plotScatter.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "1672b53e",
   "metadata": {},
   "source": [
    "# Plot Scatter plot\n",
    "\n",
    "This notebook will help you generate a scatterplot in Python. **Scatterplots** help us visually inspect the relationship between two continuous variables. This notebook could be used to plot your **resistance** vs. **time constant** observations from the RC circuit lab, for example.\n",
    "\n",
    "After plotting, we'll also show how to generate a linear regression line for your data. **Linear regression** is a common tool to look for a linear relationship between two variables.\n",
    "\n",
    "![](https://imgs.xkcd.com/comics/linear_regression.png)\n",
    "\n",
    "<br>\n",
    "<div align=\"center\"><i>Comic: XKCD https://xkcd.com/1725/<i></div>\n",
    "\n",
    "<mark>If you're new to Jupyter Notebooks and/or Python, please be sure to work through the Introduction notebook before this one.</mark>\n",
    "    \n",
    "<hr>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fa2f211c",
   "metadata": {},
   "source": [
    "## Setup\n",
    "\n",
    "At the start of almost every coding notebook, we'll import the packages we need. To plot our scatter plot, we just need package: `matplotlib.pyplot`. \n",
    "\n",
    "> **Task**: Import the `matplotlib.pyplot` package as `plt`, just as you did in the introduction notebook."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "b5627e3c",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Import necessary packages here\n",
    "\n",
    "\n",
    "# These lines are additional configuration steps for matplotlib\n",
    "%matplotlib inline \n",
    "%config InlineBackend.figure_format = 'retina'"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5200e250",
   "metadata": {},
   "source": [
    "## Define values to plot\n",
    "With matplotlib imported, we can now use the scatter function by calling `plt.scatter()`. However, we need to define what to plot first. One straightforward way to think about this is to define an x variable and a y variable. Below, there are **lists** of values (defined in brackets `[ ]`) assigned to `x` and `y`. Replace these with your own values, depending on what you'd like to plot on the x and y axis.\n",
    "\n",
    "**Note**: Remember that in a scatterplot, each dot has both an x and a y value. Therefore, these lists should be the same length. The coordinate for each point will be the values at the same **index** in `x` and `y`. For example, the coordinate for the very first point will be `x[0],y[0]`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "53dc0802",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Replace your scatterplot values here\n",
    "x = [1,2,3,4,5,6]\n",
    "y = [4,5,6,7,8,9]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "01196ae2",
   "metadata": {},
   "source": [
    "## Plot & label\n",
    "We can now plot our values using the code below. Remember that you can add axis labels using `plt.xlabel()`. If you need a reminder for how to do this, refer to the Introduction notebook."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "de064aab",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 248,
       "width": 362
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(x,y)\n",
    "\n",
    "# Add labels here\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d87969f8",
   "metadata": {},
   "source": [
    "## Add a linear regression line (*optional*)\n",
    "If we have an a priori hypothesis about the relationship between our variables, or would like to predict additional data points, we can attempt to fit a linear regression line to our data. To do so, we will do the following:\n",
    "\n",
    "1. Import two more packages: `numpy` (numerical python; the convention is to import this as `np`) and the `stats` package from `scipy` (scientific python).\n",
    "2. Convert our x and y lists into arrays, so that we can perform math on them.\n",
    "3. Perform a linear regression using `linregress()` from the `stats` library. The `linregress()` function calculates a **linear least-squares regression** for two sets of measurements. It returns several parameters, including the slope (`slope`), the y-intercept (`intercept`), the correlation coefficient (`r_value`), the two-tailed p-value (`p_value`), and the standard error of the estimate (`std_err`).\n",
    "4. Plot the regression line, using the computed slope and intercept to construct it (mx+b).\n",
    "5. Plot the original data points."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "0e4f8519",
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 248,
       "width": 362
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 1 - Import additional packages\n",
    "import numpy as np\n",
    "from scipy import stats\n",
    "\n",
    "# 2 - Convert x and y to numpy arrays\n",
    "x_array = np.array(x)\n",
    "y_array = np.array(y)\n",
    "\n",
    "# 3 - Perform linear regression\n",
    "slope, intercept, r_value, p_value, std_err = stats.linregress(x_array,y_array)\n",
    "\n",
    "# 4 - Plot a regression line, using the slope & intercept\n",
    "plt.plot(x_array, slope*x_array+intercept, color='gray',label='fitted line')\n",
    "\n",
    "# 5 - Plot our original data points and show\n",
    "plt.scatter(x_array,y_array,label='original data')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ec9121ea",
   "metadata": {},
   "source": [
    "It is also a good idea to print the statistics from our linear regression above. These are contained in `r_value` and `p_value`:\n",
    "* `r_value`: This is the correlation coefficient, also known as the R-value. It measures the strength and direction of the linear relationship between the two variables. It ranges from -1 to 1, where a value of -1 indicates a strong negative linear relationship, a value of 0 indicates no linear relationship, and a value of 1 indicates a strong positive linear relationship.\n",
    "* `p_value`: This is the two-tailed p-value. A small p-value (typically less than 0.05) indicates that the correlation is statistically significant and that there is a low probability that the observed correlation occurred by chance.\n",
    "\n",
    "It can also be helpful to look at `std_err`: the standard error of the estimate. It represents the standard deviation of the residuals (the differences between the observed y values and the predicted y values). A small standard error indicates that the fitted line is a good fit for the data.\n",
    "\n",
    "> **Task**: Print your values below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "fbf0433b",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "6f7c51f4",
   "metadata": {},
   "source": [
    "Finally, sometimes it is useful to have the fitted line equation. We can create a text string by adding variables together, like so:\n",
    "```\n",
    "text_string = 'this is ' + variable\n",
    "```\n",
    "*However*, Python will not allow us to add anything that isn't a string -- we have to convert it to a string first using the `str()` function. To do so, we could write:\n",
    "```\n",
    "text_string = 'this is ' + str(variable)\n",
    "```\n",
    ">**Task**: Below, create a text string for the fitted line equation, in the form of Y = MX + B, where M is your slope, and B is your intercept. In other words, it should look something like this:\n",
    "```\n",
    "Y = 1.0X + 3.0\n",
    "```\n",
    "\n",
    "Assign the fitted line equation to a variable called `label`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "0b6da971",
   "metadata": {},
   "outputs": [],
   "source": [
    "label = ..."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3af4ca17",
   "metadata": {},
   "source": [
    "## Add your regression line to the plot *(optional)*\n",
    "\n",
    "It is useful to report the fitted line equation either on the plot itself or in the figure caption. The code below will show you how to add text using `plt.text()`. This function takes three inputs: the x,y location of the text as well as the string itself (s). If you'd like, you can integrate this into your code above."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "acfadb0b",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 252,
       "width": 380
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure()\n",
    "plt.text(x = 0.1, y = 0.1, s = label)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3ca35305",
   "metadata": {},
   "source": [
    "## Fit a curved line\n",
    "Alternatively, we can perform a Least Squares Regression to fit to a Curve. To do so, we'll use `scipy.optimize.curve_fit()`. [[Documentation](https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.curve_fit.html)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "a3865aec",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.9239011751642454\n",
      "0.4739203931704783\n",
      "0.278745874411597 <-- This is your Rheobase in the hyperbolic function\n",
      "2.749230408204977 <-- This is your Chronaxie in the hyperbolic function\n",
      "Y=0.28+0.28*2.75/x\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 248,
       "width": 372
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 1 - Import packages\n",
    "import numpy as np\n",
    "from scipy import stats\n",
    "from scipy.optimize import curve_fit\n",
    "\n",
    "# 2 - Convert x and y to numpy arrays\n",
    "x_array = np.array(x)\n",
    "y_array = np.array(y)\n",
    "\n",
    "# 3 - Define a curve function\n",
    "def func(x, a, b):\n",
    "    #return (a*x)+b #linear function\n",
    "    #return np.exp(np.log(a)+(x*np.log(b))) #exponential function y=a*(b^x)\n",
    "    #return np.exp(np.log(a)+(b*np.log(x))) #power function y=a*(x^b)\n",
    "    return a+((a*b)/x) #hyperbolic function\n",
    "\n",
    "# 4 - Fit the curve!\n",
    "popt, pcov = curve_fit(func,x_array,y_array)\n",
    "\n",
    "# 5 - Plot a regression line, using the slope & intercept\n",
    "plt.plot(x_array, func(x_array, *popt), 'r-')\n",
    "\n",
    "#To get the r squared and S_value use this code\n",
    "residuals = y_array- func(x_array, *popt)\n",
    "ss_res = np.sum(residuals**2)\n",
    "ss_tot = np.sum((y_array-np.mean(y_array))**2)\n",
    "r_squared = 1 - (ss_res / ss_tot)\n",
    "\n",
    "perr = np.sqrt(np.diag(pcov))\n",
    "S_value=(perr[0]+perr[1])/2\n",
    "print(r_squared)\n",
    "print(S_value)\n",
    "\n",
    "#To get the equation for the curve (example for Hyperbolic function)\n",
    "a = popt[0]\n",
    "b = popt[1]\n",
    "\n",
    "#label = 'Y=' + str(round(a,2)) + \"*x^\" + str(round(b,2)) #Power function\n",
    "label = 'Y=' + str(round(a,2)) + '+' + str(round(a,2)) + '*' + str(round(b,2))  + '/x' \n",
    "print(str(a) + ' <-- This is your Rheobase in the hyperbolic function')\n",
    "print(str(b) + ' <-- This is your Chronaxie in the hyperbolic function')\n",
    "print(label)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6e538ac8",
   "metadata": {},
   "source": [
    "<hr>\n",
    "\n",
    "## Additional notes & resources\n",
    "\n",
    "Another way to generate a scatterplot with a linear regression line is the [seaborn regplot function](https://seaborn.pydata.org/generated/seaborn.regplot.html)!"
   ]
  }
 ],
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