtK+ffu0evVq/elPf+qktwAAAEJZpz+BtaqqSuXl5f711NRUbdmyRUVFRRo2bJh+9atf6fnnn9fkyZM7e9cAACAEOcyF2aSXMa/XK5fLpdraWsXGxtouBwAAtEFbP7/5bhoAAGAVYQQAAFhFGAEAAFYRRgAAgFWEEQAAYBVhBAAAWEUYAQAAVhFGAACAVYQRAABgFWEEAABYRRgBAABWEUYAAIBVhBEAAGAVYQQAAFhFGAEAAFYRRgAAgFWEEQAAYBVhBAAAWEUYAQAAVhFGAACAVYQRAABgFWEEAABYRRgBAABWEUYAAIBVhBEAAGAVYQQAAFhFGAEAAFYRRgAAgFWEEQAAYBVhBAAAWEUYAQAAVgUVRlasWKGhQ4cqNjZWsbGxGjVqlLZu3dpi/6KiIjkcjouWd999t8OFAwCA8BAZTOdevXrp6aefVr9+/SRJL774ou677z4dPnxYaWlpLY47ceKEYmNj/evx8fHtLBcAAISboMLIxIkTA9afeuoprVixQvv37281jCQkJKhnz57tKhAAAIS3ds8ZaWho0IYNG3Tu3DmNGjWq1b7Dhw+X2+3WuHHjtHv37ku+ts/nk9frDVgAAEB4CjqMHD16VFdffbWcTqeysrL02muvafDgwc32dbvdys/PV0FBgQoLCzVgwACNGzdOe/bsaXUfubm5crlc/sXj8QRbJgAACBEOY4wJZkBdXZ3Ky8v12WefqaCgQP/+7/+u4uLiFgPJt02cOFEOh0ObNm1qsY/P55PP5/Ove71eeTwe1dbWBsw9AQAAly+v1yuXy3XJz++g5oxIUrdu3fwTWNPT03XgwAEtW7ZML7zwQpvGjxw5UuvXr2+1j9PplNPpDLY0AAAQgjr8nBFjTMBZjEs5fPiw3G53R3cLAADCRFBnRpYsWaK7775bHo9Hn3/+uTZs2KCioiJt27ZNkpSTk6PKykqtW7dOkpSXl6eUlBSlpaWprq5O69evV0FBgQoKCjr/nQAAgJAUVBj5+OOPNXv2bFVVVcnlcmno0KHatm2b7rrrLklSVVWVysvL/f3r6uq0aNEiVVZWKiYmRmlpadq8ebMyMzM7910AAICQFfQEVhvaOgEGAABcPtr6+c130wAAAKsIIwAAwCrCCAAAsIowAgAArCKMAAAAqwgjAADAKsIIAACwijACAACsIowAAACrCCMAAMAqwggAALCKMAIAAKwijAAAAKsIIwAAwCrCCAAAsIowAgAArCKMAAAAqwgjAADAKsIIAACwijACAACsIowAAACrCCMAAMAqwggAALCKMAIAAKwijAAAAKsIIwAAwCrCCAAAsIowAgAArCKMAAAAqwgjAADAqkjbBdjS0CDt3StVVUlut5SRIUVE2K4KAIArT1BnRlasWKGhQ4cqNjZWsbGxGjVqlLZu3drqmOLiYo0YMULR0dHq27evVq5c2aGCO0NhoZSSIt1xh3T//U1/pqQ0tQMAgK4VVBjp1auXnn76aZWUlKikpER///d/r/vuu0/Hjh1rtn9ZWZkyMzOVkZGhw4cPa8mSJcrOzlZBQUGnFN8ehYXSlCnShx8GtldWNrUTSAAA6FoOY4zpyAtcd911+s1vfqMf/ehHF21bvHixNm3apNLSUn9bVlaW3nnnHe3bt6/N+/B6vXK5XKqtrVVsbGy7a21oaDoD8u0gcoHDIfXqJZWVcckGAICOauvnd7snsDY0NGjDhg06d+6cRo0a1Wyfffv2afz48QFtEyZMUElJierr61t8bZ/PJ6/XG7B0hr17Ww4ikmSMVFHR1A8AAHSNoMPI0aNHdfXVV8vpdCorK0uvvfaaBg8e3Gzf6upqJSYmBrQlJibq/PnzOnv2bIv7yM3Nlcvl8i8ejyfYMptVVdW5/QAAQMcFHUYGDBigI0eOaP/+/frHf/xHzZ07V8ePH2+xv8PhCFi/cFXo2+3flJOTo9raWv9SUVERbJnNcrs7tx8AAOi4oG/t7datm/r16ydJSk9P14EDB7Rs2TK98MILF/VNSkpSdXV1QFtNTY0iIyMVFxfX4j6cTqecTmewpV1SRkbTnJDKyqZLMt92Yc5IRkan7xoAALSgww89M8bI5/M1u23UqFHauXNnQNuOHTuUnp6uqKioju46aBER0rJlTX//9omZC+t5eUxeBQCgKwUVRpYsWaK9e/fqgw8+0NGjR/X444+rqKhIM2fOlNR0eWXOnDn+/llZWTpz5owWLlyo0tJSrVmzRqtXr9aiRYs6910EYdIk6dVXpRtuCGzv1aupfdIkO3UBAHClCuoyzccff6zZs2erqqpKLpdLQ4cO1bZt23TXXXdJkqqqqlReXu7vn5qaqi1btmjBggX6wx/+oOTkZD3//POaPHly576LIE2aJN13H09gBQDgctDh54x0hc56zggAAOg63/lzRgAAADoDYQQAAFhFGAEAAFYRRgAAgFWEEQAAYBVhBAAAWEUYAQAAVhFGAACAVYQRAABgVdDf2mvDhYfEer1ey5UAAIC2uvC5famHvYdEGPn8888lSR6Px3IlAAAgWJ9//rlcLleL20Piu2kaGxv10Ucf6ZprrpHD4bBdjlVer1cej0cVFRV8T893jGPdNTjOXYPj3DU4zoGMMfr888+VnJysq65qeWZISJwZueqqq9SrVy/bZVxWYmNj+UXvIhzrrsFx7hoc567Bcf5/rZ0RuYAJrAAAwCrCCAAAsIowEmKcTqeeeOIJOZ1O26WEPY511+A4dw2Oc9fgOLdPSExgBQAA4YszIwAAwCrCCAAAsIowAgAArCKMAAAAqwgjIaSyslKzZs1SXFycunfvrmHDhungwYO2ywor58+f189//nOlpqYqJiZGffv21S9/+Us1NjbaLi3k7dmzRxMnTlRycrIcDoc2btwYsN0YoyeffFLJycmKiYnR7bffrmPHjtkpNoS1dpzr6+u1ePFiDRkyRD169FBycrLmzJmjjz76yF7BIepSv8/f9OMf/1gOh0N5eXldVl+oIYyEiE8//VRjxoxRVFSUtm7dquPHj+u3v/2tevbsabu0sPLMM89o5cqVWr58uUpLS/Xss8/qN7/5jX7/+9/bLi3knTt3TjfffLOWL1/e7PZnn31Wv/vd77R8+XIdOHBASUlJuuuuu/zfTYW2ae04f/nllzp06JB+8Ytf6NChQyosLNTJkyd17733Wqg0tF3q9/mCjRs36q233lJycnIXVRaiDELC4sWLza233mq7jLB3zz33mHnz5gW0TZo0ycyaNctSReFJknnttdf8642NjSYpKck8/fTT/ravv/7auFwus3LlSgsVhodvH+fmvP3220aSOXPmTNcUFYZaOs4ffvihueGGG8x///d/mz59+ph//dd/7fLaQgVnRkLEpk2blJ6erqlTpyohIUHDhw/XqlWrbJcVdm699Vb913/9l06ePClJeuedd/SXv/xFmZmZlisLb2VlZaqurtb48eP9bU6nU2PHjtWbb75psbLwV1tbK4fDwVnWTtbY2KjZs2fr0UcfVVpamu1yLnsh8UV5kE6fPq0VK1Zo4cKFWrJkid5++21lZ2fL6XRqzpw5tssLG4sXL1Ztba0GDhyoiIgINTQ06KmnntKMGTNslxbWqqurJUmJiYkB7YmJiTpz5oyNkq4IX3/9tR577DHdf//9fKlbJ3vmmWcUGRmp7Oxs26WEBMJIiGhsbFR6erqWLl0qSRo+fLiOHTumFStWEEY60SuvvKL169fr5ZdfVlpamo4cOaL58+crOTlZc+fOtV1e2HM4HAHrxpiL2tA56uvrNX36dDU2Nurf/u3fbJcTVg4ePKhly5bp0KFD/P62EZdpQoTb7dbgwYMD2gYNGqTy8nJLFYWnRx99VI899pimT5+uIUOGaPbs2VqwYIFyc3NtlxbWkpKSJP3/GZILampqLjpbgo6rr6/XtGnTVFZWpp07d3JWpJPt3btXNTU16t27tyIjIxUZGakzZ87opz/9qVJSUmyXd1kijISIMWPG6MSJEwFtJ0+eVJ8+fSxVFJ6+/PJLXXVV4D+LiIgIbu39jqWmpiopKUk7d+70t9XV1am4uFijR4+2WFn4uRBETp06pV27dikuLs52SWFn9uzZ+utf/6ojR474l+TkZD366KPavn277fIuS1ymCRELFizQ6NGjtXTpUk2bNk1vv/228vPzlZ+fb7u0sDJx4kQ99dRT6t27t9LS0nT48GH97ne/07x582yXFvK++OILvffee/71srIyHTlyRNddd5169+6t+fPna+nSperfv7/69++vpUuXqnv37rr//vstVh16WjvOycnJmjJlig4dOqQ///nPamho8J+Nuu6669StWzdbZYecS/0+fzvkRUVFKSkpSQMGDOjqUkOD7dt50Havv/66uemmm4zT6TQDBw40+fn5tksKO16v1zzyyCOmd+/eJjo62vTt29c8/vjjxufz2S4t5O3evdtIumiZO3euMabp9t4nnnjCJCUlGafTaW677TZz9OhRu0WHoNaOc1lZWbPbJJndu3fbLj2kXOr3+du4tbd1DmOM6dL0AwAA8A3MGQEAAFYRRgAAgFWEEQAAYBVhBAAAWEUYAQAAVhFGAACAVYQRAABgFWEEAABYRRgBAABWEUYAAIBVhBEAAGAVYQQAAFj1v2FCNCBq3FbrAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "xdata = np.array([5.0, 10.0, 15.0])\n",
    "ydata = np.array([3.0, 6.0, 7.0])\n",
    "plt.plot(xdata, ydata, 'bo', label='observed')\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can try to fit a straight line through these three points, but you can already see that the three points don't lie on a line, so there is no straight line that goes exactly through the three points. The straight line is written as $y=ax+b$, where $a$ is the slope of the line and $b$ is called the intercept (it is the value of $y$ for $x=0$). We write a function that takes as input arguments an array of observed $x$ values and an array of corresponding $y$ values, and values for the slope $a$ and intercept $b$. The function returns the sum of squared errors, where the error is defined as the difference betweeen the observed value of $y$ and the value of the straight line at that same $x$ value. The equation for the error at point $i$ is $\\varepsilon_i$ and may be written as\n",
    "\n",
    "$\\varepsilon_i = y_i - (ax_i + b)$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "def sse(a, b, x=xdata, y=ydata):\n",
    "    error = y - (a * x + b)\n",
    "    return np.sum(error ** 2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As you can see, different values of $a$ and $b$ give different values for the sum of squared errors `sse`. The `sse` for $a=1$, $b=2$ is larger than for $a=1$, $b=1$. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "sse of a=1, b=2: 152.0\n",
      "sse of a=1, b=1: 115.0\n"
     ]
    }
   ],
   "source": [
    "print('sse of a=1, b=2:', sse(a=1, b=2))\n",
    "print('sse of a=1, b=1:', sse(a=1, b=1))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "What we can do is compute the `sse` function for a larger number of $a$ and $b$ values. If we do that on a regular grid, we can create contours of the `sse` function. The `sse` function is constant along any contour. A contour map of the `sse` function is similar to an elevation map. The goal is now to find the combination of $a$ and $b$ that gives the smallest value of the sum of squared errors. In the graph below, you can see that the smallest value of `sse` is obtained at $a\\approx 0.4$, $b\\approx 1.3$ (you have to look closely for the darkest blue in the figure; the area beyond the yellow is $E>10$)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "a, b = np.meshgrid(np.linspace(0.2, 0.6, 50), np.linspace(0, 2, 50))\n",
    "ssevec = np.vectorize(sse)\n",
    "z = ssevec(a, b)\n",
    "plt.figure()\n",
    "plt.contourf(a, b, z, np.linspace(0, 10, 100))\n",
    "plt.colorbar()\n",
    "plt.xlabel('a')\n",
    "plt.ylabel('b');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "How do we minimize the sum of squared errors? As usual, we find the minimum of a function by taking the derivative and setting it to zero. This is a little involved, but not too difficult. The sum of squared errors is written as $E$\n",
    "\n",
    "$$\n",
    "E=\\sum_{i=1}^N\\varepsilon_i^2=\n",
    "\\sum_{i=1}^N[y_i-(ax_i+b)]^2\n",
    "$$\n",
    "\n",
    "where $N$ is the number of observations. The slope $a$ and intercept $b$ are determined such that $E$ is minimized, which means that the following derivatives are zero\n",
    "\n",
    "$$\\frac{\\partial E}{\\partial a}=0 \\qquad \\frac{\\partial E}{\\partial b}=0$$\n",
    "\n",
    "Differentiation gives (using the chain rule)\n",
    "\n",
    "$$\n",
    "\\frac{\\partial E}{\\partial a}=\\sum_{i=1}^N[2(y_i-ax_i-b)(-x_i)]=\n",
    "2a\\sum_{i=1}^Nx_i^2+2b\\sum_{i=1}^Nx_i-2\\sum_{i=1}^Nx_iy_i\n",
    "$$\n",
    "\n",
    "$$\n",
    "\\frac{\\partial E}{\\partial b}=\\sum_{i=1}^N[2(y_i-ax_i-b)(-1)]=\n",
    "2a\\sum_{i=1}^Nx_i+2bN-2\\sum_{i=1}^Ny_i\n",
    "$$\n",
    "\n",
    "Setting the derivatives equal to zero and division by 2 gives\n",
    "\n",
    "$$\n",
    "a\\sum_{i=1}^Nx_i^2+b\\sum_{i=1}^Nx_i-\\sum_{i=1}^Nx_iy_i=0\n",
    "$$\n",
    "\n",
    "$$\n",
    "a\\sum_{i=1}^Nx_i+bN-\\sum_{i=1}^Ny_i=0\n",
    "$$\n",
    "\n",
    "This system of two linear equations with two unknowns ($a$ and $b$) may be solved to give\n",
    "\n",
    "$$ a=\\frac{N\\sum_{i=1}^Nx_iy_i-\\sum_{i=1}^Nx_i\\sum_{i=1}^Ny_i}\n",
    "{N\\sum_{i=1}^Nx_i^2-\\sum_{i=1}^Nx_i\\sum_{i=1}^Nx_i}\n",
    "$$\n",
    "\n",
    "$$\n",
    "b=\\bar{y}-a\\bar{x}\n",
    "$$\n",
    "where $\\bar{x}$ and $\\bar{y}$ are the mean values of $x$ and $y$, respectively. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exercise 4. <a name=\"back4\"></a>Fitting a straight line revisited\n",
    "Compute the optimal values (in the least squares sense) of $a$ and $b$ using the two equations derived above and the corresponding sum of squared errors (using the `xdata` and `ydata` arrays for the three points given above). Next, use the `linregress` function of the `scipy.stats` package to compute the optimal values and verify that the `linregress` function gives the same answers. Create a graph that shows the three data points and the fitted straight line."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a href=\"#ex4answer\">Answers to Exercise 4</a>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### The correlation coefficient, $p$-value and standard error. \n",
    "The `linregress` function returns 5 values. Besides the slope and intercept, these are somewhat cryptically defined as the correlation coefficient, the $p$-value, and the standard error. Each of these three values are a quantification of the goodness of fit. According to statisticians, these terms in the `scipy.stats` documentation are somewhat imprecisely defined (they will likely be updated in the future). This is what they mean:\n",
    "\n",
    "The square of the correlation coefficient $r$ is the *r-squared value* and is defined as\n",
    "\n",
    "$$r^2 = 1 - \\sum{(y_i - \\hat{y}_i)^2} \\left/ \\sum{(y_i - \\bar{y})^2} \\right. $$\n",
    "\n",
    "where $y_i$ is the $y$ value of data point $i$, while $\\hat{y}_i$ is the fitted values at data point $i$. It can also be written as \n",
    "\n",
    "$$r^2 = \\frac{\\text{var}(y) - \\text{var}(y-\\hat{y})}{\\text{var}(y)}$$\n",
    "\n",
    "So the $r^2$ value is the variance of $y$ minues the variance of the remaining residuals (the data values minus the fitted values), divided by the variance of $y$, and is also referred to as the 'percentage of variance explained'. If the model goes exactly through the data (a perfect fit), then the variance of the residuals is zero, and $r^2=1$. If the model doesn't do much better than simply the mean of $y$, then the  $r^2$ is very close zero. A value of $r^2$ close to 1 is generally a good thing, but it is not possible to say anything definitive about the goodness of fit by just reporting the $r^2$ value (although many people do)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The standard error returned by the `linregress` model is the estimated standard deviation of the fitted slope. The equation is"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$s = \\sqrt{\\frac{\\sum(y_i-\\hat{y}_i)^2}{N-2}} \\left/ \\sqrt{\\sum{(x_i-\\bar{x})^2}} \\right.$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The standard deviation of the slope should be interpreted similar to the standard deviation of the mean. The computed slope is a statistical value so it has an estimated standard deviation. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The $p$-value is related to the question whether the estimated slope is significantly different from zero. When the slope is significantly different from zero, you can state that there is a linear relationship between the two variables. The $p$-value is related to the question whether the estimated slope is significantly different from zero when you perform a $t$-test. When the $p$-value is less than 0.05, this means that when you perform a two-sided $t$-test you can reject the null hypothesis that the slope is zero in favor of the alternative hypothesis that the slope is not zero. In layman terms: it means that there is less than 5% chance that the slope is zero and more than 95% chance that the slope is not zero. Or even simpler: the slope is significantly different from zero. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exercise 5. <a name=\"back5\"></a>Verification of goodness of fit parameters\n",
    "Implement the equations for $r^2$ and $s$ given above to verify that the values returned by the `linregress` function are correct. Perform a two-sided hypothesis test with significance level 5% where the null hypothesis is that the slope of the fitted line is zero and the alternative hypothesis is that the slope is not zero. Draw the probability density function of a $t$-distribution with mean 0 and standard deviation equal to the computed value of $s$. Use $N-2$ as the number of degrees of freedom (You subtract the number of parameters from $N$ as you used up these two degrees of freedom). Draw red vertical lines indicating the 2.5% and 97.5% percentiles according to the $t$-distribution. Draw a heavy black vertical line at the position of the computed value of the slope. Decide whether you can reject the null hypothesis that the slope is zero in favor of the alternative hypothesis that the slope is not 0 and add that as a title to the figure."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a href=\"#ex5answer\">Answers to Exercise 5</a>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Meaning of the $p$-value\n",
    "If you did the previous exercise correctly, you found out that the slope was not significantly different from zero (you could not reject the null hypothesis that the slope is zero with significance level 5%). The $p$ value returned by the `linregress` function means that if you would have performed the hypothesis with significance level $p$, then you would not have rejected the hypothesis. Let's try it. First we recompute the $p$ and $s$ value of the fitted line"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "p value: 0.1789123750220667 s value: 0.11547005383792511\n"
     ]
    }
   ],
   "source": [
    "from scipy.stats import linregress\n",
    "slope, intercept, r, p, s = linregress(xdata, ydata)\n",
    "print('p value:', p, 's value:', s)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "upper and lower bound for significance level 0.1789123750220667 is: -0.4000000000044717 0.4000000000044717\n"
     ]
    }
   ],
   "source": [
    "from scipy.stats import t\n",
    "p1, p2 = t.ppf([p / 2, 1 - p / 2], 1, loc=0, scale=s)\n",
    "print('upper and lower bound for significance level', p, 'is:', p1, p2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Just to be complete, we can compute the $p$ value from the $t$ distribution as"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "p-value from t-distribution: [[0.33333333 0.322417   0.31213621 ... 0.12433906 0.12266646 0.12103772]\n",
      " [0.33333333 0.322417   0.31213621 ... 0.12433906 0.12266646 0.12103772]\n",
      " [0.33333333 0.322417   0.31213621 ... 0.12433906 0.12266646 0.12103772]\n",
      " ...\n",
      " [0.33333333 0.322417   0.31213621 ... 0.12433906 0.12266646 0.12103772]\n",
      " [0.33333333 0.322417   0.31213621 ... 0.12433906 0.12266646 0.12103772]\n",
      " [0.33333333 0.322417   0.31213621 ... 0.12433906 0.12266646 0.12103772]]\n"
     ]
    }
   ],
   "source": [
    "print('p-value from t-distribution:', 2 * (1 - t.cdf(a, 1, loc=0, scale=s)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Recall that the $p$-value only makes sense if the residuals are independent and Normally distributed. For the problem we are looking at with 3 data points that is, of course, impossible to say. But when you have more data, you really need to check or, alternatively, use a method that doesn't require the Normality assumption. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "One last thing about the significance level. We state that the slope is signficantly different from zero when $p<0.05$. But that means that there is still a 5% chance that the slope is different from zero by chance. Let's try that in the following exercise"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true,
    "jupyter": {
     "outputs_hidden": true
    }
   },
   "source": [
    "### Exercise 6. <a name=\"back6\"></a>Getting a value of $p<0.05$ by chance\n",
    "Perform the following experiment: Generate 100 $x$ values randomly from a uniform distribution between 0 and 10 using the `np.random.rand` function. Generate 100 $y$ values randomly from a uniform distribution between 0 and 10. Fit a straight line using `linregress`. Perform the experiment 1000 time and count the number of times that the $p$-value is smaller than 0.05. As you will see, you will get approximately 50 out of the 1000 experiments where a line is fitted with a $p$-value smaller than 0.05 just by chance (as there really is no correlation between the random $x$ and $y$ values).  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a href=\"#ex6answer\">Answers to Exercise 6</a>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Answers to the exercises"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a name=\"ex1answer\">Answers to Exercise 1</a>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "slope, intercept: 6.077443700312609 42.58245735877516\n"
     ]
    },
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from scipy.stats import linregress\n",
    "x, y = np.loadtxt('xydatafit.dat')\n",
    "slope, intercept, r_value, p_value, std_err = linregress(x, y)\n",
    "yfit = slope * x + intercept\n",
    "plt.figure()\n",
    "plt.plot(x, y, 'bo', label='observed')\n",
    "plt.plot(x, yfit, 'r', label='fit')\n",
    "rmse = np.sqrt(np.sum((yfit - y) ** 2) / len(y))\n",
    "plt.title('RMSE: '+str(rmse))\n",
    "plt.legend(loc='best')\n",
    "print('slope, intercept:', slope, intercept)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a href=\"#back1\">Back to Exercise 1</a>\n",
    "\n",
    "<a name=\"ex2answer\">Answers to Exercise 2</a>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x, y = np.loadtxt('xydatafit.dat')\n",
    "a, b, c = np.polyfit(x, y, 2)\n",
    "yfit = a * x ** 2 + b * x + c\n",
    "plt.figure()\n",
    "plt.plot(x, y, 'bo', label='observed')\n",
    "plt.plot(x, yfit, 'r', label='fit')\n",
    "rmse = np.sqrt(np.sum((yfit - y) ** 2) / len(y))\n",
    "plt.legend(loc='best')\n",
    "plt.title('RMSE: '+str(rmse));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a href=\"#back2\">Back to Exercise 2</a>\n",
    "\n",
    "<a name=\"ex3answer\">Answers to Exercise 3</a>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from scipy.optimize import curve_fit\n",
    "\n",
    "def func(x, A, a, b):\n",
    "    y = A * np.exp(a * x) + b\n",
    "    return y\n",
    "\n",
    "popt, pcov = curve_fit(func, x, y)\n",
    "yfit = func(x, *popt)\n",
    "plt.figure()\n",
    "plt.plot(x, y, 'bo', label='observed')\n",
    "plt.plot(x, yfit, 'r', label='fit')\n",
    "plt.legend(loc='best')\n",
    "rmse2 = np.sqrt(np.sum((yfit - y) ** 2) / len(y))\n",
    "plt.title('RMSE: '+str(rmse2));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a href=\"#back3\">Back to Exercise 3</a>\n",
    "\n",
    "<a name=\"ex4answer\">Answers to Exercise 4</a>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "def sse(a, b, x=xdata, y=ydata):\n",
    "    error = y - (a * x + b)\n",
    "    return np.sum(error ** 2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "optimal values of a and b: 0.4 1.333333333333333\n",
      "sse: 0.6666666666666667\n"
     ]
    }
   ],
   "source": [
    "xdata = np.array([5.0, 10.0, 15.0])\n",
    "ydata = np.array([3.0, 6.0, 7.0])\n",
    "N = len(xdata)\n",
    "a = (N * np.sum(xdata * ydata) - np.sum(xdata) * np.sum(ydata) ) / \\\n",
    "    (N * np.sum(xdata ** 2) - np.sum(xdata) * np.sum(xdata))\n",
    "b = np.mean(ydata) - a * np.mean(xdata)\n",
    "print('optimal values of a and b:', a, b)\n",
    "print('sse:', sse(a, b))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "slope and intercept according to linregress: 0.4 1.333333333333333\n"
     ]
    }
   ],
   "source": [
    "from scipy.stats import linregress\n",
    "slope, intercept, r, p, s = linregress(xdata, ydata)\n",
    "print('slope and intercept according to linregress:', slope, intercept)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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WZs+WvvsuYEOL5NLg4mPXE+M6cA4B4DLOnrU3P6xaVfrsM7s6aPBgKSFB6t79qm7u689cNVUU8v93rzxz5ozy5cvncDW4EWf+/47eIS66IykAeN2CBdLAgVJiom23aiVNnixVr+5sXT7EVcElODhYRYoU0aFDhyRJ+fPnV1CAJ0+3McbozJkzOnTokIoUKaJgP91nAACuyU8/SXFx0uef2/bNN0vjx9sVRHzPZeGq4CIp8+7JF8IL3KlIkSLcCRsAzpyRRo2yG8mlpkohIXZa6MUXpYIFna7OJ7kuuAQFBSkyMlIlS5ZUWlqa0+XgOoSEhDDSAiCwGSN98ok0aJC0d6/ti42V3nzT7oSLy3JdcLkgODiYLz8AgPskJNjlzQsX2nbZstIbb0gPPMC00FVw5aoiAABc59QpadgwqWZNG1pCQ+2U0PbtUseOhJar5NoRFwAAXMEY6d//lp55Rtq/3/a1bStNnCjdcoujpbkRwQUAAG/ZutVuzb94sW1XqCBNmiS1a+dsXS7GVBEAAJ6WnGxHWOrUsaElPFx65RVp2zZCyw1ixAUAAE8xRnr/fWnIEOngQdvXoYM0YYIdbcENI7gAAOAJGzdK/fpJy5fbduXKdnnz3Xc7W5efYaoIAIAbceKEXd5cr54NLfnz203lNm8mtHgBIy4AAFyPjAxp1ixp6FDp8GHb17mzNG6c3ZsFXkFwAQDgWq1da6eFVq2y7ZgYezPEP/3J2boCAFNFAABcrWPHpKeflho2tKGlYEF7n6GNGwktuYQRFwAAriQ9XXrnHen556WjR21ft242tERFOVtbgCG4AACQkx9+sNNCa9bYdo0a0pQpUsuWztYVoJgqAgAgO4cPS48/LjVubENL4cJ2m/516wgtDmLEBQCAP0pPl6ZNszdAPHHC9vXsKY0eLZUu7Whp8MKIy/nz5/Xiiy+qQoUKypcvnypWrKhXX31VGRkZnn4rAAA8a8UKqUEDOzV04oTdsn/5cmnmTEKLj/D4iMuYMWM0bdo0zZo1S9WrV9eaNWv06KOPKiIiQgMHDvT02wEAcOMOHrT7sbz3nm0XKSK9/rr01FNScLCjpSErjweX77//Xu3bt1fbtm0lSeXLl9eHH36oNRcuagIAwFecP28vtB0xwt4YMShI6t3b7nxbooTT1SEbHp8quv322/Xtt99q586dkqSNGzdq+fLluvfee7M9PiUlRcnJyVl+AADwuqVLpbp1pUGDbGhp0MDuzTJ9OqHFh3l8xGXo0KFKSkpSTEyMgoODlZ6ertdff11du3bN9vj4+Hi98sorni4DAIDs/fab9Oyz0ocf2naxYlJ8vPTYY0wLuYDHR1zmzJmj2bNn64MPPtC6des0a9YsjRs3TrNmzcr2+OHDhyspKSnzZ9++fZ4uCQAAKTXVbhhXpYoNLUFBdhfcnTulJ54gtLhEkDHGePIFo6OjNWzYMPXt2zez77XXXtPs2bO1Y8eOKz4/OTlZERERSkpKUuHChT1ZGgAgUH3zjdS/v3The6hxY2nqVHtHZ3hEbn1/e3zE5cyZM8qTJ+vLBgcHsxwaAJD79u61d2y+6y4bWkqUkGbMsMueCS2u5PFrXNq1a6fXX39dZcuWVfXq1bV+/XpNmDBBjz32mKffCgCA7KWkSOPH2yXNZ85IefLYvVleecUudYZreXyq6OTJk3rppZf0ySef6NChQ4qKilLXrl318ssvKzQ09IrPZ6oIAHBDvvpKGjBA2rXLtps3t0uea9Vyti4/l1vf3x4PLjeK4AIAuC6JiXZp82ef2Xbp0tK4cfYuzkFBztYWAFx7jQsAALnq7Fk7BVStmg0tefNKzzwjJSRI3bsTWvwMN1kEALiTMdKCBVJcnB1tkaRWrey0ULVqjpYG72HEBQDgPj/9JN13n9S+vQ0tN98szZkjffstocXPEVwAAO5x5oz04otS9erSF19IISHSsGF2qXOXLkwLBQCmigAAvs8Yad48afBguzeLJMXGSm++aXfCRcAguAAAfFtCgt31dtEi2y5bVpo4UerQgRGWAMRUEQDAN506ZaeBata0oSU01E4Tbd8uPfAAoSVAMeICAPAtxkj//rdd0rx/v+1r29aOstxyi6OlwXkEFwCA79i61U4LLV5s2xUrSpMm2RVEgJgqAgD4guRke+Ft7do2tISHS6++aoMMoQV/wIgLAMA5xkjvvy8NGSIdPGj7OnSQ3nhDKl/eycrgowguAABnbNxo79i8fLltV65slzfffbezdcGnMVUEAMhdJ07Y61jq1bOhJX9+adQoafNmQguuiBEXAEDuyMiQZs60S5wPH7Z9nTtL48dL0dGOlgb3ILgAALxv7Vo7LbRqlW1XrSpNniy1bu1sXXAdpooAAN5z9Kj09NNSw4Y2tBQsKP3tb9KGDYQWXBdGXAAAnpeeLr3zjjR8uHTsmO3r1s2GlqgoZ2uDqxFcAACe9cMPdlpozRrbrllTmjJFatHC2brgF5gqAgB4xuHDUu/eUuPGNrQULmx3vV23jtACj2HEBQBwY86fl/7xD3sDxBMnbF/PntKYMVKpUo6WBv9DcAEAXL8VK6S+fe1mcpJUp440darUtKmjZcF/MVUEALh2Bw/aUZXbb7ehpUgRG1jWrCG0wKsYcQEAXL20NBtQRoywN0YMCrLXtYwaJZUo4XR1CAAEFwDA1Vm61K4W2rLFths0sCGmUSNn60JAYaoIAJCz/fvtHix33GFDS7Fi0ttv22XPhBbkMkZcAADZS021y5lffVU6dcpOC/XpI732mlS0aI5PTU+Xli2TDhyQIiOl5s2l4OBcqht+jeACALjUN9/YOzjv2GHbTZrYTeTq1bviU+fNkwYOlH799b99ZcrYDNSxo5fqRcBgqggA8F9790qdOkl33WVDS4kS0owZ0vLlVx1aOnXKGlokO9vUqZN9HLgRBBcAgJSSYlcGVa0qzZ0r5ckjDRgg7dwp9epl21eQnm5HWoy59LELfXFx9jjgehFcACDQffmlVKOG9MIL0pkz9oKU9evt3E6RIlf9MsuWXTrS8kfGSPv22eOA60VwAYBAlZgodegg3Xuv9NNPUunS0uzZdtlzrVrX/HIHDnj2OCA7BBcACDRnz0qvvCJVqyZ99pmUN6/0zDNSQoLUvbtdPXQdIiM9exyQHVYVAUCgMEZasMBeaJKYaPvuvFOaPNmGmBvUvLldPbR/f/bXuQQF2cebN7/ht0IAY8QFAALBTz9J990ntW9vQ8vNN0tz5thlzx4ILZLdp2XSJPvniwdtLrQnTmQ/F9wYggsA+LMzZ6QXX5SqV5e++EIKCZGGDbNLnbt0ue5pocvp2FH6+GObi/6oTBnbzz4uuFFMFQGAPzLGbpoyeLDdm0WSYmOlN9+UqlTx6lt37GgHdtg5F95AcAEAf7Njh92DZdEi2y5b1s7RdOjg8RGWywkOtrc2AjyNqSIA8BenTklDh9qlzIsWSWFh0ksvSdu3Sw88kGuhBfAmRlwAwO2MsRfaPvusXdIjSW3b2itlK1VytjbAwwguAOBmW7famyEuXmzbFSvawHLffc7WBXgJU0UA4EbJyfbC29q1bWgJD5defdUGGUIL/BgjLgDgJsbYbfmHDJF+/932PfCANGGCVL68o6UBuYHgAgBusXGj1K+ftHy5bVeubHe9bdPG2bqAXMRUEQD4uhMn7HUs9erZ0JI/vxQfL23eTGhBwGHEBQB8VUaGNHOm3en28GHb16WLNG6cFB3taGmAUwguAOCL1q6V+vaVfvjBtqtWtdNCrVs7WxfgMKaKAMCXHD0q9ekjNWxoQ0vBgnaEZcMGQgsgRlwAwDekp0v//Kf0/PPSsWO2r1s36W9/k6KinK0N8CEEFwBw2g8/2GmhtWttu2ZNacoUqUULZ+sCfBBTRQDglMOHpd69pcaNbWgpXNjuertuHaEFuAxGXAAgt50/L02bZm+AeOKE7evVSxo9WipVysnKAJ9HcAGA3LRihZ0W2rjRtuvWtdNCTZs6WxfgEkwVAUBuOHhQ+vOfpdtvt6GlSBFp6lRp9WpCC3ANCC4A4E1padLEiVKVKtK//iUFBUlPPCHt3Cn95S9ScLDTFQKuwlQRAHjLkiV2q/4tW2y7YUM7LdSokaNlAW7GiAsAeNr+/VLXrlKrVja0FCsmTZ8urVpFaAFuEMEFADwlNdVuGBcTI330kZ0WevppOy30+ONSHv4vF7hRTBUBgCd8842dFtqxw7abNLHTQvXqOVsX4GeI/wBwI/bulTp1ku66y4aWkiXtHZ2XLye0AF5AcAGA65GSIr3+up0WmjvXrg4aOFBKSJB69mRaCPASpooA4Fp9+aU0YID000+23by5nRaqVcvZuoAAwD8JAOBqJSZK7dtL995rQ0vp0tLs2dLSpYQWIJcw4gIgV6SnS8uWSQcOSJGRdpDCNXuvnT0rjR1r7yV07pyUN6+dFnr5ZXtjRAC5xisjLvv379cjjzyiYsWKKX/+/KpTp47WXrhdO4CAM2+eVL683dakWzf73/Llbb9PM0aaP1+qXl0aOdKGljvvtFv2jxtHaAEc4PERl+PHj6tZs2Zq1aqVvvzyS5UsWVK7d+9WkSJFPP1WAFxg3jy76MaYrP3799v+jz+WOnZ0prYc/fSTvY7lyy9tu0wZacIEW3RQkLO1AQEsyJiL/+/kxgwbNkwrVqzQsmXLruv5ycnJioiIUFJSkgrzrxnA1dLT7cjKr79m/3hQkM0DiYk+NG10+rQUH283kktNlUJCpGeekV54QSpY0OnqAJ+VW9/fHp8qmj9/vho0aKDOnTurZMmSqlu3rqZPn37Z41NSUpScnJzlB4B/WLbs8qFFsqMw+/bZ4xxnjF3WXLWqXeacmiq1aWO37I+PJ7QAPsLjwWXPnj166623VLlyZX399dfq06ePBgwYoPfeey/b4+Pj4xUREZH5Ex0d7emSADjkwAHPHuc1O3bYkNKpk01S5cpJn3xip4luvdXh4gD8kcenikJDQ9WgQQOtXLkys2/AgAFavXq1vv/++0uOT0lJUUpKSmY7OTlZ0dHRTBUBfmDJEnsh7pUsXizdcYe3q8nGyZPSX/8qvfGGdP68FBYmDR1qf/Lnd6AgwL1ya6rI4xfnRkZGqlq1aln6qlatqrlz52Z7fFhYmMLCwjxdBgAf0Ly5vYZl//5LL86V/nuNS/PmuVyYMdKcOfbald9+s3333SdNnChVqpTLxQC4Fh6fKmrWrJkSEhKy9O3cuVPlypXz9FsB8HHBwdKkSfbPFy/EudCeODGXL8zdssUuae7a1YaWihWlBQvsD6EF8HkeDy6DBg3SqlWrNGrUKP3000/64IMP9Pbbb6tv376efisALtCxo13yfPPNWfvLlMnlpdBJSdLgwVKdOnYOKzxcevVVaetWO9oCwBU8fo2LJP3v//6vhg8frl27dqlChQoaPHiwnnjiiat6LsuhAf/k2M65xtht+YcMkX7/3fY98IDdk6V8+VwoAAgMufX97ZXgciMILgA8ZuNGqW9facUK265cWZo82a4gAuBRrt3HBQAcd/y41L+/VK+eDS3589u9WDZvJrQALsdNFgH4j4wMaeZMadgw6fBh29eli72vEHtEAX6B4ALAP6xZI/XrJ/3wg21XrWqnhVq3drYuAB7FVBEAdzt6VOrTR2rUyIaWggXtCMvGjYQWwA8x4gLAndLTpX/+U3r+eenYMdvXvbs0dqwUFeVsbQC8huACwH1WrbLTQmvX2nbNmtKUKVKLFs7WBcDrmCoC4B6HD0u9e0tNmtjQUriw3Zp33TpCCxAgGHEB4PvOn5emTZNeekk6ccL29eoljR4tlSrlZGUAchnBBYBvW77cTgtt3GjbdevaaaGmTZ2tC4AjmCoC4JsOHJD+/Gd7b4CNG6WbbpL+/ndp9WpCCxDAGHEB4FvS0uyIyogR0smT9jbSjz8ujRolFS/udHUAHEZwAeA7liyx00Jbt9p2w4bS1Kn2vwAgpooA+IL9+6WuXaVWrWxoKVZMmj7dLnsmtAD4A4ILAOekptoN46pUkT76SMqTR/rLX6SdO+30UB7+LwpAVkwVAXDGokX2Ds4JCbbdpImdFqpb19m6APg0/jkDIHft3St16iTFxtrQUrKkvaPz8uWEFgBXRHABkDtSUqTXX5diYqS5c6XgYGngQBteevZkWgjAVWGqCID3ffGFDSk//WTbLVpIkydLtWo5WxcA1+GfOAC8Z88eqX17qW1bG1oiI6X337fLngktAK4DwQWA5509K40cKVWrJs2fL+XNKz3zjLRjh9Stm91UDgCuA1NFADzHGGnBAikuTkpMtH133mmnhapVc7Q0AP6BERcAnrFrl50Sat/ehpYyZaR//1v65htCCwCPIbgAuDGnT0svvCDVqCF9+aUUEiINHy5t3y517sy0EACPYqoIwPUxRpo3Txo0SNq3z/a1aSO9+aZ0663O1gbAbxFcAFy7HTvsrrfffGPb5cpJEyfaaSJGWAB4EVNFAK7eyZPSc89JNWva0BIWJr38srRtm9ShA6EFgNcx4gLgyoyxN0F89lnpt99sX7t20htvSJUqOVsbgIBCcAGQsy1b7LTQkiW2XbGivY6lbVtHywIQmJgqApC9pCRp8GCpTh0bWsLDpVdflbZuJbQAcAwjLgCyMkaaPVsaMkT6/Xfb98AD0oQJUvnyjpYGAAQXAP+1YYPUr5+0YoVt33qrnRZq08bRsgDgAqaKAEjHj9vAUr++DS0FCkijR0ubNhFaAPgURlyAQJaRIc2cKQ0bJh0+bPu6dJHGj7db9gOAjyG4AIFqzRo7yvLDD7ZdrZq9GeKddzpbFwDkgKkiINAcPSo99ZTUqJENLYUK2RGWDRsILQB8HiMuQKBIT5emT7c3RDx2zPY98og0dqwUGelsbQBwlQguQCBYtcpOC61da9s1a0pTp0rNmztbFwBcI6aKAH926JDUu7fUpIkNLYULS5MmSevWEVoAuBIjLoA/On9emjZNeukl6cQJ29erl13iXKqUk5UBwA0huAD+ZvlyOy20caNt161rp4WaNHG2LgDwAKaKAH9x4IDUo4edAtq4UbrpJumtt6TVqwktAPwGwQVwu7Q06Y03pCpV7D2GgoKkJ56Qdu6U+vSRgoOdrhAAPIapIsDNliyx00Jbt9p2o0bSlClSw4aOlgUA3sKIC+BG+/dLXbtKrVrZ0FKsmN2j5fvvCS0A/BrBBXCT1FS7YVyVKtJHH0l58kh/+YudFnr8cdsGAD/GVBHgFosWSf37SwkJtt2kiV0tVLeus3UBQC7in2eAr9u7V+rUSYqNtaGlZEl7R+flywktAAIOwQXwVSkp0uuvSzEx0ty5dnXQwIF2WqhnT6aFAAQkpooAX/TFFzak/PSTbbdoYVcL1azpbF0A4DD+yQb4kj17pPvvl9q2taElMlJ6/3277JnQAgAEF8AnnD0rjRwpVasmLVgg5c0rPfusvaalWze7qRwAgKkiwFHGSPPnS3Fx0s8/277WraXJk6WqVZ2sDAB8EiMugFN27bJTQh062NBSpoz073/bZc+EFgDIFsEFyG2nT0svvCDVqCF9+aUUEiINHy7t2CF17sy0EADkgKkiILcYY5c1Dx4s7dtn+9q0kd58U7r1VmdrAwCXILgAuWH7dmnAAOmbb2y7XDlp4kSpfXtGWADgGjBVBHjTyZPSc89JtWrZ0BIWJr38srRtm722hdACANeEERfAG4yxN0F89lnpt99sX7t20htvSJUqOVsbALgYwQXwtC1bpH79pKVLbbtSJWnSJLuCCABwQ5gqAjwlKUkaNEiqU8eGlnz5pL/+1QYZQgsAeAQjLsCNMkb617/stSy//277OnaUJkywF+ECADyG4ALciA0b7LTQihW2feutdtfb2FhHywIAf8VUEXA9jh+3gaV+fRtaChSQRo+WNm8mtACAF3k9uMTHxysoKEhxcXHefivA+zIypHfesSMrU6fa9kMP2V1vhw6VQkOdrhAA/JpXp4pWr16tt99+W7Vq1fLm2wC5Y80aqW9f6ccfbbtaNTstdOedztYFAAHEayMup06dUvfu3TV9+nTddNNNlz0uJSVFycnJWX4An3L0qPTUU1KjRja0FCokjR9vr28htABArvJacOnbt6/atm2rP/3pTzkeFx8fr4iIiMyf6Ohob5UEXJv0dGnaNDst9PbbdvXQI49ICQn2fkMhIU5XCAABxytTRR999JHWrVun1atXX/HY4cOHa/DgwZnt5ORkwguct2qVnRZat862a9WSpkyRmjd3ti4ACHAeDy779u3TwIEDtXDhQoWHh1/x+LCwMIWFhXm6DOD6HDokDRsmzZhh2xERdhO5p5+W8rJ7AAA4LcgYYzz5gp9++qkeeOABBQcHZ/alp6crKChIefLkUUpKSpbHLpacnKyIiAglJSWpcOHCniwNuLzz5+200EsvSSdO2L5evewS51KlnKwMAFwht76/Pf5PyNatW2vz5s1Z+h599FHFxMRo6NChOYYWwBHLl9tpoU2bbLtePTst1KSJs3UBAC7h8eBSqFAh1ahRI0tfgQIFVKxYsUv6AUcdOGC36Z8927ZvukkaNUp64gmJgA0APomdcxF40tLsfYSqVLGhJShIevJJaedOqU8fQgsA+LBcudpwyZIlufE2wJUtXiz17y9t3WrbjRrZaaGGDZ2tCwBwVRhxQWD49Vfp4YfthnFbt0rFi0v//Kf0/feEFgBwEYIL/FtqqjR2rBQTI82ZI+XJYy/ETUiQeve2bQCAa7AxBfzXokV2WighwbabNrXTQnXrOlsXAOC68c9N+J+9e6UHH5RiY21oKVVKmjXLLnsmtACAqxFc4D/OnZNef91OC82bZ1cHDRxow8uf/2xXDwEAXI2pIviHL76QBgyQdu+27RYt7LRQzZrO1gUA8ChGXOBue/ZI998vtW1rQ0tkpPTBB9KSJYQWAPBDBBe409mz0ogRUrVq0oIF9gaIQ4bYaaGuXZkWAgA/xVQR3MUYaf58KS5O+vln29e6tTR5slS1qpOVAQByAcEF7rFrl72O5auvbDs62m7d/+CDjLAAQIBgqgi+7/Rp6YUXpBo1bGgJCZGGD5e2b5c6dSK0AEAAYcQFvssYae5cafBgad8+23f33dKkSdKttzpbGwDAEQQX+Kbt2+200Dff2Hb58tLEiXYFESMsABCwmCqCbzl5UnruOalWLRtawsKkl1+Wtm2T2rcntABAgGPEBb7BGOmjj6Rnn5V++832tWtnR1kqVnS0NACA7yC4wHlbtkj9+klLl9p2pUr2Opa2bZ2tCwDgc5gqgnOSkux+LHXq2NCSL5/017/aIENoAQBkgxEX5D5jpH/9y17L8vvvtq9jR7snS7lyztYGAPBpBBfkrg0b7LTQihW2XaWK9OabUmyso2UBANyBqSLkjuPHbWCpX9+GlgIFpNGjpU2bCC0AgKvGiAu8KyNDmjFDGjZMOnLE9j30kDRunFSmjLO1AQBch+AC71mzRurbV/rxR9uuVs3eDPHOO52tCwDgWkwVwfOOHJGeekpq1MiGlkKFpPHj7fUthBYAwA1gxAWek54uTZ9ub4h47Jjte+QRaexYKTLS2doAAH6B4ALP+P57e/HtunW2XauWNGWK1Lz5ZZ+Sni4tWyYdOGBzTfPmUnBwLtULAHAlpopwYw4dkh57TGra1IaWiAi7vHnt2hxDy7x59r6JrVpJ3brZ/5Yvb/sBALgcgguuz/nz9kLbW2+1q4Yk6dFHpZ07pf79pbyXH8ybN0/q1En69des/fv3237CCwDgcgguuHbLltn9WAYMsNv216tnp4refVcqWTLHp6anSwMH2s1zL3ahLy7OHgcAwMUILrh6Bw5IPXpILVrYjeNuukl66y27cqhx46t6iWXLLh1p+SNjpH377HEAAFyM4IIrS0uz9xGqUkWaPVsKCpKefNJOC/Xpc01X1B444NnjAACBhVVFyNnixXa10LZttt2okV0t1LDhdb3c1a6KZvU0ACA7jLgge7/+Kj38sN0wbts2qXhx6Z//tNeyXGdokexCozJl7KBNdoKCpOjoHBckAQACGMEFWaWmSmPGSDEx0pw5Up48dtv+hASpd2/bvgHBwdKkSfbPF4eXC+2JE9nPBQCQPYIL/mvhQqlmTXtDxNOn7d4sa9faqaGiRT32Nh07Sh9/LN18c9b+MmVsf8eOHnsrAICf4RoXSL/8Ig0e/N8NVEqVstv09+hx+TmdG9Sxo9S+PTvnAgCuDcElkJ07J40bJ40aJZ09a1ND//7SyJF2B1wvCw6W7rjD628DAPAjBJdA9fnndie43bttu0ULOyVUs6azdQEAkAOucQk0e/ZI998v3XefDS1RUdIHH0hLlhBaAAA+j+ASKM6elUaMkKpVkxYssPcSGjJE2rFD6trVa9eyAADgSUwV+TtjpM8+kwYNkn7+2fa1bm1vkFi1qqOlAQBwrQgu/mzXLnsjxK++su3oaLt1/4MPMsICAHAlpor80enT0vPPSzVq2NASGmrb27dLnToRWgAArsWIiz8xRpo71+7Jsm+f7bv7bunNN6XKlZ2tDQAADyC4+Ivt2+200Dff2Hb58nbv/PvvZ4QFAOA3mCpyu5Mn7eqgWrVsaAkLs6uHtm2zW9MSWgAAfoQRF7cyRvroI+nZZ6XffrN97drZUZaKFR0tDQAAbyG4uNGWLVK/ftLSpbZdqZK95XLbts7WBQCAlzFV5CZJSVJcnFSnjg0t+fJJr71mgwyhBQAQABhxcYOMDOlf/5Kee046dMj2PfigNH68VK6cs7UBAJCLCC6+bsMGqW9faeVK265SxS5vjo11tCwAAJzAVJGvOn7cXsdSv74NLQUKSGPGSJs2EVoAAAGLERdfk5EhzZghDRsmHTli+x56SBo3TipTxtnaAABwGMHFl6xZY6eFfvzRtqtVk6ZMkVq1crYuAAB8BFNFvuDIEenJJ6VGjWxoKVTI3gxxwwZCCwAAf8CIi5PS06Xp06UXXpCOHbN9jzwijR0rRUY6WxsAAD6I4OKU77+3F9+uW2fbtWrZaaHmzZ2tCwAAH8ZUUW47dEh67DGpaVMbWiIipMmTpbVrCS0AAFwBIy655fx56a23pJdesjvgSjbAxMdLJUs6WxsAAC5BcMkNy5bZaaFNm2y7Xj1p6lSpcWNn6wIAwGWYKvKmAwekHj2kFi1saClaVJo2za4cIrQAAHDNCC7ekJZmlzNXqSLNni0FBdnlzjt3Sk89JQUHO10hAACuxFSRpy1ebKeFtm2z7UaN7LRQgwbO1gUAgB9gxMVTfv3Vbs1/5502tBQvLv3zn3bZM6EFAACP8HhwiY+PV8OGDVWoUCGVLFlSHTp0UEJCgqffxnekptqbH8bESP/+t5Qnj922f+dOqXdv2wYAAB7h8W/VpUuXqm/fvlq1apUWLVqk8+fPKzY2VqdPn/b0Wzlv4UKpZk17Q8TTp6Vmzex+LFOmSDfd5HR1AAD4nSBjjPHmGxw+fFglS5bU0qVL1aJFi0seT0lJUUpKSmY7OTlZ0dHRSkpKUuHChb1Z2vX75Rdp8GBp3jzbLlXKbtPfo4e9EBcAgACTnJysiIgIr39/e30eI+n/N1srWrRoto/Hx8crIiIi8yc6OtrbJV2/c+ek116Tqla1oSU4WIqLkxISpD//mdACAICXeXXExRij9u3b6/jx41q2bFm2x7hmxOXzz6WBA6Xdu227ZUs7JVSjhrN1AQDgA3JrxMWry6H79eunTZs2afny5Zc9JiwsTGFhYd4s48bs2WNHVRYssO2oKGn8eLuCiBEWAAByldemivr376/58+dr8eLFKlOmjLfexnvOnpVGjJCqVbOhJW9eacgQaccO6eGHCS0AADjA4yMuxhj1799fn3zyiZYsWaIKFSp4+i28yxjps8+kQYOkn3+2fX/6k72Dc0yMo6UBABDoPB5c+vbtqw8++ECfffaZChUqpIMHD0qSIiIilC9fPk+/nWft3GmvY/nqK9uOjrZb9z/4ICMsAAD4AI9fnBt0mS/4GTNmqFevXld8fm5d3JPF6dPS66/ba1dSU6XQUOnZZ6Xnn5cKFMidGgAAcDHXXpzr5W1hPMsY6eOP7Z4sv/5q++65R5o0Sapc2dnaAADAJQL3Jovbt0v9+0vffmvb5ctLEydK99/PtBAAAD4q8G6kc/KkXR1Uq5YNLWFhdvXQtm1S+/aEFgAAfFjgjLgYI334ob125cAB23f//dIbb0gVKzpbGwAAuCqBEVw2b5b69ZO++862K1WS3nxTuvdeZ+sCAADXxL+nipKS7K63deva0JIvn73X0JYthBYAAFzIP0dcMjKkf/1Leu456dAh2/fgg3a5c7lyztYGAACum/8Fl/Xr7bTQypW2XaWKnRaKjXW2LgAAcMP8Z6ro+HGpb1+pQQMbWgoUkMaMkTZtIrQAAOAn3D/ikpEhvfuuNHy4dOSI7Xv4Yelvf5PceHNHAABwWe4OLmvW2FGWH3+07WrVpClTpFatnK0LAAB4hTunio4ckZ58UmrUyIaWQoXszRA3bCC0AADgx9w14pKeLr39tvTCC/aaFknq0UMaO1YqXdrZ2gAAgNe5J7h8/71dLbRunW3XqiVNnSrdfruzdQEAgFzj+1NFhw5Jjz4qNW1qQ0tEhDR5srR2LaEFAIAA47vB5fx5u//KrbdKM2favscek3butCMved0zWAQAADzDd7/9mze3d2yWpHr17LRQ48bO1gQAABzluyMu27ZJRYtK06bZlUOEFgAAAp7vjrg8+qjdRK5YMacrAQAAPsJ3g8vEiVLhwk5XAQAAfIjvThUBAABchOACAABcg+ACAABcg+ACAABcg+ACAABcg+ACAABcg+ACAABcg+ACAABcg+ACAABcg+ACAABcg+ACAABcg+ACAABcg+ACAABcg+ACAABcg+ACAABcg+ACAABcg+ACAABcg+ACAABcg+ACAABcg+ACAABcg+ACAABcg+ACAABcg+ACAABcg+ACAABcg+ACAABcg+ACAABcg+ACAABcg+ACAABcg+ACAABcg+ACAABcg+ACAABcg+ACAABcg+ACAABcg+ACAABcg+ACAABcg+ACAABcg+ACAABcg+ACAABcg+ACAABcg+ACAABcg+ACAABcg+ACAABcg+ACAABcg+ACAABcw2vB5e9//7sqVKig8PBw1a9fX8uWLfPWWwEAgADhleAyZ84cxcXF6YUXXtD69evVvHlz3XPPPdq7d6833g4AAASIIGOM8fSL3nbbbapXr57eeuutzL6qVauqQ4cOio+Pz3JsSkqKUlJSMttJSUkqW7as9u3bp8KFC3u6NAAA4AXJycmKjo7WiRMnFBER4bX3yevpF0xNTdXatWs1bNiwLP2xsbFauXLlJcfHx8frlVdeuaQ/Ojra06UBAAAvO3r0qLuCy5EjR5Senq5SpUpl6S9VqpQOHjx4yfHDhw/X4MGDM9snTpxQuXLltHfvXq9+cF9zIakG2kgTn5vPHQj43HzuQHBhxqRo0aJefR+PB5cLgoKCsrSNMZf0SVJYWJjCwsIu6Y+IiAioE35B4cKF+dwBhM8dWPjcgSVQP3eePN5dsOzxVy9evLiCg4MvGV05dOjQJaMwAAAA18LjwSU0NFT169fXokWLsvQvWrRITZs29fTbAQCAAOKVqaLBgwerR48eatCggZo0aaK3335be/fuVZ8+fa743LCwMI0YMSLb6SN/xufmcwcCPjefOxDwub37ub2yHFqyG9CNHTtWBw4cUI0aNfTGG2+oRYsW3ngrAAAQILwWXAAAADyNexUBAADXILgAAADXILgAAADXILgAAADXcCS4/P3vf1eFChUUHh6u+vXra9myZTkev3TpUtWvX1/h4eGqWLGipk2blkuVekZ8fLwaNmyoQoUKqWTJkurQoYMSEhJyfM6SJUsUFBR0yc+OHTtyqeobN3LkyEvqL126dI7Pcfu5vqB8+fLZnr++fftme7xbz/d3332ndu3aKSoqSkFBQfr000+zPG6M0ciRIxUVFaV8+fLpjjvu0NatW6/4unPnzlW1atUUFhamatWq6ZNPPvHSJ7g+OX3utLQ0DR06VDVr1lSBAgUUFRWlP//5z/rtt99yfM2ZM2dm+3fg3LlzXv40V+9K57tXr16X1N+4ceMrvq6bz7ekbM9bUFCQ/va3v132NX39fF/N95ZTv9+5HlzmzJmjuLg4vfDCC1q/fr2aN2+ue+65R3v37s32+MTERN17771q3ry51q9fr+eff14DBgzQ3Llzc7ny67d06VL17dtXq1at0qJFi3T+/HnFxsbq9OnTV3xuQkKCDhw4kPlTuXLlXKjYc6pXr56l/s2bN1/2WH841xesXr06y+e+sCFj586dc3ye28736dOnVbt2bU2ZMiXbx8eOHasJEyZoypQpWr16tUqXLq277rpLJ0+evOxrfv/993rooYfUo0cPbdy4UT169FCXLl30ww8/eOtjXLOcPveZM2e0bt06vfTSS1q3bp3mzZunnTt36v7777/i6xYuXDjL+T9w4IDCw8O98RGuy5XOtyTdfffdWer/4osvcnxNt59vSZecs3fffVdBQUF68MEHc3xdXz7fV/O95djvt8lljRo1Mn369MnSFxMTY4YNG5bt8c8995yJiYnJ0vfUU0+Zxo0be61Gbzt06JCRZJYuXXrZYxYvXmwkmePHj+deYR42YsQIU7t27as+3h/P9QUDBw40lSpVMhkZGdk+7g/nW5L55JNPMtsZGRmmdOnSZvTo0Zl9586dMxEREWbatGmXfZ0uXbqYu+++O0tfmzZtzMMPP+zxmj3h4s+dnR9//NFIMr/88stlj5kxY4aJiIjwbHFelN3n7tmzp2nfvv01vY4/nu/27dubO++8M8dj3Ha+L/7ecvL3O1dHXFJTU7V27VrFxsZm6Y+NjdXKlSuzfc73339/yfFt2rTRmjVrlJaW5rVavSkpKUmSruoOmnXr1lVkZKRat26txYsXe7s0j9u1a5eioqJUoUIFPfzww9qzZ89lj/XHcy3Zv/ezZ8/WY489lu2NRv/I7ef7jxITE3Xw4MEs5zQsLEwtW7a87O+7dPm/Bzk9x9clJSUpKChIRYoUyfG4U6dOqVy5cipTpozuu+8+rV+/PncK9KAlS5aoZMmSuvXWW/XEE0/o0KFDOR7vb+f7999/1+eff67evXtf8Vg3ne+Lv7ec/P3O1eBy5MgRpaenX3KzxVKlSl1yU8YLDh48mO3x58+f15EjR7xWq7cYYzR48GDdfvvtqlGjxmWPi4yM1Ntvv625c+dq3rx5qlKlilq3bq3vvvsuF6u9Mbfddpvee+89ff3115o+fboOHjyopk2b6ujRo9ke72/n+oJPP/1UJ06cUK9evS57jD+c74td+J2+lt/3C8+71uf4snPnzmnYsGHq1q1bjncKjomJ0cyZMzV//nx9+OGHCg8PV7NmzbRr165crPbG3HPPPXr//ff1n//8R+PHj9fq1at15513KiUl5bLP8bfzPWvWLBUqVEgdO3bM8Tg3ne/svrec/P32yr2KruTif3UaY3L8l2h2x2fX7wb9+vXTpk2btHz58hyPq1KliqpUqZLZbtKkifbt26dx48a55tYJ99xzT+afa9asqSZNmqhSpUqaNWuWBg8enO1z/OlcX/DOO+/onnvuUVRU1GWP8YfzfTnX+vt+vc/xRWlpaXr44YeVkZGhv//97zke27hx4ywXsjZr1kz16tXT5MmT9eabb3q7VI946KGHMv9co0YNNWjQQOXKldPnn3+e4xe5v5xvSXr33XfVvXv3K16r4qbzndP3lhO/37k64lK8eHEFBwdfkqwOHTp0SQK7oHTp0tkenzdvXhUrVsxrtXpD//79NX/+fC1evFhlypS55uc3btzYJ9P41SpQoIBq1qx52c/gT+f6gl9++UXffPONHn/88Wt+rtvP94UVZNfy+37hedf6HF+UlpamLl26KDExUYsWLcpxtCU7efLkUcOGDV39dyAyMlLlypXL8TP4y/mWpGXLlikhIeG6ft999Xxf7nvLyd/vXA0uoaGhql+/fuYKiwsWLVqkpk2bZvucJk2aXHL8woUL1aBBA4WEhHitVk8yxqhfv36aN2+e/vOf/6hChQrX9Trr169XZGSkh6vLPSkpKdq+fftlP4M/nOuLzZgxQyVLllTbtm2v+bluP98VKlRQ6dKls5zT1NRULV269LK/79Ll/x7k9BxfcyG07Nq1S9988811BW9jjDZs2ODqvwNHjx7Vvn37cvwM/nC+L3jnnXdUv3591a5d+5qf62vn+0rfW47+fl/1Zbwe8tFHH5mQkBDzzjvvmG3btpm4uDhToEAB8/PPPxtjjBk2bJjp0aNH5vF79uwx+fPnN4MGDTLbtm0z77zzjgkJCTEff/xxbpd+3Z5++mkTERFhlixZYg4cOJD5c+bMmcxjLv7cb7zxhvnkk0/Mzp07zZYtW8ywYcOMJDN37lwnPsJ1eeaZZ8ySJUvMnj17zKpVq8x9991nChUq5Nfn+o/S09NN2bJlzdChQy95zF/O98mTJ8369evN+vXrjSQzYcIEs379+szVM6NHjzYRERFm3rx5ZvPmzaZr164mMjLSJCcnZ75Gjx49sqwqXLFihQkODjajR48227dvN6NHjzZ58+Y1q1atyvXPdzk5fe60tDRz//33mzJlypgNGzZk+Z1PSUnJfI2LP/fIkSPNV199ZXbv3m3Wr19vHn30UZM3b17zww8/OPERs5XT5z558qR55plnzMqVK01iYqJZvHixadKkibn55pv9+nxfkJSUZPLnz2/eeuutbF/Dbef7ar63nPr9zvXgYowxU6dONeXKlTOhoaGmXr16WZYF9+zZ07Rs2TLL8UuWLDF169Y1oaGhpnz58pf9i+GrJGX7M2PGjMxjLv7cY8aMMZUqVTLh4eHmpptuMrfffrv5/PPPc7/4G/DQQw+ZyMhIExISYqKiokzHjh3N1q1bMx/3x3P9R19//bWRZBISEi55zF/O94Vl3Bf/9OzZ0xhjl0yOGDHClC5d2oSFhZkWLVqYzZs3Z3mNli1bZh5/wf/8z/+YKlWqmJCQEBMTE+NzAS6nz52YmHjZ3/nFixdnvsbFnzsuLs6ULVvWhIaGmhIlSpjY2FizcuXK3P9wOcjpc585c8bExsaaEiVKmJCQEFO2bFnTs2dPs3fv3iyv4W/n+4J//OMfJl++fObEiRPZvobbzvfVfG859fsd9P8FAgAA+DzuVQQAAFyD4AIAAFyD4AIAAFyD4AIAAFyD4AIAAFyD4AIAAFyD4AIAAFyD4AIAAFyD4AIAAFyD4AIAAFyD4AIAAFzj/wBrkxCBEqoOGgAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(xdata, ydata, 'bo', label='observed')\n",
    "plt.xlim(0, 20)\n",
    "plt.ylim(0, 10)\n",
    "x = np.linspace(0, 20, 2)\n",
    "yfit = a * x + b\n",
    "plt.plot(x, yfit, 'r', label='fit')\n",
    "plt.legend(loc='best');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a href=\"#back4\">Back to Exercise 4</a>\n",
    "\n",
    "<a name=\"ex5answer\">Answers to Exercise 5</a>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "r squared according to formula: 0.923076923076923\n",
      "r squared according to linregress: 0.9230769230769231\n"
     ]
    }
   ],
   "source": [
    "yfit = a * xdata + b\n",
    "print('r squared according to formula:', end=' ')\n",
    "print(1 - sum((ydata - yfit) ** 2) / sum((ydata - np.mean(ydata)) ** 2))\n",
    "print('r squared according to linregress:', r**2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "std of slope according to formula: 0.11547005383792515\n",
      "std of slope according to linregress: 0.11547005383792511\n"
     ]
    }
   ],
   "source": [
    "print('std of slope according to formula:', end=' ')\n",
    "print(np.sqrt(np.sum((ydata - yfit)**2) / (N - 2)) / np.sqrt(np.sum((xdata - np.mean(xdata)) ** 2)))\n",
    "print('std of slope according to linregress:', s)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from scipy.stats import t\n",
    "x = np.linspace(-1.5, 1.5, 100)\n",
    "y = t.pdf(x, 1, loc=0, scale=s)\n",
    "plt.figure()\n",
    "plt.plot(x, y)\n",
    "p025, p975 = t.ppf([0.025, 0.975], 1, loc=0, scale=s)\n",
    "plt.axvline(p025, color='r')\n",
    "plt.axvline(p975, color='r')\n",
    "plt.axvline(a, color='k', lw=5)\n",
    "plt.title('H0 cannot be rejected: slope is not significantly different from zero');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a href=\"#back5\">Back to Exercise 5</a>\n",
    "\n",
    "<a name=\"ex6answer\">Answers to Exercise 6</a>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "number of 1000 experiments where p < 0.05: 38\n"
     ]
    }
   ],
   "source": [
    "count = 0\n",
    "for i in range(1000):\n",
    "    x = np.random.rand(100)\n",
    "    y = np.random.rand(100)\n",
    "    slope, intercept, r, p, s = linregress(x, y)\n",
    "    if p < 0.05:\n",
    "        count += 1\n",
    "print('number of 1000 experiments where p < 0.05:', count)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a href=\"#back6\">Back to Exercise 6</a>"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.13.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}