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    "# Multiple Regression\n",
    "\n",
    "This chapter extends simple regression to models with several predictors. You will interpret coefficients, assess model assumptions, and evaluate prediction quality with training and testing data.\n"
   ]
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   "source": [
    "<h2>Chapter Video</h2>\n",
    "\n",
    "<iframe width=\"560\" height=\"315\" src=\"https://www.youtube-nocookie.com/embed/zITIFTsivN8\" title=\"What Is Multiple Regression and How Is It Used?\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" allowfullscreen referrerpolicy=\"strict-origin-when-cross-origin\"></iframe>\n",
    "\n",
    "<div class=\"video-credit\">\n",
    "<p><strong>Video credit:</strong> StatQuest with Josh Starmer. <em>What Is Multiple Regression and How Is It Used?</em>. YouTube. <a href=\"https://youtube.com/watch?v=zITIFTsivN8\">Watch on YouTube</a>.</p>\n",
    "<p class=\"video-rights\">This embedded video is provided for educational reference only. All rights are retained by the respective copyright holder.</p>\n",
    "</div>\n"
   ]
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   "id": "f4bffc87",
   "source": "```{contents}\n:local:\n:depth: 2\n```",
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    "<h2>Learning Objectives</h2>\n",
    "\n",
    "By the end of this chapter, you will be able to:\n",
    "\n",
    "1. Explain how multiple regression extends simple linear regression.\n",
    "2. Interpret regression coefficients while holding other predictors fixed.\n",
    "3. Recognize multicollinearity and other modeling assumptions.\n",
    "4. Evaluate model quality with errors and train/test comparisons.\n",
    "5. Use multiple regression for applied prediction and explanation questions.\n"
   ]
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    "<h2>Chapter Flow</h2>\n",
    "\n",
    "```{div} chapter-flow\n",
    "{doc}`Linear Regression <1301-linear-regression>`\n",
    "\n",
    "{doc}`Multiple Regression <1302-multiple-regression>`\n",
    "```\n"
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    "<h2>Glossary</h2>\n",
    "\n",
    "| # | Term | Explanation |\n",
    "|---:|---|---|\n",
    "| 1 | Multiple regression | Regression with more than one predictor. |\n",
    "| 2 | Predictor | An input variable used in a model. |\n",
    "| 3 | Target | The outcome variable being modeled. |\n",
    "| 4 | Coefficient | A model parameter attached to a predictor. |\n",
    "| 5 | Intercept | The predicted target when all predictors equal zero. |\n",
    "| 6 | Holding constant | Interpreting one predictor while other predictors stay fixed. |\n",
    "| 7 | Feature matrix | A table of predictor values used for modeling. |\n",
    "| 8 | Response vector | The target values used for modeling. |\n",
    "| 9 | Multicollinearity | Strong association among predictors. |\n",
    "| 10 | Additivity | A model assumption that predictor effects combine by addition. |\n",
    "| 11 | Linearity | A model assumption that relationships are represented by straight-line effects. |\n",
    "| 12 | Residual | Observed value minus predicted value. |\n",
    "| 13 | Residual diagnostic | A check based on residual patterns. |\n",
    "| 14 | Training data | Data used to fit a model. |\n",
    "| 15 | Test data | Data reserved to evaluate model performance. |\n",
    "| 16 | Mean squared error | Average squared prediction error. |\n",
    "| 17 | Root mean squared error | Square root of mean squared prediction error. |\n",
    "| 18 | R-squared | The proportion of outcome variation explained by a model. |\n",
    "| 19 | Overfitting | When a model fits training data too closely and generalizes poorly. |\n",
    "| 20 | Interpretability | How easily a model can be explained. |\n",
    "| 21 | Prediction pipeline | The steps used to prepare data, fit a model, and evaluate predictions. |\n"
   ]
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   "metadata": {},
   "source": [
    "<h2><a href=\"overview.html\" target=\"_blank\" rel=\"noopener noreferrer\">Chapter Overview Slides</a></h2>\n"
   ]
  }
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