Univariate Linear Regression.ipynb

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   "source": [
    "<h2 align=\"center\"> Univariate Linear Regression </h2>"
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    " "
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   "source": [
    "### Task 2: Load the Data and Libraries\n",
    "---"
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   "source": [
    "import matplotlib.pyplot as plt \n",
    "plt.style.use('ggplot')\n",
    "%matplotlib inline"
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   "source": [
    "import numpy as np\n",
    "import pandas as pd  \n",
    "import seaborn as sns \n",
    "plt.rcParams['figure.figsize'] = (12, 8)"
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    "### Task 3: Visualize the Data\n",
    "---"
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    "### Task 4: Compute the Cost $J(\\theta)$\n",
    "---"
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    "The objective of linear regression is to minimize the cost function\n",
    "\n",
    "$$J(\\theta) = \\frac{1}{2m} \\sum_{i=1}^m (h_\\theta(x^{(i)}) - y^{(i)} )^2$$\n",
    "\n",
    "where $h_{\\theta}(x)$ is the hypothesis and given by the linear model\n",
    "\n",
    "$$h_{\\theta}(x) = \\theta^Tx = \\theta_0 + \\theta_1x_1$$"
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    "### Task 5: Gradient Descent\n",
    "---"
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   "source": [
    "Minimize the cost function $J(\\theta)$ by updating the below equation and repeat unitil convergence\n",
    "        \n",
    "$\\theta_j := \\theta_j - \\alpha \\frac{1}{m} \\sum_{i=1}^m (h_{\\theta}(x^{(i)}) - y^{(i)})x_j^{(i)}$ (simultaneously update $\\theta_j$ for all $j$)."
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    "### Task 6: Visualising the Cost Function $J(\\theta)$\n",
    "---"
   ]
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    "### Task 7: Plotting the Convergence\n",
    "---"
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    "Plot $J(\\theta)$ against the number of iterations of gradient descent:"
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    "### Task 8: Training Data with Linear Regression Fit\n",
    "---"
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    "### Task 9: Inference using the optimized $\\theta$ values\n",
    "---"
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   "source": [
    "$h_\\theta(x) = \\theta^Tx$"
   ]
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