Linear Regression with gui.ipynb

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   "source": [
    "# Linear regression\n",
    "\n",
    "In statistics, linear regression is a linear approach for modelling the relationship between a scalar response and one or more explanatory variables (also known as dependent and independent variables). e.g. a model that assumes a linear relationship between the input variables (x) and the single output variable (y). More specifically, that y can be calculated from a linear combination of the input variables (x).  The case of one explanatory variable is called simple linear regression\n",
    "\n",
    "Linear regression models are often fitted using the least squares approach, but they may also be fitted in other ways, such as by minimizing the \"lack of fit\" in some other norm (as with least absolute deviations regression), or by minimizing a penalized version of the least squares cost function as in ridge regression ($L_2$-norm penalty) and lasso ($L_1$-norm penalty). Conversely, the least squares approach can be used to fit models that are not linear models. Thus, although the terms \"least squares\" and \"linear model\" are closely linked, they are not synonymous.\n",
    "\n",
    "In this section, we implement least squares approch for fitting a set of data points on 2D plane\n",
    "\n",
    "Given a set of data points, the best fit straight line equation is $$y = a_0 + a_1 x $$\n",
    "\n",
    "where $a_0$ and $a_1$ are obtained by solving the equations:\n",
    "$$\n",
    "\\begin{split}\n",
    "n \\, a_0 + \\left( \\Sigma x_i \\right) a_1 &= \\Sigma y_i \\\\\n",
    "\\left( \\Sigma x_i \\right)  a_0 + \\left( \\Sigma x_i^2 \\right) a_1 &= \\Sigma\\, x_iy_i\n",
    "\\end{split}\n",
    "$$\n",
    "\n",
    "## Correlation Coefficient\n",
    "\n",
    "How do we know how good the fit is?\n",
    "By correlation coefficient\n",
    "\n",
    "$S_r$ : Square differences between the data points and the straight line\n",
    "\n",
    "$$ S_r = \\sum_{i = 1}^{n} (y_i - a_0 - a_1x_i)^2$$\n",
    "\n",
    "$S_t$ : Square differences between the data points and the mean\n",
    "\n",
    "$$ S_t = \\sum_{i = 1}^{n} \\left(y_i - \\overline{y}\\right)^2$$\n",
    "\n",
    "Coefficient of determination \n",
    "\n",
    "$$ r^2 = \\frac{S_t - S_r}{S_t}$$\n",
    "\n",
    "Correlation coefficient\n",
    "\n",
    "$$r = \\sqrt{r^2}$$\n",
    "\n",
    "# Exponential Model\n",
    "Exponential regression refers to the process of arriving at an equation for the exponential curve that best fits a set of data. Exponential regression is very similar to linear regression, where we try to arrive at an equation for the (straight) line that best fits a set of data.\n",
    "\n",
    "Often, we come across situations where a set of data doesn’t follow a straight line or a parabola. In such situations, the exponential curve is generally the best fit. This includes situations where there is slow growth initially and then a quick acceleration of growth, or in situations where there is rapid decay initially and then a sudden deceleration of decay.\n",
    "\n",
    "Given that $y = ae^{bx}$ and the linear fit equation iis $Y = a_0 + a_1X$, after simplifying we obtain that\n",
    "$$ \\underbrace{\\ln(y)}_{Y} = \\underbrace{\\ln(a)}_{a_0} + \\underbrace{b}_{a_1} \\underbrace{x}_{X} $$\n",
    "\n",
    "Let:\n",
    "$$\n",
    "\\begin{split}\n",
    "Y &= \\ln(y)\\\\\n",
    "X &= x\\\\\n",
    "a_0 &= \\ln(a)\\\\\n",
    "a_1 &= b\n",
    "\\end{split}\n",
    "$$\n",
    "\n",
    "# Power Model\n",
    "\n",
    "Power regression is one in which the response variable is proportional to the explanatory variable raised to a power. \n",
    "\n",
    "Given that $y = ax^b$ and the linear fit equation iis $Y = a_0 + a_1X$, after simplifying we obtain that\n",
    "$$ \\underbrace{\\log(y)}_{Y} = \\underbrace{\\log(a)}_{a_0} + \\underbrace{b}_{a_1} \\underbrace{\\log(x)}_{X} $$\n",
    "\n",
    "Let:\n",
    "\n",
    "$$\n",
    "\\begin{split}\n",
    "Y &= \\log(y)\\\\\n",
    "X &= \\log(x)\\\\\n",
    "a_0 &= \\log(a)\\\\\n",
    "a_1 &= b\n",
    "\\end{split}\n",
    "$$\n",
    "\n",
    "\n",
    "# Growth Rate Model\n",
    " \n",
    "\n",
    "Given that $y = \\dfrac{ax}{b+x}$ and the linear fit equation iis $Y = a_0 + a_1X$, after simplifying we obtain that\n",
    "$$ \\underbrace{\\frac{1}{y}}_{Y} = \\underbrace{\\frac{1}{a}}_{a_0} + \\underbrace{\\frac{b}{a}}_{a_1} \\underbrace{\\frac{1}{x}}_{X} $$\n",
    "\n",
    "Let:\n",
    "\n",
    "$$\n",
    "\\begin{split}\n",
    "Y &= \\frac{1}{y}\\\\\n",
    "X &= \\frac{1}{x}\\\\\n",
    "a_0 &= \\frac{1}{a}\\\\\n",
    "a_1 &= \\frac{b}{a}\n",
    "\\end{split}\n",
    "$$"
   ]
  },
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Implementation\n",
    "\n",
    "We define `linear_regression` function, the function takes two inputs, first input is a list of data points, second input is the model of regression, by default the model is `linear`, there are `exponential`, `power` and `growth rate` model. The function returns two values, first value is a list of parameters of the best fit equation, the second is the correlation coefficient, third input `plot_function` is optional and by default equals false, if it equals true it wil return s plot of the data points vs. the least squares solution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# import needed packages\n",
    "# by default, python calls list by reference, resulting in changing the original set\n",
    "# using deepcopy to copy the data to prevent from changing the origninal set\n",
    "\n",
    "from copy import deepcopy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def linear_regression(points, model = 'linear', plot_function = False):\n",
    "    \n",
    "    \n",
    "    ####################################\n",
    "    # implement linear model\n",
    "    \n",
    "    if model.lower() in ['l', 'linear']:\n",
    "        \n",
    "        points_linear = deepcopy(points)\n",
    "        \n",
    "        number_of_points = len(points_linear)\n",
    "\n",
    "        sigma_x = 0\n",
    "        for i in range(len(points_linear)):\n",
    "            sigma_x += points_linear[i][0]\n",
    "\n",
    "        sigma_y = 0\n",
    "        for i in range(len(points_linear)):\n",
    "            sigma_y += points_linear[i][1]\n",
    "\n",
    "        sigma_x_squared = 0\n",
    "        for i in range(len(points_linear)):\n",
    "            sigma_x_squared += (points_linear[i][0])^2\n",
    "\n",
    "        sigma_xy = 0\n",
    "        for i in range(len(points_linear)):\n",
    "            sigma_xy += (points_linear[i][0] * points_linear[i][1])\n",
    "\n",
    "        A = matrix([[number_of_points, sigma_x], [sigma_x, sigma_x_squared]])\n",
    "\n",
    "        b = matrix([[sigma_y], [sigma_xy]])\n",
    "\n",
    "        solution = A.solve_right(b).n()\n",
    "\n",
    "        S_r = 0\n",
    "        for i in range(len(points_linear)):\n",
    "            S_r += (points_linear[i][1] - list(solution.dict().values())[0] - list(solution.dict().values())[1] * points_linear[i][0])^2\n",
    "\n",
    "        S_t = 0\n",
    "        for i in range(len(points_linear)):\n",
    "            S_t += (points_linear[i][1] - (sigma_y / number_of_points))^2\n",
    "\n",
    "\n",
    "        correlation_coefficient = sqrt((S_t - S_r) / S_t)\n",
    "\n",
    "        if plot_function == False:\n",
    "        \n",
    "            return list(solution.dict().values()), correlation_coefficient\n",
    "    \n",
    "        if plot_function == True:\n",
    "            \n",
    "            a0, a1 = var('a0 a1')\n",
    "\n",
    "            model(x) = a0  + a1 * x\n",
    "            \n",
    "            linear_regression_plot = point(points) + plot(model(a0 = list(solution.dict().values())[0], a1 = list(solution.dict().values())[1]), (x, find_min_x_of_points(points), find_max_x_of_points(points) + 1), color = 'red')\n",
    "            \n",
    "            return list(solution.dict().values()), correlation_coefficient, linear_regression_plot\n",
    "            \n",
    "    \n",
    "    ####################################\n",
    "    # implement exponential model\n",
    "    \n",
    "    if model.lower() in ['e', 'exp', 'exponential']:\n",
    "        \n",
    "        points_exponential = deepcopy(points)\n",
    "        \n",
    "        for i in range(len(points_exponential)):\n",
    "            points_exponential[i][1] = ln(points_exponential[i][1]).n()\n",
    "            \n",
    "        exponential_solution, correlation_coefficient = linear_regression(points_exponential)\n",
    "         \n",
    "        exponential_solution[0] = e^(exponential_solution[0])\n",
    "        \n",
    "        if plot_function == False:\n",
    "            \n",
    "            return exponential_solution, correlation_coefficient\n",
    "    \n",
    "        if plot_function == True:\n",
    "            \n",
    "            a, b = var('a b')\n",
    "\n",
    "            model_2 = a * e^(b * x) \n",
    "            \n",
    "            linear_regression_plot = point(points) + plot(model_2(a = exponential_solution[0], b = exponential_solution[1]), (x, find_min_x_of_points(points), find_max_x_of_points(points) + 1), color = 'red')\n",
    "            \n",
    "            return exponential_solution, correlation_coefficient, linear_regression_plot\n",
    "            \n",
    "    \n",
    "    \n",
    "    ####################################\n",
    "    # implement power model\n",
    "    \n",
    "    if model.lower() in ['p', 'power']:\n",
    "        \n",
    "        points_power = deepcopy(points)\n",
    "        \n",
    "        for i in range(len(points_power)):\n",
    "            points_power[i][0] = log(points_power[i][0], 10).n()\n",
    "            points_power[i][1] = log(points_power[i][1], 10).n()\n",
    "            \n",
    "        power_solution, correlation_coefficient = linear_regression(points_power)\n",
    "        \n",
    "        power_solution[0] = 10^(power_solution[0])\n",
    "        \n",
    "        if plot_function == False:\n",
    "        \n",
    "            return power_solution, correlation_coefficient\n",
    "        \n",
    "        if plot_function == True:\n",
    "\n",
    "            a, b = var('a b')\n",
    "\n",
    "            model_3 = a * x^b \n",
    "            \n",
    "            linear_regression_plot = point(points) + plot(model_3(a = power_solution[0], b = power_solution[1]), (x, find_min_x_of_points(points), find_max_x_of_points(points) + 1), color = 'red')\n",
    "            \n",
    "            return power_solution, correlation_coefficient, linear_regression_plot\n",
    "    \n",
    "    \n",
    "    \n",
    "    ####################################\n",
    "    # implement growth rate model\n",
    "    \n",
    "    if model.lower() in ['g', 'growth', 'growth rate']:\n",
    "        \n",
    "        points_growth = deepcopy(points)\n",
    "            \n",
    "        for i in range(len(points_growth)):\n",
    "            points_growth[i][0] = 1 / points_growth[i][0]\n",
    "            points_growth[i][1] = 1 / points_growth[i][1]\n",
    "            \n",
    "        growth_solution, correlation_coefficient = linear_regression(points_growth)\n",
    "        \n",
    "        growth_solution[0] = 1 / growth_solution[0]\n",
    "        growth_solution[1] = growth_solution[0] * growth_solution[1]\n",
    "        \n",
    "    \n",
    "        if plot_function == False:\n",
    "        \n",
    "            return growth_solution, correlation_coefficient\n",
    "        \n",
    "        if plot_function == True:\n",
    "\n",
    "            a, b = var('a b')\n",
    "\n",
    "            model_4 = a * x / (b + x) \n",
    "            \n",
    "            linear_regression_plot = point(points) + plot(model_4(a = growth_solution[0], b = growth_solution[1]), (x, find_min_x_of_points(points), find_max_x_of_points(points) + 1), color = 'red')\n",
    "            \n",
    "            return growth_solution, correlation_coefficient, linear_regression_plot\n",
    "        \n",
    "        \n",
    "##############################\n",
    "# To plot -> we must specify a range of x e.g. from x = 0 to x = 15\n",
    "# To find that range automaticly, we define find_min_x_of_points() and find_min_x_of_points()\n",
    "# which finds the minimum and maximum x value of a list of point\n",
    "\n",
    "def find_min_x_of_points(points):\n",
    "    min = points[0][0]\n",
    "    for point in points:\n",
    "        if point[0] < min :\n",
    "            min = point[0]\n",
    "    return min\n",
    "\n",
    "def find_max_x_of_points(points):\n",
    "    max = points[0][0]\n",
    "    for point in points:\n",
    "        if point[0] > max :\n",
    "            max = point[0]\n",
    "    return max"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Implementation of a graphical user interface\n",
    "\n",
    "Using `ipywidgets` which are interactive HTML widgets for Jupyter notebooks and the IPython kernel, we can define the `GUI_linear_regression` function which enable the user to enter a list of points anf choose the model interactively."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "import ipywidgets as widgets\n",
    "from IPython.display import display\n",
    "\n",
    "\n",
    "# by default, numbers in sage are from sage.rings.real_mpfr.RealLiteral\n",
    "# Using R_type_cast, we can type cast any float or integer value to proper types\n",
    "from sage.rings.real_mpfr import RRtoRR\n",
    "R_type_cast = RealField()\n",
    "\n",
    "\n",
    "def GUI_linear_regression():\n",
    "    pointsgui = widgets.Text(\n",
    "    value = '',\n",
    "    placeholder = 'e.g. [[18, 153], [19, 156], [21, 169]]',\n",
    "    description = 'Enter points: ',\n",
    "    disabled = False\n",
    "    )\n",
    "    display(pointsgui)\n",
    "\n",
    "    modelgui = widgets.RadioButtons(\n",
    "    options=['linear', 'exponential', 'power', 'growth rate'],\n",
    "    value = 'linear', # Defaults to 'linear'\n",
    "    description = 'Model: ',\n",
    "    disabled = False\n",
    "    )\n",
    "    display(modelgui)\n",
    "    \n",
    "    button = widgets.Button(description = 'Run')\n",
    "    output = widgets.Output()\n",
    "\n",
    "    display(button, output)\n",
    "\n",
    "    def on_button_clicked(b):\n",
    "        with output:\n",
    "            show_results()\n",
    "            \n",
    "\n",
    "    button.on_click(on_button_clicked)\n",
    "    \n",
    "    def show_results():\n",
    "        points_2_gui = eval(pointsgui.value)\n",
    "        for onepoint in points_2_gui:\n",
    "            onepoint[0], onepoint[1] = R_type_cast(onepoint[0]), R_type_cast(onepoint[1])\n",
    "        solution_test, correlation_coefficient_test, graph_test = linear_regression(points_2_gui ,model = modelgui.value, plot_function = True)\n",
    "        print(f\"Parameters are {solution_test[0]}, {solution_test[1]}\\nCorrelation coefficient is {correlation_coefficient_test}\" )\n",
    "        show(graph_test)\n",
    "    \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Test with an example 1\n",
    "\n",
    "Find the least squares fit of a straight line to the given data:\n",
    "\n",
    "\n",
    "|x|18|19|21|23|23|25|34|35|37|39|42|54|56|65|72|\n",
    "|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|\n",
    "|y|153|156|169|172|174|174|172|174|177|180|181|187|198|199|202|\n",
    "\n",
    "plot the data points vs. the least squares solution, and find the correlation coefficient."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[[18, 153],\n",
       " [19, 156],\n",
       " [21, 169],\n",
       " [23, 172],\n",
       " [23, 174],\n",
       " [25, 174],\n",
       " [34, 172],\n",
       " [35, 174],\n",
       " [37, 177],\n",
       " [39, 180],\n",
       " [42, 181],\n",
       " [54, 187],\n",
       " [56, 198],\n",
       " [65, 199],\n",
       " [72, 202]]"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "points_1 = [[18, 153], [19, 156], [21, 169], [23, 172], [23, 174], [25, 174], [34, 172], [35, 174], [37, 177], [39, 180], [42, 181], [54, 187], [56, 198], [65, 199], [72, 202]]\n",
    "\n",
    "points_1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Required coefficients [148.999345110692, 0.769111586748874]\n",
      "Correlation coefficient = 0.935392145341174\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "Graphics object consisting of 2 graphics primitives"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "solution_1, correlation_coefficient_1, graph_1 = linear_regression(points_1 ,model = 'linear', plot_function = True)\n",
    "\n",
    "print(f'Required coefficients {solution_1}\\nCorrelation coefficient = {correlation_coefficient_1}')\n",
    "show(graph_1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Compare it to `find_fit` function provided by `sage`, results are almost identical"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[a0 == 148.99934509893097, a1 == 0.7691115870622297]"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "var('a0 a1')\n",
    "model(x) = a0  + a1 * x\n",
    "\n",
    "find_fit(points_1, model)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Test GUI with an example 1.1\n",
    "\n",
    "Find the least squares fit of a straight line to the given data:\n",
    "\n",
    "\n",
    "|x|5|10|15|20|25|\n",
    "|-|-|-|-|-|-|\n",
    "|y|-0.45|-21.13|-43.5|-72.53|-98.17|\n",
    "\n",
    "plot the data points vs. the least squares solution, and find the correlation coefficient."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "# points_1_gui = [[5, -0.45], [10, -21.13], [15, -43.50], [20, -72.53], [25, -98.17]]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "4da24a2a4ca84a929cc4639a70fe1403",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Text(value='', description='Enter points: ', placeholder='e.g. [[18, 153], [19, 156], [21, 169]]')"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "7ec29ed7fbb94808945eb52cd06cc2aa",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "RadioButtons(description='Model: ', options=('linear', 'exponential', 'power', 'growth rate'), value='linear')"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "2494b4cca45748529b072049a0ae9a83",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Button(description='Run', style=ButtonStyle())"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "269f6919340143e8b91882e1fc4ad204",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Output()"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "GUI_linear_regression()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Test with an example 2\n",
    "\n",
    "Find the least squares fit of the exponential model to the given data:\n",
    "\n",
    "\n",
    "|x|1|2|3|4|5|6|7|8|9|10|\n",
    "|-|-|-|-|-|-|-|-|-|-|-|\n",
    "|y|620.00|621.88|899.80|1239.93|1970.63|2089.04|2751.31|3954.92|5893.7|8513.1|\n",
    "\n",
    "plot the data points vs. the least squares solution, and find the correlation coefficient."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[[1, 620.000000000000],\n",
       " [2, 621.880000000000],\n",
       " [3, 899.800000000000],\n",
       " [4, 1239.93000000000],\n",
       " [5, 1970.63000000000],\n",
       " [6, 2089.04000000000],\n",
       " [7, 2751.31000000000],\n",
       " [8, 3954.92000000000],\n",
       " [9, 5893.70000000000],\n",
       " [10, 8513.10000000000]]"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "points_2 = [[1,620.00], [2,621.88], [3,899.80], [4,1239.93], [5,1970.63], [6,2089.04], [7,2751.31], [8,3954.92], [9, 5893.7], [10, 8513.1]]\n",
    "\n",
    "points_2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Required coefficients [386.108386444157, 0.298007006799214]\n",
      "Correlation coefficient = 0.992541929629623\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "Graphics object consisting of 2 graphics primitives"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "solution_2, correlation_coefficient_2, graph_2 = linear_regression(points_2 ,model = 'exponential', plot_function = True)\n",
    "\n",
    "print(f'Required coefficients {solution_2}\\nCorrelation coefficient = {correlation_coefficient_2}')\n",
    "show(graph_2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "e97bca9e09f942b7bd0b25ee1dcf16e1",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Text(value='', description='Enter points: ', placeholder='e.g. [[18, 153], [19, 156], [21, 169]]')"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "fc13bd0ab7224755aec288400241e7d9",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "RadioButtons(description='Model: ', options=('linear', 'exponential', 'power', 'growth rate'), value='linear')"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "fef126cbd3ff49ee9592fcb4f549085c",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Button(description='Run', style=ButtonStyle())"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "e53a9709704248b1b94772f9bd6a81dc",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Output()"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "GUI_linear_regression()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Test with an example 3\n",
    "\n",
    "Find the least squares fit of the power model to the given data:\n",
    "\n",
    "\n",
    "|x|1|2|3|4|5|6|7|8|9|10|11|12|13|14|15|\n",
    "|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|\n",
    "|y|0.339|2.082|6.731|16.799|35.423|75.224|117.506|162.077|197.054|337.557|405.831|603.241|643.630|830.005|879.403|\n",
    "\n",
    "plot the data points vs. the least squares solution, and find the correlation coefficient."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[[1, 0.339000000000000],\n",
       " [2, 2.08200000000000],\n",
       " [3, 6.73100000000000],\n",
       " [4, 16.7995000000000],\n",
       " [5, 35.4230000000000],\n",
       " [6, 75.2240000000000],\n",
       " [7, 117.506000000000],\n",
       " [8, 162.077000000000],\n",
       " [9, 197.054000000000],\n",
       " [10, 337.557000000000],\n",
       " [11, 405.831000000000],\n",
       " [12, 603.241000000000],\n",
       " [13, 643.630000000000],\n",
       " [14, 830.005000000000],\n",
       " [15, 879.403000000000]]"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "points_3 = [[1, 0.339], [2, 2.082], [3, 6.731], [4, 16.7995], [5, 35.423], [6, 75.224], [7, 117.506], [8, 162.077], [9, 197.054], [10, 337.557], [11, 405.831], [12, 603.241], [13, 643.630], [14, 830.005], [15, 879.403]]\n",
    "points_3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Required coefficients [0.289032615005079, 3.01877203227069]\n",
      "Correlation coefficient = 0.998729161187500\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "Graphics object consisting of 2 graphics primitives"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "solution_3, correlation_coefficient_3, graph_3 = linear_regression(points_3 ,model = 'power', plot_function = True)\n",
    "\n",
    "print(f'Required coefficients {solution_3}\\nCorrelation coefficient = {correlation_coefficient_3}')\n",
    "show(graph_3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "267e37ee38f54440b3c95fd29b4018af",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Text(value='', description='Enter points: ', placeholder='e.g. [[18, 153], [19, 156], [21, 169]]')"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "48e35d53d2d8441f8a61524fecdb031e",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "RadioButtons(description='Model: ', options=('linear', 'exponential', 'power', 'growth rate'), value='linear')"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "ce7d72952c0a4da98870bb1612a98431",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Button(description='Run', style=ButtonStyle())"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "0dda1ebc33304c7fbe6988fab2700913",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Output()"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "GUI_linear_regression()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Test with an example 4\n",
    "\n",
    "Find the least squares fit of the growth rate model to the given data:\n",
    "\n",
    "\n",
    "|x|1|3|5|7|9|\n",
    "|-|-|-|-|-|-|\n",
    "|y|0.85|1.4|1.73|1.68|1.96|\n",
    "\n",
    "\n",
    "\n",
    "plot the data points vs. the least squares solution, and find the correlation coefficient."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[[1, 0.850000000000000],\n",
       " [3, 1.40000000000000],\n",
       " [5, 1.73000000000000],\n",
       " [7, 1.68000000000000],\n",
       " [9, 1.96000000000000]]"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "points_4 = [[1, 0.85], [3, 1.4], [5, 1.73], [7, 1.68], [9, 1.96]]\n",
    "\n",
    "points_4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Required coefficients [2.19177854653905, 1.58559002228765]\n",
      "Correlation coefficient = 0.995146563071319\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "Graphics object consisting of 2 graphics primitives"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "solution_4, correlation_coefficient_4, graph_4 = linear_regression(points_4 ,model = 'growth', plot_function = True)\n",
    "\n",
    "print(f'Required coefficients {solution_4}\\nCorrelation coefficient = {correlation_coefficient_4}')\n",
    "show(graph_4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "227875c3c07e494186eb75e9e5b0ec3a",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Text(value='', description='Enter points: ', placeholder='e.g. [[18, 153], [19, 156], [21, 169]]')"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "51c3f870c65c449292ec0f36872be00a",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "RadioButtons(description='Model: ', options=('linear', 'exponential', 'power', 'growth rate'), value='linear')"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "f9d41b720cf14bbf97007e268ffcc1a3",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Button(description='Run', style=ButtonStyle())"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "6fed89dc84aa4010890d1e01a5bee42b",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Output()"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "GUI_linear_regression()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "SageMath 9.2",
   "language": "sage",
   "name": "sagemath"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.7"
  },
  "widgets": {
   "application/vnd.jupyter.widget-state+json": {
    "state": {
     "0742f96e7c554eaf947d133402603b95": {
      "model_module": "@jupyter-widgets/base",
      "model_module_version": "1.2.0",
      "model_name": "LayoutModel",
      "state": {}
     },
     "0aefc032e74b4293a7c36e99dbfd884d": {
      "model_module": "@jupyter-widgets/controls",
      "model_module_version": "1.5.0",
      "model_name": "DescriptionStyleModel",
      "state": {
       "description_width": ""
      }
     },
     "0cf6f6441f6e4b51901446c74e3b536f": {
      "model_module": "@jupyter-widgets/base",
      "model_module_version": "1.2.0",
      "model_name": "LayoutModel",
      "state": {}
     },
     "0dda1ebc33304c7fbe6988fab2700913": {
      "model_module": "@jupyter-widgets/output",
      "model_module_version": "1.0.0",
      "model_name": "OutputModel",
      "state": {
       "layout": "IPY_MODEL_2acc1fb369f247d8a7ff71264c4910f7",
       "outputs": [
        {
         "name": "stdout",
         "output_type": "stream",
         "text": "Parameters are 0.289032615005081, 3.01877203227068\nCorrelation coefficient is 0.998729161187500\n"
        },
        {
         "data": {
          "image/png": 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\n",
          "text/plain": "Graphics object consisting of 2 graphics primitives"
         },
         "metadata": {},
         "output_type": "display_data"
        }
       ]
      }
     },
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       "value": "[[1, 0.85], [3, 1.4], [5, 1.73], [7, 1.68], [9, 1.96]]"
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     "2494b4cca45748529b072049a0ae9a83": {
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       "description": "Enter points: ",
       "layout": "IPY_MODEL_b732f3d64ea84bff909ef30c3b13358e",
       "placeholder": "e.g. [[18, 153], [19, 156], [21, 169]]",
       "style": "IPY_MODEL_1af100e92c1b4f8ea4a8f278aa30aef7",
       "value": " [[1, 0.339], [2, 2.082], [3, 6.731], [4, 16.7995], [5, 35.423], [6, 75.224], [7, 117.506], [8, 162.077], [9, 197.054], [10, 337.557], [11, 405.831], [12, 603.241], [13, 643.630], [14, 830.005], [15, 879.403]]"
      }
     },
     "269f6919340143e8b91882e1fc4ad204": {
      "model_module": "@jupyter-widgets/output",
      "model_module_version": "1.0.0",
      "model_name": "OutputModel",
      "state": {
       "layout": "IPY_MODEL_c14bab1249c549f382cbbeb80bad2fee",
       "outputs": [
        {
         "name": "stdout",
         "output_type": "stream",
         "text": "Parameters are 26.8960000000000, -4.93680000000000\nCorrelation coefficient is 0.997918957473488\n"
        },
        {
         "data": {
          "image/png": 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\n",
          "text/plain": "Graphics object consisting of 2 graphics primitives"
         },
         "metadata": {},
         "output_type": "display_data"
        }
       ]
      }
     },
     "2acc1fb369f247d8a7ff71264c4910f7": {
      "model_module": "@jupyter-widgets/base",
      "model_module_version": "1.2.0",
      "model_name": "LayoutModel",
      "state": {}
     },
     "2b5af27d0d7843179298225135c166c8": {
      "model_module": "@jupyter-widgets/controls",
      "model_module_version": "1.5.0",
      "model_name": "DescriptionStyleModel",
      "state": {
       "description_width": ""
      }
     },
     "401fe276253b4aa09bfc0040d9592608": {
      "model_module": "@jupyter-widgets/controls",
      "model_module_version": "1.5.0",
      "model_name": "ButtonStyleModel",
      "state": {}
     },
     "487bbe53dae84ea99711460dcfc83569": {
      "model_module": "@jupyter-widgets/base",
      "model_module_version": "1.2.0",
      "model_name": "LayoutModel",
      "state": {}
     },
     "48e35d53d2d8441f8a61524fecdb031e": {
      "model_module": "@jupyter-widgets/controls",
      "model_module_version": "1.5.0",
      "model_name": "RadioButtonsModel",
      "state": {
       "_options_labels": [
        "linear",
        "exponential",
        "power",
        "growth rate"
       ],
       "description": "Model: ",
       "index": 2,
       "layout": "IPY_MODEL_6d81c9f2558e40ea9a6d2cb7ec332118",
       "style": "IPY_MODEL_2b5af27d0d7843179298225135c166c8"
      }
     },
     "4bdeca41422344bb83911704de9af5fc": {
      "model_module": "@jupyter-widgets/base",
      "model_module_version": "1.2.0",
      "model_name": "LayoutModel",
      "state": {}
     },
     "4da24a2a4ca84a929cc4639a70fe1403": {
      "model_module": "@jupyter-widgets/controls",
      "model_module_version": "1.5.0",
      "model_name": "TextModel",
      "state": {
       "description": "Enter points: ",
       "layout": "IPY_MODEL_e703702ffa2a475ab3689f87babc0af1",
       "placeholder": "e.g. [[18, 153], [19, 156], [21, 169]]",
       "style": "IPY_MODEL_cd0ff43059aa467eba1c1f608aea632d",
       "value": " [[5, -0.45], [10, -21.13], [15, -43.50], [20, -72.53], [25, -98.17]]"
      }
     },
     "51c3f870c65c449292ec0f36872be00a": {
      "model_module": "@jupyter-widgets/controls",
      "model_module_version": "1.5.0",
      "model_name": "RadioButtonsModel",
      "state": {
       "_options_labels": [
        "linear",
        "exponential",
        "power",
        "growth rate"
       ],
       "description": "Model: ",
       "index": 3,
       "layout": "IPY_MODEL_13aa4f4f2d004d09bb16eb26fc1f8a69",
       "style": "IPY_MODEL_b5dc04657eef458d81a01159387d20dd"
      }
     },
     "58c7cc419830425da53f4b7f6a4cb686": {
      "model_module": "@jupyter-widgets/controls",
      "model_module_version": "1.5.0",
      "model_name": "DescriptionStyleModel",
      "state": {
       "description_width": ""
      }
     },
     "5c828890439348448e461f8b3777bffb": {
      "model_module": "@jupyter-widgets/controls",
      "model_module_version": "1.5.0",
      "model_name": "DescriptionStyleModel",
      "state": {
       "description_width": ""
      }
     },
     "6d81c9f2558e40ea9a6d2cb7ec332118": {
      "model_module": "@jupyter-widgets/base",
      "model_module_version": "1.2.0",
      "model_name": "LayoutModel",
      "state": {}
     },
     "6fed89dc84aa4010890d1e01a5bee42b": {
      "model_module": "@jupyter-widgets/output",
      "model_module_version": "1.0.0",
      "model_name": "OutputModel",
      "state": {
       "layout": "IPY_MODEL_0cf6f6441f6e4b51901446c74e3b536f",
       "outputs": [
        {
         "name": "stdout",
         "output_type": "stream",
         "text": "Parameters are 2.19177854653905, 1.58559002228765\nCorrelation coefficient is 0.995146563071319\n"
        },
        {
         "data": {
          "image/png": 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\n",
          "text/plain": "Graphics object consisting of 2 graphics primitives"
         },
         "metadata": {},
         "output_type": "display_data"
        }
       ]
      }
     },
     "7e3b37f575394f4ebf7000447404827c": {
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      "state": {
       "_options_labels": [
        "linear",
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       ],
       "description": "Model: ",
       "index": 0,
       "layout": "IPY_MODEL_4bdeca41422344bb83911704de9af5fc",
       "style": "IPY_MODEL_58c7cc419830425da53f4b7f6a4cb686"
      }
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     "aa5f4dd107ac4ee693fa0524c8eac63a": {
      "model_module": "@jupyter-widgets/controls",
      "model_module_version": "1.5.0",
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     "b5dc04657eef458d81a01159387d20dd": {
      "model_module": "@jupyter-widgets/controls",
      "model_module_version": "1.5.0",
      "model_name": "DescriptionStyleModel",
      "state": {
       "description_width": ""
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     },
     "c055168ea901441d820f8ee248b8c321": {
      "model_module": "@jupyter-widgets/base",
      "model_module_version": "1.2.0",
      "model_name": "LayoutModel",
      "state": {}
     },
     "c14bab1249c549f382cbbeb80bad2fee": {
      "model_module": "@jupyter-widgets/base",
      "model_module_version": "1.2.0",
      "model_name": "LayoutModel",
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     },
     "c8233c9441d741218e994fbb9c5b9e84": {
      "model_module": "@jupyter-widgets/base",
      "model_module_version": "1.2.0",
      "model_name": "LayoutModel",
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     },
     "cd0ff43059aa467eba1c1f608aea632d": {
      "model_module": "@jupyter-widgets/controls",
      "model_module_version": "1.5.0",
      "model_name": "DescriptionStyleModel",
      "state": {
       "description_width": ""
      }
     },
     "ce7d72952c0a4da98870bb1612a98431": {
      "model_module": "@jupyter-widgets/controls",
      "model_module_version": "1.5.0",
      "model_name": "ButtonModel",
      "state": {
       "description": "Run",
       "layout": "IPY_MODEL_7e3b37f575394f4ebf7000447404827c",
       "style": "IPY_MODEL_401fe276253b4aa09bfc0040d9592608"
      }
     },
     "d59610aa835543a0b65185d9e5bcc463": {
      "model_module": "@jupyter-widgets/base",
      "model_module_version": "1.2.0",
      "model_name": "LayoutModel",
      "state": {}
     },
     "e53a9709704248b1b94772f9bd6a81dc": {
      "model_module": "@jupyter-widgets/output",
      "model_module_version": "1.0.0",
      "model_name": "OutputModel",
      "state": {
       "layout": "IPY_MODEL_83196c44a2e445319dd972ae4d22ab47",
       "outputs": [
        {
         "name": "stdout",
         "output_type": "stream",
         "text": "Parameters are 386.108386444157, 0.298007006799214\nCorrelation coefficient is 0.992541929629623\n"
        },
        {
         "data": {
          "image/png": 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\n",
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         },
         "metadata": {},
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 },
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}