statistics/10_days/26_day8pearsoncorrelationcoefficientii.ipynb

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    "Solution to: [Day 8: Pearson Correlation Coefficient II](https://www.hackerrank.com/challenges/s10-mcq-7/problem)"
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    "<h1 id=\"tocheading\">Table of Contents</h1>\n",
    "<div id=\"toc\"></div>\n",
    "\n",
    "- Table of Contents\n",
    "- Solution\n",
    "    - Write into regression form\n",
    "    - Pearon's Coefficient Formula\n",
    "    - Multiply equations\n",
    "    - Direction"
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    "# Solution\n",
    "\n",
    "## Write into regression form\n",
    "\n",
    "\\begin{equation}\n",
    "\\large\n",
    "y = -2 + -\\frac{3}{4} x\n",
    "\\end{equation}\n",
    "\n",
    "and\n",
    "\n",
    "\\begin{equation}\n",
    "\\large\n",
    "x = -\\frac{7}{4} + - \\frac{3}{4} y\n",
    "\\end{equation}\n",
    "\n",
    "\n",
    "Thus:\n",
    "- b1 = $-\\frac{3}{4}$\n",
    "- b2 = $-\\frac{3}{4}$"
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    "## Pearon's Coefficient Formula\n",
    "\n",
    "- p = pearson coefficient\n",
    "- x_sd = standard deviation of x\n",
    "- y_sd = standard deviation of y\n",
    "\n",
    "\\begin{equation}\n",
    "\\large\n",
    "p = b1 \\frac {x\\_sd}{y\\_sd}\n",
    "\\end{equation}\n",
    "\n",
    "and\n",
    "\n",
    "\\begin{equation}\n",
    "\\large\n",
    "p = b2 \\frac {x\\_sd}{y\\_sd}\n",
    "\\end{equation}\n"
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   "source": [
    "## Multiply equations\n",
    "\n",
    "\\begin{equation}\n",
    "\\large\n",
    "p^{2} = \n",
    "-\\frac{3}{4} * \n",
    "-\\frac{3}{4}\n",
    "\\end{equation}\n",
    "\n",
    "\\begin{equation}\n",
    "\\large\n",
    "p^{2} = \n",
    "\\frac{9}{16}\n",
    "\\end{equation}\n",
    "\n",
    "\\begin{equation}\n",
    "\\large\n",
    "p = \n",
    "\\frac{3}{4}\n",
    "\\end{equation}"
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   "source": [
    "## Direction\n",
    "\n",
    "As both original lines are negative, they are negatively correlated by definition.\n",
    "\n",
    "Answer:\n",
    "\n",
    "\\begin{equation}\n",
    "\\large\n",
    "p = \n",
    "- \\frac{3}{4}\n",
    "\\end{equation}"
   ]
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