R Squared and Adjusted R Squared.ipynb

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    "# R Squared\n",
    "\n",
    "`- SSres = SUM(Yi - Yi hat)^2`\n",
    "    \n",
    "    - where SSres is Sum of Square of Residuals.\n",
    "\n",
    "`- SStot = SUM(Yi - Yavg)^2`\n",
    "\n",
    "    - where SStot is Total Sum of Squares.\n",
    "\n",
    "`- R Squared = 1 - (SSres / SStot)`\n",
    "- If SS residual is zero, so basically your trend line that your modeling goes through all your records then in that case R-squared is equal to 1.\n",
    "- The closer the R-squared to 1 the better the further away it is from 1 so, the lower it is the worse.\n",
    "- R Squared can be negative as if SS residual fits your data worse than then your average line."
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    "# Adjusted R Squared\n",
    "`- Adj R Squared = 1 - (1 - R Squared) [ (n - 1) / (n - p - 1) ] )`\n",
    "    \n",
    "    - where, p is number of regressors and n is sample size.\n",
    "- Adjusted R Squared has a penalization factor.\n",
    "- It penalizes you for adding independent variable that dont help your model.\n",
    "- When p increases, `(n - p -1)` decreases, and when this whole part decreases the denominator decreases the ratio increases and as the ratio increases `(1 - R Squared) [ (n - 1) / (n - p - 1) ] )` increases as well.\n",
    "- As adding more regressor the adjusted r-squared is decreasing.\n",
    "- As R-squared increases `(1 - R Squared)` decreases so whole adjusted r-squared increases."
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