Logit-Python_beta.ipynb

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    "<h1>Table of Contents<span class=\"tocSkip\"></span></h1>\n",
    "<div class=\"toc\"><ul class=\"toc-item\"><li><span><a href=\"#Equation-1:\" data-toc-modified-id=\"Equation-1:-1\"><span class=\"toc-item-num\">1&nbsp;&nbsp;</span>Equation 1:</a></span></li><li><span><a href=\"#Equation-2.\" data-toc-modified-id=\"Equation-2.-2\"><span class=\"toc-item-num\">2&nbsp;&nbsp;</span>Equation 2.</a></span></li><li><span><a href=\"#Equation-3.\" data-toc-modified-id=\"Equation-3.-3\"><span class=\"toc-item-num\">3&nbsp;&nbsp;</span>Equation 3.</a></span></li><li><span><a href=\"#Equation-4.-Calculate-Probability-of-an-event\" data-toc-modified-id=\"Equation-4.-Calculate-Probability-of-an-event-4\"><span class=\"toc-item-num\">4&nbsp;&nbsp;</span>Equation 4. Calculate Probability of an event</a></span></li><li><span><a href=\"#Equation-5.-Log-Odds-of-an-event\" data-toc-modified-id=\"Equation-5.-Log-Odds-of-an-event-5\"><span class=\"toc-item-num\">5&nbsp;&nbsp;</span>Equation 5. Log-Odds of an event</a></span></li><li><span><a href=\"#Equation-4.\" data-toc-modified-id=\"Equation-4.-6\"><span class=\"toc-item-num\">6&nbsp;&nbsp;</span>Equation 4.</a></span></li><li><span><a href=\"#Equation-5.\" data-toc-modified-id=\"Equation-5.-7\"><span class=\"toc-item-num\">7&nbsp;&nbsp;</span>Equation 5.</a></span></li></ul></div>"
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    "# Using Logistic Regression for Binary Classification: An Easy-To-Understand Guide\n",
    "\n",
    "by Matthew Curcio\n",
    "\n",
    "For individuals who have studied cell biology or biochemistry, logistic regression may be familiar as [dose-response curves](https://en.wikipedia.org/wiki/Dose%E2%80%93response_relationship) in clinical testing, the sigmoidal curve of [Oxgen binding to Haemoglobin](https://en.wikipedia.org/wiki/Hill_equation_(biochemistry)), [median lethal dose curve](https://en.wikipedia.org/wiki/Median_lethal_dose) drug safety or even an [exponential growth given limited resources](https://en.wikipedia.org/wiki/Logistic_function).\n",
    "\n",
    "When Data Scientists discuss Logistic Regression (Logit) it is often used as a binary classifier. But, It can help you understand an outcome or make a prediction by providing three useful pieces of information.\n",
    "\n",
    "1. Presence or Absence of a substance or quality\n",
    "2. Probability of an event\n",
    "3. Odds for or against an event\n",
    "\n",
    "In plain English, a classifier is used to define or predict **Yes:No** answers, for example: \n",
    "- Success:Failure  \n",
    "- Fraud:Safe  \n",
    "- Benign:Malignant, *or even*\n",
    "- Buy:Sell\n",
    "\n",
    "But, Logit can help answer many more questions than **Yes:No**, \n",
    "\n",
    "- What is the probability customers will leave my business?   \n",
    "- Is this transaction Fraudulent or Safe?   \n",
    "- What is the probability that an event may occur?   \n",
    "- What are the odds of being diagnosed with cancer if you smoke versus if you do not? \n",
    "\n",
    "<!--\n",
    "It can even help Data Scientists determine which factors are important for keeping your customers and the probability of an event occurring.\n",
    "-->\n",
    "\n",
    "First, let’s take an example, A graphic showing the projected world population between 1950 and 2100:\n",
    "\n",
    "![World Population between 1950-2100](assets/world-pop-1950-2100.cc.jpg)\n",
    "\n",
    "When we look at the projected world population, we see each continent is added like a stacked bar chart but now over time. Further back in time, we approach zero population of humans. In the future, we will find a maximum value, an asymptote, that will be reached.\n",
    "\n",
    "But let’s see if we can simplify this complicated s-shaped curve. \n",
    "\n",
    "If we only consider any two points on our curve, we could use a linear set of equations.\n",
    "This would make sense since each continent has its own growth rate per time ($\\beta_{continent}$) and starting population ($x_{continent}$) at $t=0$ plus a constant ($\\beta_0$).\n",
    "\n",
    "### Equation 1. \n",
    "\n",
    "$$Population ~ (t=0 → t) = \\beta_{Asia} \\cdot x_{Asia} ~+~ \\beta_{Africa} \\cdot x_{Africa} ~+~ ... ~+~ \\beta_{Oceania} \\cdot x_{Oceania} ~+~ \\beta_0$$\n",
    "\n",
    "If we look at EQ2, we see the same formula in matrix format. A (1 row by 6 column) matrix times a (1 column by 6 row) matrix + b = Y, our population at time = t.\n",
    "\n",
    "We can rewrite this in matrix format:\n",
    "\n",
    "### Equation 2.\n",
    "\n",
    "$$World ~ Population ~=~ \n",
    "\\left( \\begin{array}{c} Growth~Rate \\\\ \\overline{\\beta_{Oceania}} \\\\ \\beta_{S.America} \\\\ \\beta_{N.America} \\\\ \\beta_{Europe} \\\\ \\beta_{Africa} \\\\ \\beta_{Asia}  \\end{array} \\right)^{\\large T}\n",
    "\\left( \\begin{array}{c} Population \\\\ \\overline{x_{Oceania}} \\\\ x_{S.America} \\\\ x_{N.America} \\\\ x_{Europe} \\\\ x_{Africa} \\\\ x_{Asia}  \\end{array} \\right)\n",
    "+  \\beta_0$$\n",
    "\n",
    "### Equation 3. \n",
    "\n",
    "$$Population(t=0 ~ → ~ t) = MX + b$$\n",
    "\n",
    ">NOTE: By convention capital letters represent matrices.\n",
    "\n",
    "How you may ask, can we have a linear regression fit a curved s-shaped line? \n",
    "\n",
    "- Using logs and exponents, we can transform the regression line.\n",
    "\n",
    "### Equation 4. \n",
    "\n",
    "$$ln(e^{(-MX + b)}) = MX + b$$\n",
    "\n",
    "Now let’s consider a logistic curve."
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    "## Plotting A Logistic Curve"
   ]
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",
      "text/plain": [
       "<Figure size 1000x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "%matplotlib inline\n",
    "\n",
    "def plot_logit():\n",
    "    x = np.linspace(-6,6,21)\n",
    "    y = 1/(1+np.exp(-1*x))\n",
    "\n",
    "    plt.figure(figsize=(10,5)) # 10 is width, 5 is height\n",
    "    plt.plot(x, y,'g',marker='D')  # g=green\n",
    "    #plt.title('A Simple Logistic Curve',fontsize=24)  \n",
    "    plt.xlabel('X',fontsize=24)\n",
    "    plt.ylabel('Probability',fontsize=24)\n",
    "    plt.xlim(-6,6)\n",
    "    plt.ylim(-0.1,1.1)\n",
    "\n",
    "    plt.axhline(y=0.5, color='r', linestyle='-.')\n",
    "    plt.axhline(y=0, color='b', linestyle='dotted')\n",
    "    plt.axhline(y=1, color='b', linestyle='dotted')\n",
    "    plt.axvline(x = 0, color = 'g')\n",
    "    plt.text(-5, 0.55,'Y=0 If Pr(x) < 0.5',fontsize=18)\n",
    "    plt.text(1.5, 0.55,'Y=1 If Pr(x) >= 0.5',fontsize=18)\n",
    "    #plt.text(-1.9, 0.92,'Inflection Pt, x=0',fontsize=18)\n",
    "    plt.yticks(np.arange(0, 1.3, 0.5),fontsize=14)\n",
    "    plt.xticks(np.arange(-6,6,2),fontsize=14)\n",
    "    plt.show()\n",
    "\n",
    "\n",
    "plot_logit()"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "1. Our x-axis can be time or any other independent value. \n",
    "2. The y-axis, we see Probability, from 0 to 1. \n",
    "\n",
    "Remember, Probabilities are only between zero chance to 100% certainty. \n",
    "\n",
    "On our simple graph, where x=0, we see an inflection point at 50% Probability. At that point, the probability of success (p) is 1/2, and the probability of failure (1-p) is also 1/2. Can we use this fact as our next transformation?\n",
    "\n",
    "### Equation 5. Calculate Probability of an event\n",
    "\n",
    "$$ln( Probability ) = MX + b$$\n",
    "\n",
    "### Equation 6. Log-Odds of an event\n",
    "\n",
    "$$ln \\left( \\frac{p}{1-p} \\right) = MX + b$$\n",
    "\n",
    "In other words, if the Probability = 0.5 then we find the odds of our event occurring at x=0 is [(0.5) : (0.5)]. \n",
    "\n",
    "If we were flipping a coin that it would be 1:1 odds. The ln(p / (1-p)) in equation 4 is commonly called log-odds. But if we wanted just odds, we would transform using the exponent.\n",
    "\n",
    "### Equation 7. \n",
    "\n",
    "$$\\large e^{ \\left( ln(\\frac{p}{1-p}) \\right) } = e^{MX + b}$$\n",
    "\n",
    "$$\\large \\frac{p}{1-p} = e^{MX + b}$$\n",
    "\n",
    "Next, We can expand our matrix multiplication to get Equation 5. \n",
    "\n",
    "### Equation 8. \n",
    "\n",
    "$$\\large \\frac{p}{1-p} = e^{~β_{Asia} \\cdot xAsia + β_{Africa} \\cdot xAfrica +...+ β_{Oceania} \\cdot xOceania + β_0}$$"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "https://www.kaggle.com/code/neisha/heart-disease-prediction-using-logistic-regression"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Using Python to calculate a logistic regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "https://www.kaggle.com/code/neisha/heart-disease-prediction-using-logistic-regression"
   ]
  }
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