{
"nbformat": 4,
"nbformat_minor": 0,
"metadata": {
"colab": {
"provenance": [],
"toc_visible": true
},
"kernelspec": {
"name": "ir",
"display_name": "R"
},
"language_info": {
"name": "R"
}
},
"cells": [
{
"cell_type": "markdown",
"source": [
"# 第8回 回帰分析\n"
],
"metadata": {
"id": "obnzB1V21pax"
}
},
{
"cell_type": "markdown",
"source": [
"[](https://colab.research.google.com/github/slt666666/biostatistics_text_wed/blob/main/source/_static/colab_notebook/chapter8.ipynb)\n",
"\n",
"※Web上ではテーブルや記号など一部LaTeXが反映されず見にくくなってしまっていますが、Google Colabだとちゃんと見えます。"
],
"metadata": {
"id": "ho8Gr-J0SDjj"
}
},
{
"cell_type": "markdown",
"source": [
"## はじめに\n",
"\n",
"統計的な手法の中で、もっともよく使用されている手法の中に回帰分析があります。\n",
"\n",
"回帰分析は非常に使いやすく、直感的に理解しやすい手法でもあるため、多くの方が既に使用した経験もあるのではないでしょうか。\n",
"\n",
"回帰分析についてもこれまで扱ってきた推定や検定が使用されており、またRを用いることで簡単に分析を実施できる。\n",
"\n",
"本項では、回帰分析や重回帰分析について扱います。\n",
"\n",
"まずは二つの変数の関連性の強さを示す**相関**について触れ、その後**回帰**について学びます。"
],
"metadata": {
"id": "2bLFQcxy824O"
}
},
{
"cell_type": "markdown",
"source": [
"## 相関\n",
"\n",
"序盤の記述統計学のところで扱いましたが、\n",
"\n",
"2つの変数$x, y$のデータが$(x_1, y_1), (x_2, y_2), \\cdots, (x_n, y_n)$で与えられたとき、変数$x$と変数$y$の間の相関係数$r_{xy}$は\n",
"\n",
"$r_{xy}=\\frac{\\sum (x_i-\\bar{x})(y_i-\\bar{y})/n}{\\sqrt{\\sum (x_i-\\bar{x})^2/n}\\sqrt{\\sum (y_i-\\bar{y})^2/n}}=\\frac{\\sum (x_i-\\bar{x})(y_i-\\bar{y})}{\\sqrt{\\sum (x_i-\\bar{x})^2}\\sqrt{\\sum (y_i-\\bar{y})^2}}$\n",
"\n",
"で定義されます。\n",
"\n",
"ただ、相関係数は$x, y$がともに正規分布に従っているという前提が必要な値になります。\n",
"\n",
"例えばある植物の草丈$(X)$と収穫量$(Y)$を測定して、以下の観測値が得られたとすると、\n",
"\n",
"\\begin{array}{ccccc} \\hline\n",
" 個体 & x & y \\\\ \\hline\n",
" 1 & 75 & 158 \\\\\n",
" 2 & 67 & 149 \\\\\n",
" 3 & 65 & 143 \\\\\n",
" 4 & 71 & 153 \\\\\n",
" 5 & 72 & 147 \\\\ \\hline\n",
"\\end{array}\n",
"\n",
"$X$と$Y$の相関係数はRの`cor`関数で計算できます。"
],
"metadata": {
"id": "xxXbNlXfipcb"
}
},
{
"cell_type": "code",
"source": [
"# x, y の相関係数をcor関数で求める\n",
"x <- c(75, 67, 65, 71, 72)\n",
"y <- c(158, 149, 143, 153, 147)\n",
"\n",
"cor(x, y)\n",
"\n",
"plot(x, y)"
],
"metadata": {
"id": "mu4Q79clV0LL",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 454
},
"outputId": "8727d4c1-481a-4e4c-bd95-34cc7e1fa65c"
},
"execution_count": null,
"outputs": [
{
"output_type": "display_data",
"data": {
"text/html": [
"0.815989012292334"
],
"text/markdown": "0.815989012292334",
"text/latex": "0.815989012292334",
"text/plain": [
"[1] 0.815989"
]
},
"metadata": {}
},
{
"output_type": "display_data",
"data": {
"text/plain": [
"plot without title"
],
"image/png": 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AFCggAhQYCQIEBIECAkCBASBAgJAoQE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\ngJAgQEgQICQIEBIECAkChAQB/w+gkW9qm3W8ggAAAABJRU5ErkJggg=="
},
"metadata": {
"image/png": {
"width": 420,
"height": 420
}
}
}
]
},
{
"cell_type": "markdown",
"source": [
"### 相関係数の検定\n",
"\n",
"相関係数が高いほど2変数間の相関は強いということですが、この点に関しても検定が出来ます。\n",
"\n",
"計算した相関係数$r$から、2変数が有意に相関関係にあるかどうかの検定です(あんまりやらないですが。)\n",
"\n",
"母集団における相関係数$\\rho$とすると、\n",
"\n",
"帰無仮説$H_0:\\rho=0$、対立仮説$H_1:\\rho \\ne 0$\n",
"\n",
"この時、帰無仮説の下で、\n",
"\n",
"$t=r\\sqrt{\\dfrac{n-2}{1-r^2}}$\n",
"\n",
"が自由度$n-2$の$t$分布$t(n-2)$に従います。\n",
"\n",
"この統計量をもとに帰無仮説を評価することになります。\n",
"\n",
"今回の場合、$t=0.816\\times \\sqrt{\\dfrac{5-2}{1-0.816^2}}=2.445$\n",
"\n",
"と$t$値を計算できるので、自由度$n-2 = 3$の$t$分布に基づいて$t_{1-\\alpha/2}(3)$を求めると、"
],
"metadata": {
"id": "1f68uMm2qc8S"
}
},
{
"cell_type": "code",
"source": [
"# qt関数でt分布のパーセント点を求める\n",
"qt(0.975, 3)"
],
"metadata": {
"id": "-jF_H5kwpjWM",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 34
},
"outputId": "1c432867-c2b3-49df-96ac-f3bab7f5c506"
},
"execution_count": null,
"outputs": [
{
"output_type": "display_data",
"data": {
"text/html": [
"3.18244630528371"
],
"text/markdown": "3.18244630528371",
"text/latex": "3.18244630528371",
"text/plain": [
"[1] 3.182446"
]
},
"metadata": {}
}
]
},
{
"cell_type": "markdown",
"source": [
"ということで、$t < t_{0.05/2}$となり、帰無仮説は棄却されない。\n",
"\n",
"つまり、$x,y$は有意水準5%の下では相関関係にあるとは言えない。という結果になります。\n",
"\n",
"ただし、下記に書いた注意点もふまえて、数値として相関係数を検定することは殆どありません。"
],
"metadata": {
"id": "pJyKQL1Ir10e"
}
},
{
"cell_type": "markdown",
"source": [
"### 相関係数の注意点\n",
"\n",
"相関係数$r$は$r \\geqq 0.6$だと強い相関がある、等の指標として用いられます。\n",
"\n",
"しかし、相関係数だけで変数間の関係性を判断するのは非常に危険です。\n",
"\n",
"Jan Vanhoveさんという方の作成したRプログラムで、ある相関係数を示す様々なデータプロットの様子を示す事が出来ます。\n",
"\n",
"下の`r=0.6`のところを色々変えると、相関係数がその数値になる場合のデータを何パターンも表示してくれます。"
],
"metadata": {
"id": "NgA9oIEisK9u"
}
},
{
"cell_type": "code",
"source": [
"# 相関係数のパターンをいくつか図示する\n",
"source(\"https://github.com/slt666666/biostatistics_text_wed/raw/refs/heads/main/source/_static/scripts/plot_r.R\")\n",
"plot_r(r = 0.6, n = 50)"
],
"metadata": {
"id": "dHdUmZNrryJ8",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 437
},
"outputId": "3eea0275-e6d2-4c49-e85b-6c5c92ea9c8b"
},
"execution_count": null,
"outputs": [
{
"output_type": "display_data",
"data": {
"text/plain": [
"Plot with title “All correlations: r(50) = 0.6”"
],
"image/png": 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lR6ejo1nLPJcbmFSuwaGxvZRw98+/bN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vr4CAgPT0dAMDgynNC/LJ6+npISU+7+7upqenn4eFtgQAACAASURBVFInFCiQU9Q4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\nwDaoal1orZIo+u2+medWSH+1qwMAFBQUPHv2LD4+vq2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VWHufTUK78dGOjvtuu9bNvXz5ckNDAzs7e0tLy82bNx/y82/+8uVjd7dKdfUD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\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CAwMNDb29vCwsLAwMDAwAAGg7W0tFA/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\nCQCzWW5urr6+vrCwcGBgoKmp6YEDB/z9/WkdFDB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},
"metadata": {
"image/png": {
"width": 420,
"height": 420
}
}
}
]
},
{
"cell_type": "markdown",
"source": [
"これを見ると、実際に散布図を作成してみないと、相関係数の高さとは関係なく、本当に$x,y$の間に意味のある相関があるかは分からないと理解できるかと思います。\n",
"\n",
"このことからも、これまで様々な検定や統計量を扱ってきましたが、これらはあくまでもデータを表す統計値の1つでしかなく、**生データの可視化**が最も重要だと言えます。"
],
"metadata": {
"id": "vOfuXbh0wW1Q"
}
},
{
"cell_type": "markdown",
"source": [
"## 回帰分析\n",
"\n",
"続いて、2変数の関係性は、相関だけではなく**回帰**という手法を用いても表現できます。\n",
"\n",
"\\begin{array}{ccccc} \\hline\n",
" 個体 & x & y \\\\ \\hline\n",
" 1 & 75 & 158 \\\\\n",
" 2 & 67 & 149 \\\\\n",
" 3 & 65 & 143 \\\\\n",
" 4 & 71 & 153 \\\\\n",
" 5 & 72 & 147 \\\\ \\hline\n",
"\\end{array}\n",
"\n",
"この様に草丈$(X)$と収穫量$(Y)$のデータがあるときに、$X$と$Y$の説明の関係性を定量的なモデルである**回帰方程式**として表すことが回帰分析になります。\n",
"\n",
"説明される変数$Y$は**従属変数**や**目的変数**、説明する変数$X$は**説明変数**と呼びます。\n",
"\n",
"回帰分析は$Y$を$X$で**説明**しようとすることが重要であり、単純に$X, Y$の間に関係があるかどうかだけ調べる**相関**とは異なっています。\n",
"\n",
"得られたデータから`ggplot`ライブラリの`geom_point`関数で散布図を描き、`geom_smooth(method=\"lm\", se=FALSE)`関数で回帰直線を描いてみると"
],
"metadata": {
"id": "9MsgesM5w2iw"
}
},
{
"cell_type": "code",
"source": [
"# ggplotを使用して、回帰直線付きの散布図を描く\n",
"library(ggplot2)\n",
"\n",
"x <- c(75, 67, 65, 71, 72)\n",
"y <- c(158, 149, 143, 153, 147)\n",
"data <- data.frame(x=x,y=y)\n",
"\n",
"g <- ggplot(data, aes(x=x, y=y))\n",
"g <- g + geom_point(size=7)\n",
"g <- g + geom_smooth(method=\"lm\",se=FALSE)\n",
"g <- g + theme(text = element_text(size = 24))\n",
"g"
],
"metadata": {
"id": "8ytMgoMjubMn",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 456
},
"outputId": "0645b1ab-759e-4bf5-f21c-1cece463fe4c"
},
"execution_count": null,
"outputs": [
{
"output_type": "stream",
"name": "stderr",
"text": [
"\u001b[1m\u001b[22m`geom_smooth()` using formula = 'y ~ x'\n"
]
},
{
"output_type": "display_data",
"data": {
"text/plain": [
"plot without title"
],
"image/png": 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cJHZVl+7bXXNmzYIAjC1VdfvWDBgpoc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\nAABQCYIdAACAShDsAAAAVOL/A7n6aMy1U5f6AAAAAElFTkSuQmCC"
},
"metadata": {
"image/png": {
"width": 420,
"height": 420
}
}
}
]
},
{
"cell_type": "markdown",
"source": [
"$X$(草丈)が伸びるに従って、$Y$収穫量も増加していそうな気がします。\n",
"\n",
"草丈($X$)によって説明できる部分と、それ以外の部分(切片)に分けてこの関係性を表すと、\n",
"\n",
"$y = \\beta_1 + \\beta_2x$\n",
"\n",
"と表すことができ、これは$y$の$x$上への**回帰方程式**と呼ばれます。\n",
"\n",
"今回の様に$y$が$x$の線形関数である場合、**線形回帰**と呼び、それ以外の場合は、**非線形回帰**と呼ぶ。\n",
"\n",
"ここで、$i$番目の個体の収穫量を$Y_i$、草丈を$X_i$、偶然生じたばらつきの部分を$\\epsilon_i$とすると、母集団における収穫量$Y$と草丈$X$の関係性は、\n",
"\n",
"$Y_i = \\beta_1+\\beta_2X_i+\\epsilon_i$ $(i=1,2,...,n)$\n",
"\n",
"と表せます。(このモデルは**母回帰方程式**と呼ばれます。)\n",
"\n",
"この$\\beta_1, \\beta_2$を**偏回帰係数**と呼び、母集団の値なので通常は未知な値となります。\n",
"\n",
"回帰分析では、この偏回帰係数について推定や検定を行うことになります。\n",
"\n",
"また、$\\epsilon_i$は**誤差項**と呼び、\n",
"\n",
"* 期待値は0になる。$E(\\epsilon_i) = 0$\n",
"* 分散は一定。$V(\\epsilon_i) = \\sigma^2$\n",
"\n",
"となります。そのため、$i$番目の個体の$X$の値$X_i$に対して、$Y_i$の期待値は\n",
"\n",
"$E(Y_i) = \\beta_1+\\beta_2X_i$\n",
"\n",
"となることを意味しています。\n",
"\n",
"↓誤差項のイメージ図\n",
"\n",
"![\"title\"](\"https://github.com/slt666666/biostatistics_text_wed/blob/main/source/_static/images/chapter9/lm.png?raw=true\")
"
],
"metadata": {
"id": "nXeFjIe_QKCU"
}
},
{
"cell_type": "markdown",
"source": [
"### 回帰係数の推定\n",
"\n",
"### **最小二乗法による回帰係数の推定**\n",
"\n",
"$Y_i = \\beta_1+\\beta_2X_i+\\epsilon_i$ $(i=1,2,...,n)$\n",
"\n",
"という回帰式において、$\\beta_1, \\beta_2$の推定を行います。\n",
"\n",
"下図の様な回帰式があった場合、$X_i$によって説明できない誤差項は\n",
"\n",
"![\"title\"](\"https://github.com/slt666666/biostatistics_text_wed/blob/main/source/_static/images/chapter8/lm.png?raw=true\")
\n",
"\n",
"$\\epsilon_i = Y_i - (\\beta_1 + \\beta_2X_i)$\n",
"\n",
"となります。この$\\epsilon$が出来るだけ小さくなる回帰式が適切な直線だと考えられます。\n",
"\n",
"そこで、$\\epsilon_i$の正負の符号を取り除いた和を、\n",
"\n",
"$S = \\sum\\epsilon_i^2 = \\sum \\lbrace Y_i - (\\beta_1 + \\beta_2X_i) \\rbrace^2$\n",
"\n",
"とすると、$S$は$Y_i$が$\\beta_1 + \\beta_2X_i$で説明できない部分の総和を表しています。\n",
"\n",
"この$S$を出来るだけ小さくする様に$\\beta_1, \\beta_2$の推定を行う方法の1つが**最小二乗法**になります。\n",
"\n",
"推定される$\\hat{\\beta_1}, \\hat{\\beta_2}$を$\\beta_1, \\beta_2$の**最小二乗推定量**と呼びます。\n",
"\n",
"$S$を最小にする$\\hat{\\beta_1}, \\hat{\\beta_2}$は偏微分により求める事が出来るので、\n",
"\n",
"$\\dfrac{\\partial S}{\\partial \\beta_1} = -2\\sum(Y_i-\\beta_1-\\beta_2X_i) = 0$\n",
"\n",
"$\\dfrac{\\partial S}{\\partial \\beta_2} = -2\\sum(Y_i-\\beta_1-\\beta_2X_i)X_i = 0$\n",
"\n",
"を解くことで求まります。\n",
"\n",
"この式を整理すると、\n",
"\n",
"$n\\beta_1 + (\\sum X_i)\\beta_2 = \\sum Y_i,$\n",
"\n",
"$(\\sum X_i)\\beta_1+(\\sum X_i^2)\\beta_2 = \\sum X_i Y_i$\n",
"\n",
"となり、これを解くと、$\\hat{\\beta_1}, \\hat{\\beta_2}$は\n",
"\n",
"$\\hat{\\beta_2} = \\dfrac{\\sum (X_i - \\bar{X})(Y_i - \\bar{Y})}{\\sum (X_i - \\bar{X})^2}$\n",
"\n",
"$\\hat{\\beta_1} = \\bar{Y}-\\hat{\\beta_2}\\bar{X}$\n",
"\n",
"と計算できます。この$\\hat{\\beta_1}, \\hat{\\beta_2}$は**標本偏回帰係数**と呼びます。\n",
"\n",
"この推定値により得られる$Y = \\hat{\\beta_1}+\\hat{\\beta_2}X$を**標本回帰方程式**と呼びます。\n",
"\n",
"\n"
],
"metadata": {
"id": "K28RqXTf9dIy"
}
},
{
"cell_type": "markdown",
"source": [
"\\begin{array}{ccccc} \\hline\n",
" 個体 & x & y \\\\ \\hline\n",
" 1 & 75 & 158 \\\\\n",
" 2 & 67 & 149 \\\\\n",
" 3 & 65 & 143 \\\\\n",
" 4 & 71 & 153 \\\\\n",
" 5 & 72 & 147 \\\\ \\hline\n",
"\\end{array}\n",
"\n",
"この草丈$(X)$と収穫量$(Y)$のデータから標本回帰方程式を求めてみると\n",
"\n",
"\n",
"$\\hat{\\beta_2} = \\dfrac{\\sum (X_i - \\bar{X})(Y_i - \\bar{Y})}{\\sum (X_i - \\bar{X})^2}$、$\\hat{\\beta_1} = \\bar{Y}-\\hat{\\beta_2}\\bar{X}$\n",
"\n"
],
"metadata": {
"id": "1eG3osuCF_hz"
}
},
{
"cell_type": "code",
"source": [
"# βの値を求める\n",
"x <- c(75, 67, 65, 71, 72)\n",
"y <- c(158, 149, 143, 153, 147)\n",
"\n",
"x_diff <- x - mean(x)\n",
"y_diff <- y - mean(y)\n",
"\n",
"beta2 <- sum(x_diff * y_diff) / sum(x_diff^2)\n",
"beta1 <- mean(y) - beta2 * mean(x)\n",
"\n",
"print(beta2)\n",
"print(beta1)"
],
"metadata": {
"id": "vpEEz1xjQg3r",
"colab": {
"base_uri": "https://localhost:8080/"
},
"outputId": "2a569df7-6b3f-4353-83f9-b3254bcb21e5"
},
"execution_count": null,
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": [
"[1] 1.171875\n",
"[1] 67.96875\n"
]
}
]
},
{
"cell_type": "markdown",
"source": [
"と計算されるので、$\\hat{\\beta_2}=1.171875, \\hat{\\beta_1}=67.96875$と求まります。\n",
"\n",
"そのため、標本回帰方程式は $Y = 67.96875 + 1.171875X $ と表せます。\n",
"\n",
"このとき、観測値$Y_i$と回帰方程式から得られる回帰値$\\hat{Y_i}$との差である\n",
"\n",
"$\\hat{e_i} = Y_i - \\hat{Y_i} = Y_i - \\hat{\\beta_1} - \\hat{\\beta_2}X_i$\n",
"\n",
"は、$X$で説明しきれない部分である**回帰残差**(residual)と呼ばれます。"
],
"metadata": {
"id": "N6k5EPdsIGM3"
}
},
{
"cell_type": "markdown",
"source": [
"### 回帰方程式の当てはまりの良さ(決定係数)\n",
"\n",
"こうして得られた回帰方程式がどの程度観測されたデータに当てはまっているのか、\n",
"\n",
"つまり、$X$によってどのくらい$Y$を説明できているのかは、モデルが意味のあるものか考える際に重要となります。\n",
"\n",
"回帰方程式によって$Y$の値をほとんど説明できていれば、意味のある回帰式だと考えられますが、逆に説明できていなければあまり意味は無いかもしれません。\n",
"\n",
"この当てはまりの良さをはかる基準として**決定係数**$r^2$があります。\n",
"\n",
"データ全体の$Y_i$のばらつきは$\\sum (Y_i - \\bar{Y})^2$によって計算できますが、このばらつき全体は回帰方程式で説明できる部分と出来ない部分に分ける事が出来ます。\n",
"\n",
"回帰方程式により求められた値と平均値の差の平方和$\\sum (\\hat{Y_i} - \\bar{Y})^2$が回帰方程式により説明できるばらつきとなり、\n",
"\n",
"先ほど計算した回帰残差の合計$\\sum \\hat{e_i}^2 = \\sum (Y_i - \\hat{Y_i})^2$が説明出来ないばらつきになります。\n",
"\n",
"つまり、\n",
"\n",
"$\\sum (Y_i - \\bar{Y})^2 = \\sum (\\hat{Y_i} - \\bar{Y})^2 + \\sum \\hat{e_i}^2$\n",
"\n",
"となっています。\n",
"\n",
"決定係数$r^2$は、$Y_i$のばらつき全体のうち、回帰方程式で説明できる部分の割合であり、\n",
"\n",
"$r^2 = 1 - \\dfrac{\\sum \\hat{e_i}^2}{\\sum (Y_i - \\bar{Y})^2} = \\dfrac{\\sum (\\hat{Y_i} - \\bar{Y})^2}{\\sum (Y_i - \\bar{Y})^2}$\n",
"\n",
"として計算できます。\n",
"\n",
"決定係数$r^2$は$0$から$1$の範囲の値で、回帰方程式で完全に$Y_i$を説明できる場合は$\\sum \\hat{e_i}^2=0$となり、$r^2 = 1$となります。\n",
"\n",
"逆に$r^2$が$0$に近付くほど、回帰方程式では$Y_i$のばらつきをほとんど説明できていないことを意味します。\n",
"\n",
"\\begin{array}{ccccc} \\hline\n",
" 個体 & x & y \\\\ \\hline\n",
" 1 & 75 & 158 \\\\\n",
" 2 & 67 & 149 \\\\\n",
" 3 & 65 & 143 \\\\\n",
" 4 & 71 & 153 \\\\\n",
" 5 & 72 & 147 \\\\ \\hline\n",
"\\end{array}\n",
"\n",
"この草丈$(X)$と収穫量$(Y)$のデータから得た標本回帰方程式$Y = 67.96875 + 1.171875X $の決定係数$r^2$を求めてみると"
],
"metadata": {
"id": "ANrrPTuXKZXf"
}
},
{
"cell_type": "code",
"source": [
"# y=67.96875+1.171875*xの式の決定係数を求める\n",
"x <- c(75, 67, 65, 71, 72)\n",
"y <- c(158, 149, 143, 153, 147)\n",
"\n",
"y_hat <- 67.96875+1.171875*x\n",
"sum((y_hat - mean(y))^2) / sum((y - mean(y))^2)"
],
"metadata": {
"id": "KBjS6G6I8m6_",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 34
},
"outputId": "f802d17a-c26a-480c-a543-6daad28c1a7c"
},
"execution_count": null,
"outputs": [
{
"output_type": "display_data",
"data": {
"text/html": [
"0.665838068181818"
],
"text/markdown": "0.665838068181818",
"text/latex": "0.665838068181818",
"text/plain": [
"[1] 0.6658381"
]
},
"metadata": {}
}
]
},
{
"cell_type": "markdown",
"source": [
"$r^2 = 0.6658$となり、そこそこの決定係数と分かります。\n",
"\n",
"### 回帰式の検定\n",
"\n",
"決定係数として求められる回帰式の当てはまりの良さは検定としても考える事が出来ます。\n",
"\n",
"求めた回帰式が標本によくあてはまっているかどうか検定するためには、分散分析の時と同じような考え方で実施できます。\n",
"\n",
"$y$のばらつき(変動)を回帰直線で説明できる変動とそれ以外の誤差による変動に分割し、両者を比較する形です。\n",
"\n",
"データ全体のばらつき、$Y$の総変動$S_Yを\n",
"\n",
"$S_Y = \\sum (Y_i - \\bar{Y})^2$\n",
"\n",
"回帰方程式によって説明できる変動$S_R$を\n",
"\n",
"$S_R = \\sum (\\hat{Y_i}-\\bar{Y})^2$\n",
"\n",
"誤差変動$S_e$を\n",
"\n",
"$S_e = \\sum (Y_i - \\hat{Y_i})^2$\n",
"\n",
"とすると、$S_Y = S_R + S_e$が成り立ちます。\n",
"\n",
"これらを分散分析表にまとめると、\n",
"\n",
"\\begin{array}{c|cccc} \\hline\n",
" 要因 & 平方和 & 自由度 & 平均平方 & F値 \\\\ \\hline\n",
" 全体 & S_Y & \\nu_Y = n-1 & V_Y=S_Y/\\nu_Y & \\\\\n",
" 回帰 & S_R & \\nu_R = 1 & V_r=S_R/\\nu_R & F = V_R / V_e\\\\\n",
" 誤差 & S_e & \\nu_e = n-2 & V_e=S_e/\\nu_e& \\\\ \\hline\n",
"\\end{array}\n",
"\n",
"となり、\n",
"\n",
"得られた$F$値は自由度$(\\nu_R = 1, \\nu_e = n-2)$の$F$分布$F(1, n-2)$に従うので、このことを利用して$F$検定を行うことが出来ます。\n",
"\n",
"また、この時総変動$S_Y$に対する回帰による変動$S_R$の割合\n",
"\n",
"$r^2 = \\dfrac{S_R}{S_Y}$\n",
"\n",
"が回帰式の寄与率、**決定係数**となりますが、\n",
"\n",
"この寄与率の平方根$r$は、実測値$Y_i$と回帰での予測値$\\hat{Y_i}$との間の相関係数と一致します。"
],
"metadata": {
"id": "Elk8sqBBPzHf"
}
},
{
"cell_type": "markdown",
"source": [
"### 偏回帰係数の検定\n",
"\n",
"回帰分析の目的は、標本偏回帰係数$\\hat{\\beta_1},\\hat{\\beta_2}$を推定し、回帰方程式を作ることだけではありません。\n",
"\n",
"母偏回帰係数$\\beta_1, \\beta_2$について検定することも目的の一つとなります。\n",
"\n",
"先ほどの例、\n",
"\n",
"\\begin{array}{ccccc} \\hline\n",
" 個体 & x & y \\\\ \\hline\n",
" 1 & 75 & 158 \\\\\n",
" 2 & 67 & 149 \\\\\n",
" 3 & 65 & 143 \\\\\n",
" 4 & 71 & 153 \\\\\n",
" 5 & 72 & 147 \\\\ \\hline\n",
"\\end{array}\n",
"\n",
"この草丈$(X)$と収穫量$(Y)$のデータから標本回帰方程式$Y = 67.96875 + 1.171875X $が得られましたが、\n",
"\n",
"この式に基づき、草丈は収穫量に影響を与えていない、つまり、$\\beta_2 = 0$という仮説は正しいかどうか？といった様々な仮説の検定を考えることが出来ます。\n",
"\n",
"検定をするためには、$\\hat{\\beta_1}, \\hat{\\beta_2}$がどの様な標本分布に従うのかを知る必要があります。\n",
"\n",
"### 偏回帰係数の標本分布\n",
"\n",
"最初に示した通り、$Y_i = \\beta_1+\\beta_2X_i+\\epsilon_i$ $(i=1,2,...,n)$\n",
"\n",
"という回帰式において、$\\hat{\\beta_1}, \\hat{\\beta_2}$は\n",
"\n",
"$\\hat{\\beta_2} = \\dfrac{\\sum (X_i - \\bar{X})(Y_i - \\bar{Y})}{\\sum (X_i - \\bar{X})^2}$\n",
"\n",
"$\\hat{\\beta_1} = \\bar{Y}-\\hat{\\beta_2}\\bar{X}$\n",
"\n",
"と計算されます。\n",
"\n",
"$\\epsilon_i$が正規分布$N(0, \\sigma^2)$に従うとすると、\n",
"\n",
"標本偏回帰係数$\\hat{\\beta_2}$は正規分布に従う$\\epsilon_i$の線形関数となるので、$\\hat{\\beta_2}$の標本分布も正規分布となります。\n",
"\n",
"その平均(期待値)と分散を求めると\n",
"\n",
"$E(\\hat{\\beta_2}) = \\beta_2$\n",
"\n",
"$V(\\hat{\\beta_2}) = \\dfrac{\\sigma^2}{\\sum (X_i - \\bar{X})^2}$\n",
"\n",
"と計算できるので、\n",
"\n",
"$\\hat{\\beta_2}$は正規分布$N(\\beta_2, \\dfrac{\\sigma^2}{\\sum (X_i - \\bar{X})^2})$に従います。\n",
"\n",
"しかし、この分布を検定に使うには$\\sigma^2$が未知です。\n",
"\n",
"そこで、回帰方程式の当てはまりの良さを表す誤差項$\\epsilon_i$の分散$\\sigma^2$の推定値を\n",
"\n",
"$\\hat{e_i}=Y_i - \\hat{\\beta_1}-\\hat{\\beta_2}X_i$から計算した、\n",
"\n",
"$s^2 = \\sum \\hat{e_i}^2 / (n-2)$\n",
"\n",
"を代わりに用います。この$s$を**推定値の標準誤差**と呼びます。\n",
"\n",
"$N(\\beta_2, \\dfrac{\\sigma^2}{\\sum (X_i - \\bar{X})^2})$を標準化した、$(\\hat{\\beta_2}-\\beta_2)/\\sqrt{\\sigma^2/\\sum (X_i - \\bar{X})^2}$は標準正規分布に従うので、\n",
"\n",
"この$\\sigma^2$を$s^2$で置き換えた\n",
"\n",
"$t_2 = \\dfrac{\\hat{\\beta_2}-\\beta_2}{\\sqrt{s^2/\\sum (X_i - \\bar{X})^2}}$\n",
"\n",
"は自由度$n-2$の$t$分布$t(n-2)$に従います。\n",
"\n",
"導出は省きますが、$\\hat{\\beta_1}$についても、$t_1 = \\dfrac{\\hat{\\beta_1}-\\beta_1}{\\sqrt{s^2\\sum X_i^2/n \\sum (X_i - \\bar{X})^2}}$が$t(n-2)$に従います。\n",
"\n",
"これらの統計量を基に、検定を行います。\n",
"\n",
"### 帰無仮説\n",
"\n",
"回帰方程式において、$X$が$Y$をどのように説明するかは$\\hat{\\beta_2}$で表されますが、この傾きの有意性を検定する形になります。\n",
"\n",
"特に重要なのが、帰無仮説$H_0: \\beta_2 = 0$の検定です。\n",
"\n",
"この帰無仮説が採択された場合、$X$では$Y$を説明できないことになるので、回帰式は適切なものとは言えなくなります。"
],
"metadata": {
"id": "4xOxuRvlRb7z"
}
},
{
"cell_type": "markdown",
"source": [
"### Rによる回帰分析の実施\n",
"\n",
"では計算してみましょう…と行きたいところですが、このあたりまでくると、一つずつRで計算していくのも面倒です。\n",
"\n",
"そこで、回帰分析や回帰分析に関連する検定を実施してくれる`lm`関数がRには実装されています。\n",
"\n",
"`lm`関数で回帰分析を実施するには、\n",
"\n",
"```\n",
"result <- lm(従属変数 ~ 説明変数)\n",
"summary(result)\n",
"```\n",
"というコードで実施できます。\n",
"\n",
"下記のデータを用いて、回帰分析を実施してみると、\n",
"\n",
"\\begin{array}{ccccc} \\hline\n",
" 個体 & x & y \\\\ \\hline\n",
" 1 & 75 & 158 \\\\\n",
" 2 & 67 & 149 \\\\\n",
" 3 & 65 & 143 \\\\\n",
" 4 & 71 & 153 \\\\\n",
" 5 & 72 & 147 \\\\ \\hline\n",
"\\end{array}\n",
"\n"
],
"metadata": {
"id": "JY2VqJ97WBwi"
}
},
{
"cell_type": "code",
"source": [
"# lm関数を使用して回帰分析を実施する\n",
"x <- c(75, 67, 65, 71, 72)\n",
"y <- c(158, 149, 143, 153, 147)\n",
"\n",
"result <- lm(y~x)\n",
"summary(result)"
],
"metadata": {
"id": "j4bpCqWPHt1j",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 353
},
"outputId": "727481a8-2058-4f57-c9c4-c1d421504642"
},
"execution_count": null,
"outputs": [
{
"output_type": "display_data",
"data": {
"text/plain": [
"\n",
"Call:\n",
"lm(formula = y ~ x)\n",
"\n",
"Residuals:\n",
" 1 2 3 4 5 \n",
" 2.141 2.516 -1.141 1.828 -5.344 \n",
"\n",
"Coefficients:\n",
" Estimate Std. Error t value Pr(>|t|) \n",
"(Intercept) 67.9687 33.5954 2.023 0.1362 \n",
"x 1.1719 0.4793 2.445 0.0921 .\n",
"---\n",
"Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1\n",
"\n",
"Residual standard error: 3.834 on 3 degrees of freedom\n",
"Multiple R-squared: 0.6658,\tAdjusted R-squared: 0.5545 \n",
"F-statistic: 5.978 on 1 and 3 DF, p-value: 0.09209\n"
]
},
"metadata": {}
}
]
},
{
"cell_type": "markdown",
"source": [
"`lm`関数を使用することで$\\hat{\\beta_1}, \\hat{\\beta_2}$の値や決定係数、当てはまりの良さの検定結果、そして先ほどの帰無仮説$H_0: \\beta_2 = 0$に基づく$t_2$値、それに基づく$p$値が計算されます。\n",
"\n",
"(そのほかの`Adjusted R-squared`などの値は次の重回帰分析のところで説明します。)"
],
"metadata": {
"id": "xow_B5hLZVkR"
}
},
{
"cell_type": "markdown",
"source": [
"### 回帰式による推定\n",
"\n",
"`ggplot`パッケージにある`geom_smooth`関数で回帰直線を描く事が出来ますが、このとき\n",
"\n",
"```\n",
"geom_smooth(method=\"lm\",se=TRUE)\n",
"```\n",
"\n",
"と`se`の引数を加えることで信頼区間の描写をON/OFFにする事が出来ます。"
],
"metadata": {
"id": "XbP1O1iJduTE"
}
},
{
"cell_type": "code",
"source": [
"# geom_smoothにse=TRUEを加えて信頼区間を同時に描く\n",
"library(ggplot2)\n",
"\n",
"x <- c(75, 67, 65, 71, 72)\n",
"y <- c(158, 149, 143, 153, 147)\n",
"data <- data.frame(x=x,y=y)\n",
"\n",
"g <- ggplot(data, aes(x=x, y=y))\n",
"g <- g + geom_point(size=7)\n",
"g <- g + geom_smooth(method=\"lm\",se=TRUE)\n",
"g <- g + theme(text = element_text(size = 24))\n",
"g"
],
"metadata": {
"id": "orId2rR6eIAC",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 456
},
"outputId": "9cafe5dc-c3ac-4b54-d5d0-cff5d491ed3b"
},
"execution_count": null,
"outputs": [
{
"output_type": "stream",
"name": "stderr",
"text": [
"\u001b[1m\u001b[22m`geom_smooth()` using formula = 'y ~ x'\n"
]
},
{
"output_type": "display_data",
"data": {
"text/plain": [
"plot without title"
],
"image/png": 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iMUFRUtW7asrKzszJkz999///LlyydM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},
"metadata": {
"image/png": {
"width": 420,
"height": 420
}
}
}
]
},
{
"cell_type": "markdown",
"source": [
"この信頼区間は母集団における95%信頼区間を示しています。\n",
"\n",
"$\\hat{Y_i} = \\hat{\\beta_1} + \\hat{\\beta_2}X_i = \\bar{Y}+\\hat{\\beta_2}(X_i - \\bar{X})$\n",
"\n",
"として、$\\hat{Y_i}$の分散を求めると、\n",
"\n",
"$V(\\hat{Y_i}) = V(\\bar{Y}) + (X_i - \\bar{X})^2V(\\hat{\\beta_2}) = (\\dfrac{1}{n}+\\dfrac{(X_i - \\bar{X})^2}{\\sum (X_i - \\bar{X})^2})\\sigma^2$\n",
"\n",
"となります。\n",
"\n",
"よって推定値$\\hat{Y_i}$は平均$\\hat{\\beta_1} + \\hat{\\beta_2}X_i$、分散$(\\dfrac{1}{n}+\\dfrac{(X_i - \\bar{X})^2}{\\sum (X_i - \\bar{X})^2})\\sigma^2$の正規分布に従う。\n",
"\n",
"しかし、$\\sigma^2$は未知なので先ほど扱った推定値の標準誤差$s^2 = \\sum \\hat{e_i}^2 / (n-2)$に置き換えると、\n",
"\n",
"$t$$=\\dfrac{\\hat{\\beta_1} + \\hat{\\beta_2}X_i - (\\beta_1+\\beta_2X_i)}{s\\sqrt{\\dfrac{1}{n}+\\dfrac{(X_i - \\bar{X})^2}{\\sum (X_i - \\bar{X})^2}}}$\n",
"\n",
"が自由度$n-2$の$t$分布$t(n-2)$に従うことが分かる。\n",
"\n",
"このことから$\\beta_1+\\beta_2X_i$の95％信頼区間は、\n",
"\n",
"$[\\hat{\\beta_1} + \\hat{\\beta_2}X_i-t_{\\alpha/2}(n-2)\\times s\\sqrt{\\dfrac{1}{n}+\\dfrac{(X_i - \\bar{X})^2}{\\sum (X_i - \\bar{X})^2}}, \\hat{\\beta_1} + \\hat{\\beta_2}X_i+t_{\\alpha/2}(n-2)\\times s\\sqrt{\\dfrac{1}{n}+\\dfrac{(X_i - \\bar{X})^2}{\\sum (X_i - \\bar{X})^2}}]$\n",
"\n",
"によって求められる。\n",
"\n",
"Rでは、95％信頼区間の具体的な数値は`lm`関数の結果を`predict`関数に適用することで計算できる。\n",
"\n",
"\n",
"\n"
],
"metadata": {
"id": "lZFb8JByfMz4"
}
},
{
"cell_type": "code",
"source": [
"# predict関数をlm関数の結果に適用して信頼区間を求める\n",
"x <- c(75, 67, 65, 71, 72)\n",
"y <- c(158, 149, 143, 153, 147)\n",
"\n",
"result <- lm(y~x)\n",
"\n",
"# 各xの観測値における信頼区間\n",
"interval_conf_exist <- predict(result, interval = 'confidence', level = 0.95)\n",
"interval_conf_exist\n",
"\n",
"# x=65~75における信頼区間\n",
"newx <- data.frame(x = seq(65, 75, 1))\n",
"interval_conf <- predict(result, newdata = newx, interval = 'confidence', level = 0.95)\n",
"interval_conf"
],
"metadata": {
"id": "YymPpVe_cBiv",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 617
},
"outputId": "aefe3149-95e4-4b86-a6f7-45c6111e5d7b"
},
"execution_count": null,
"outputs": [
{
"output_type": "display_data",
"data": {
"text/html": [
"\n",
"A matrix: 5 × 3 of type dbl\n",
"\n",
"\t | fit | lwr | upr |
|---|
\n",
"\n",
"\n",
"\t| 1 | 155.8594 | 146.4811 | 165.2376 |
|---|
\n",
"\t| 2 | 146.4844 | 139.3623 | 153.6064 |
|---|
\n",
"\t| 3 | 144.1406 | 134.7624 | 153.5189 |
|---|
\n",
"\t| 4 | 151.1719 | 145.5054 | 156.8384 |
|---|
\n",
"\t| 5 | 152.3438 | 146.0916 | 158.5959 |
|---|
\n",
"\n",
"
\n"
],
"text/markdown": "\nA matrix: 5 × 3 of type dbl\n\n| | fit | lwr | upr |\n|---|---|---|---|\n| 1 | 155.8594 | 146.4811 | 165.2376 |\n| 2 | 146.4844 | 139.3623 | 153.6064 |\n| 3 | 144.1406 | 134.7624 | 153.5189 |\n| 4 | 151.1719 | 145.5054 | 156.8384 |\n| 5 | 152.3438 | 146.0916 | 158.5959 |\n\n",
"text/latex": "A matrix: 5 × 3 of type dbl\n\\begin{tabular}{r|lll}\n & fit & lwr & upr\\\\\n\\hline\n\t1 & 155.8594 & 146.4811 & 165.2376\\\\\n\t2 & 146.4844 & 139.3623 & 153.6064\\\\\n\t3 & 144.1406 & 134.7624 & 153.5189\\\\\n\t4 & 151.1719 & 145.5054 & 156.8384\\\\\n\t5 & 152.3438 & 146.0916 & 158.5959\\\\\n\\end{tabular}\n",
"text/plain": [
" fit lwr upr \n",
"1 155.8594 146.4811 165.2376\n",
"2 146.4844 139.3623 153.6064\n",
"3 144.1406 134.7624 153.5189\n",
"4 151.1719 145.5054 156.8384\n",
"5 152.3438 146.0916 158.5959"
]
},
"metadata": {}
},
{
"output_type": "display_data",
"data": {
"text/html": [
"\n",
"A matrix: 11 × 3 of type dbl\n",
"\n",
"\t | fit | lwr | upr |
|---|
\n",
"\n",
"\n",
"\t| 1 | 144.1406 | 134.7624 | 153.5189 |
|---|
\n",
"\t| 2 | 145.3125 | 137.1265 | 153.4985 |
|---|
\n",
"\t| 3 | 146.4844 | 139.3623 | 153.6064 |
|---|
\n",
"\t| 4 | 147.6562 | 141.4041 | 153.9084 |
|---|
\n",
"\t| 5 | 148.8281 | 143.1616 | 154.4946 |
|---|
\n",
"\t| 6 | 150.0000 | 144.5427 | 155.4573 |
|---|
\n",
"\t| 7 | 151.1719 | 145.5054 | 156.8384 |
|---|
\n",
"\t| 8 | 152.3438 | 146.0916 | 158.5959 |
|---|
\n",
"\t| 9 | 153.5156 | 146.3936 | 160.6377 |
|---|
\n",
"\t| 10 | 154.6875 | 146.5015 | 162.8735 |
|---|
\n",
"\t| 11 | 155.8594 | 146.4811 | 165.2376 |
|---|
\n",
"\n",
"
\n"
],
"text/markdown": "\nA matrix: 11 × 3 of type dbl\n\n| | fit | lwr | upr |\n|---|---|---|---|\n| 1 | 144.1406 | 134.7624 | 153.5189 |\n| 2 | 145.3125 | 137.1265 | 153.4985 |\n| 3 | 146.4844 | 139.3623 | 153.6064 |\n| 4 | 147.6562 | 141.4041 | 153.9084 |\n| 5 | 148.8281 | 143.1616 | 154.4946 |\n| 6 | 150.0000 | 144.5427 | 155.4573 |\n| 7 | 151.1719 | 145.5054 | 156.8384 |\n| 8 | 152.3438 | 146.0916 | 158.5959 |\n| 9 | 153.5156 | 146.3936 | 160.6377 |\n| 10 | 154.6875 | 146.5015 | 162.8735 |\n| 11 | 155.8594 | 146.4811 | 165.2376 |\n\n",
"text/latex": "A matrix: 11 × 3 of type dbl\n\\begin{tabular}{r|lll}\n & fit & lwr & upr\\\\\n\\hline\n\t1 & 144.1406 & 134.7624 & 153.5189\\\\\n\t2 & 145.3125 & 137.1265 & 153.4985\\\\\n\t3 & 146.4844 & 139.3623 & 153.6064\\\\\n\t4 & 147.6562 & 141.4041 & 153.9084\\\\\n\t5 & 148.8281 & 143.1616 & 154.4946\\\\\n\t6 & 150.0000 & 144.5427 & 155.4573\\\\\n\t7 & 151.1719 & 145.5054 & 156.8384\\\\\n\t8 & 152.3438 & 146.0916 & 158.5959\\\\\n\t9 & 153.5156 & 146.3936 & 160.6377\\\\\n\t10 & 154.6875 & 146.5015 & 162.8735\\\\\n\t11 & 155.8594 & 146.4811 & 165.2376\\\\\n\\end{tabular}\n",
"text/plain": [
" fit lwr upr \n",
"1 144.1406 134.7624 153.5189\n",
"2 145.3125 137.1265 153.4985\n",
"3 146.4844 139.3623 153.6064\n",
"4 147.6562 141.4041 153.9084\n",
"5 148.8281 143.1616 154.4946\n",
"6 150.0000 144.5427 155.4573\n",
"7 151.1719 145.5054 156.8384\n",
"8 152.3438 146.0916 158.5959\n",
"9 153.5156 146.3936 160.6377\n",
"10 154.6875 146.5015 162.8735\n",
"11 155.8594 146.4811 165.2376"
]
},
"metadata": {}
}
]
},
{
"cell_type": "markdown",
"source": [
"実際に計算された信頼区間を点線で可視化すると、`geom_smooth`関数の範囲と一致しています。"
],
"metadata": {
"id": "EFQgEMyaehls"
}
},
{
"cell_type": "code",
"source": [
"# 計算された信頼区間と、geom_smooth関数で描かれる信頼区間を比較\n",
"library(ggplot2)\n",
"\n",
"x <- c(75, 67, 65, 71, 72)\n",
"y <- c(158, 149, 143, 153, 147)\n",
"data <- data.frame(x=x,y=y)\n",
"\n",
"\n",
"result <- lm(y~x)\n",
"newx <- data.frame(x = seq(65, 75, 1))\n",
"interval_conf <- predict(result, newdata = newx, interval = 'confidence', level = 0.95)\n",
"\n",
"d <- data.frame(x=newx$x,\n",
" y=interval_conf\n",
" )\n",
"\n",
"g <- ggplot(data,aes(x=x, y=y))+\n",
" geom_point(size=7) +\n",
" geom_smooth(method=\"lm\",se=TRUE) +\n",
" geom_line(d,mapping=aes(x=x, y=y.lwr),color=\"red\",linetype=2)+\n",
" geom_line(d,mapping=aes(x=x, y=y.upr),color=\"red\",linetype=2)\n",
"plot(g)"
],
"metadata": {
"id": "RkNjaKScdVzP",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 456
},
"outputId": "2fbed2bb-b38d-448f-c425-d78bd8591b89"
},
"execution_count": null,
"outputs": [
{
"output_type": "stream",
"name": "stderr",
"text": [
"\u001b[1m\u001b[22m`geom_smooth()` using formula = 'y ~ x'\n"
]
},
{
"output_type": "display_data",
"data": {
"text/plain": [
"plot without title"
],
"image/png": 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awQ6jJfn9oq9PdeSIFAhI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42gGDGNXtT/xov/I8LWhY1yPhyy+/nDt3bshmwZ9TdtkAAAHxSURBVHG1PCdoWLfP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\n8z8u3CetXwAAAABJRU5ErkJggg=="
},
"metadata": {
"image/png": {
"width": 420,
"height": 420
}
}
}
]
},
{
"cell_type": "markdown",
"source": [
"回帰分析で得られた回帰式に基づく推定で注意しておくべき点としては、\n",
"\n",
"得られた標本の観測値の範囲外(今回で言うと65~75より外側)でも同じような直線的な関係が続くかは保証できない所にあります。\n",
"\n",
"測定されている$X$の範囲外で$Y$を推定する場合を外挿法と呼び、利用には注意する必要があります。"
],
"metadata": {
"id": "4zOen3eryx5b"
}
},
{
"cell_type": "markdown",
"source": [
"## 重回帰分析\n",
"\n",
"ここまで扱ってきた回帰分析では、説明変数がたった1つしかない場合でした。\n",
"\n",
"この様な場合を**単回帰分析**と呼びます。\n",
"\n",
"しかし、多くの場合、複数の変数が従属変数に影響を与えていることが考えられます。\n",
"\n",
"例えば植物の収穫量には、草丈だけではなく、施肥量や日長、日照時間など、様々なものが説明変数として考えられます。\n",
"\n",
"この様な2つ以上の説明変数を考えた場合の回帰分析を**重回帰分析**と呼びます。\n",
"\n",
"重回帰分析における重回帰方程式は、母集団において\n",
"\n",
"$Y_i = \\beta_1 + \\beta_2X_{2i} + \\beta_3X_{3i} + \\cdots + \\beta_kX_{ki} + \\epsilon_i$\n",
"\n",
"と表現出来ます。\n",
"\n",
"$X_2 ... X_k$は説明変数、$\\epsilon$は誤差項、$\\beta_1, \\beta_2, ... \\beta_k$は、他の説明変数の影響を省いた各説明変数の影響を表しています。\n",
"\n",
"重回帰方程式には$k$個の母偏回帰係数$\\beta_1, \\beta_2, ... \\beta_k$があり、その推定は単回帰分析と同様に最小二乗法が用いられます。\n",
"\n",
"誤差項$\\epsilon_i = Y_i - (\\beta_1 + \\beta_2X_{2i} + \\beta_3X_{3i} + \\cdots + \\beta_kX_{ki})$\n",
"\n",
"の平方和$S = \\sum\\epsilon_i^2$を最小にする偏回帰係数を考える形です。\n",
"\n",
"$S$を最小にする$\\beta_1, \\beta_2, ... \\beta_k$は、それぞれの偏微分を$0$とした連立方程式\n",
"\n",
"$\\dfrac{\\partial S}{\\partial \\beta_1} = 0$, $\\dfrac{\\partial S}{\\partial \\beta_2} = 0$, ... $\\dfrac{\\partial S}{\\partial \\beta_k} = 0$\n",
"\n",
"を解くことで求まります。この解が標本偏回帰係数$\\hat{\\beta_1}, \\hat{\\beta_2}, \\hat{\\beta_3}, ... \\hat{\\beta_k}$となります。\n",
"\n",
"\n",
"\n",
"\n"
],
"metadata": {
"id": "IOww_Qs_Rb_2"
}
},
{
"cell_type": "markdown",
"source": [
"また、この解から得られた\n",
"\n",
"$Y = \\hat{\\beta_1} + \\hat{\\beta_2}X_2 + \\hat{\\beta_3}X_3 + \\cdots + \\hat{\\beta_k}X_k$\n",
"\n",
"を**標本重回帰方程式**と呼びます。\n",
"\n",
"$Y_i$の推定値は$\\hat{Y_i} = \\hat{\\beta_1} + \\hat{\\beta_2}X_{2i} + \\hat{\\beta_3}X_{3i} + \\cdots + \\hat{\\beta_k}X_{ki}$で推定されます。\n",
"\n",
"単回帰分析同様に、$Y_i$の総変動$\\sum (Y_i - \\bar{Y})^2$は重回帰方程式によって説明できる変動$\\sum (\\hat{Y_i} - \\bar{Y})^2$と誤差変動$\\sum \\hat{e_i}^2$の和で表す事が出来ます。\n",
"\n",
"$\\sum (Y_i - \\bar{Y})^2 = \\sum (\\hat{Y_i} - \\bar{Y})^2 + \\sum \\hat{e_i}^2$\n",
"\n",
"**決定係数**$R^2$は\n",
"\n",
"$R^2 = \\dfrac{\\sum (\\hat{Y_i} - \\bar{Y})^2}{\\sum (Y_i - \\bar{Y})^2} = 1 - \\dfrac{\\sum \\hat{e_i}^2}{\\sum (Y_i - \\bar{Y})^2}$\n",
"\n",
"で計算できます。\n",
"\n",
"決定係数の平方根$R$を**重相関係数**と呼びます。"
],
"metadata": {
"id": "fJsof9q9iJEX"
}
},
{
"cell_type": "markdown",
"source": [
"### 重回帰分析における偏回帰係数の検定\n",
"\n",
"重回帰分析でも単回帰分析同様に各偏回帰係数の有意性を検定できます。\n",
"\n",
"具体的には、$t_i = \\dfrac{\\hat{\\beta_i}-\\beta_i}{s.e.(\\hat{\\beta_i})}$が自由度$n-k$の$t$分布$t(n-k)$に従うことを利用します。(導出は省略)\n",
"\n",
"よって、ある１つの回帰係数について、\n",
"\n",
"帰無仮説$H_0: \\beta_i = a$の検定は単回帰分析と同じように実施できます。\n",
"\n",
"重回帰分析の場合、説明変数が複数あるので、同時に複数の偏回帰係数を検定することも出来ます。\n",
"\n",
"帰無仮説$H_0: \\beta_2 = 0 かつ \\beta_3 = 0$\n",
"\n",
"対立仮説$H_1: \\beta_2 \\ne 0または \\beta_3 \\ne 0$\n",
"\n",
"のような形です。\n",
"\n",
"この場合は回帰係数ごとに$t$検定をやるのでは不十分なので、\n",
"\n",
"$H_0$が正しい場合の重回帰方程式$Y_i = \\beta_1 + \\beta_4X_{4i} + ... + \\beta_kX_{ki}$と\n",
"\n",
"全ての説明変数を含む重回帰方程式$Y_i = \\beta_1 + \\beta_2X_{2i} + ... + \\beta_kX_{ki}$、\n",
"\n",
"それぞれから求めた残差の平方和$\\sum \\hat{e_i}^2$を$S_0, S_1$とすると、\n",
"\n",
"統計量$F = \\dfrac{(S_0 - S_1)/p}{S_1/(n-k)}$\n",
"\n",
"は帰無仮説の下で、自由度$(p, n-k)$の$F$分布$F(p, n-k)$に従うことを利用します。\n",
"\n",
"特に、すべての説明変数$X_2, X_3, ... X_k$が従属変数$Y$を説明しないという\n",
"\n",
"帰無仮説$H_0: \\beta_2 = \\beta_3 = \\cdots = \\beta_k = 0$\n",
"\n",
"対立仮説$H_1: \\beta_2, \\beta_3, \\cdots \\beta_k $の少なくとも1つは$0$ではない\n",
"\n",
"これらの仮説に基づいて検定する場合は、重回帰方程式の妥当性の検定が出来ます。\n"
],
"metadata": {
"id": "R4h1kQJt9udd"
}
},
{
"cell_type": "markdown",
"source": [
"### Rによる重回帰分析の実施\n",
"\n",
"単回帰分析同様、重回帰分析もRで簡単に実施する事が出来ます。\n",
"\n",
"下表の様なデータが得られたとき、収穫量を草丈・施肥量・葉身幅から推定するために\n",
"\n",
"$\\hat{Y_i} = \\hat{\\beta_1} + \\hat{\\beta_2}X_{2i} + \\hat{\\beta_3}X_{3i} + \\hat{\\beta_4}X_{4i}$\n",
"\n",
"という重回帰方程式を考えます。\n",
"\n",
"草丈($X_2$)、施肥量($X_3$)、葉身幅($X_4$)を表しています。\n",
"\n",
"\\begin{array}{ccccc} \\hline\n",
" 個体 & 収穫量 & 草丈 & 施肥量 & 葉身幅 \\\\ \\hline\n",
" 1 & 75 & 158 & 100 & 1.5 \\\\\n",
" 2 & 67 & 149 & 80 & 1.4 \\\\\n",
" 3 & 65 & 143 & 90 & 1.4 \\\\\n",
" 4 & 71 & 153 & 100 & 1.5 \\\\\n",
" 5 & 78 & 153 & 100 & 1.6 \\\\\n",
" 6 & 60 & 140 & 90 & 1.4 \\\\\n",
" 7 & 57 & 133 & 80 & 1.4 \\\\\n",
" 8 & 72 & 152 & 90 & 1.6 \\\\ \\hline\n",
"\\end{array}\n",
"\n",
"重回帰分析はRの`lm`関数で実施でき、データフレームの列名を使用して\n",
"\n",
"```\n",
"result <- lm(従属変数の列名 ~ 説明変数1の列名 + 説明変数2の列名 + ... + 説明変数kの列名, data=データフレーム名)\n",
"summary(result)\n",
"```\n",
"\n",
"と実施できます。"
],
"metadata": {
"id": "PxM7Bv9YIRz5"
}
},
{
"cell_type": "code",
"source": [
"# lm関数を使用して重回帰分析を行う\n",
"y <- c(75, 67, 65, 71, 78, 60, 57, 72)\n",
"x2 <- c(158, 149, 143, 153, 153, 140, 133, 152)\n",
"x3 <- c(100, 80, 90, 100, 100, 90, 80, 90)\n",
"x4 <- c(1.5, 1.4, 1.4, 1.5, 1.6, 1.4, 1.4, 1.6)\n",
"df <- data.frame(Yield=y, Height=x2, Fertilizer=x3, Leafwidth=x4)\n",
"\n",
"result <- lm(Yield~Height+Fertilizer+Leafwidth, data=df)\n",
"summary(result)"
],
"metadata": {
"id": "swwYUXfbKyV3",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 391
},
"outputId": "33b2bb31-b609-4048-b6c2-5a6819f9b968"
},
"execution_count": null,
"outputs": [
{
"output_type": "display_data",
"data": {
"text/plain": [
"\n",
"Call:\n",
"lm(formula = Yield ~ Height + Fertilizer + Leafwidth, data = df)\n",
"\n",
"Residuals:\n",
" 1 2 3 4 5 6 7 8 \n",
"-0.37609 0.87402 1.62720 -1.49850 2.83092 -1.64625 0.08231 -1.89363 \n",
"\n",
"Coefficients:\n",
" Estimate Std. Error t value Pr(>|t|) \n",
"(Intercept) -62.61385 16.38883 -3.821 0.0188 *\n",
"Height 0.57552 0.16190 3.555 0.0237 *\n",
"Fertilizer 0.06999 0.15010 0.466 0.6653 \n",
"Leafwidth 26.70583 13.66566 1.954 0.1224 \n",
"---\n",
"Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1\n",
"\n",
"Residual standard error: 2.243 on 4 degrees of freedom\n",
"Multiple R-squared: 0.9455,\tAdjusted R-squared: 0.9046 \n",
"F-statistic: 23.12 on 3 and 4 DF, p-value: 0.005473\n"
]
},
"metadata": {}
}
]
},
{
"cell_type": "markdown",
"source": [
"単回帰分析と同じように各偏回帰係数の検定結果や決定係数等を計算して出力してくれます。\n",
"\n",
"ここで、決定係数(Multiple R-squared)とは別で、**自由度調整済み決定係数**(Adjusted R-squared)とよ呼ばれる値も計算されています。\n",
"\n",
"通常の決定係数が偏差平方和から計算されるのに対し、自由度調整済みの決定係数は平均平方を用いて計算される値になります。\n",
"\n",
"自由度調整済み決定係数$R_f = \\dfrac{\\sum (y_i - \\hat{y_i})^2/(n-k-1)}{\\sum (y_i - \\bar{y})^2/(n-1)}$\n",
"\n",
"決定係数は(全然関係無いものであっても)説明変数の数が増えるほど1に近づくという性質を持っているので、説明変数の数が異なる回帰モデルどうしを比較する場合には、変数の数が考慮された自由度調整済み決定係数を使います。\n"
],
"metadata": {
"id": "UhrMCTgDN3f2"
}
},
{
"cell_type": "markdown",
"source": [
"#### (参考) 行列計算による偏回帰係数の算出\n",
"\n",
"標本偏回帰係数は**行列計算**によって求めることもできます。\n",
"\n",
"観測値$Y_1, Y_2, ..., Y_n$が得られたとき、\n",
"\n",
"\\begin{equation}\n",
" \\begin{pmatrix}\n",
" Y_{1} \\\\\n",
" Y_{2} \\\\\n",
" \\vdots \\\\\n",
" Y_{n}\n",
" \\end{pmatrix}\n",
" =\n",
" \\begin{pmatrix}\n",
" 1 & X_{11} & \\dots & X_{1k} \\\\\n",
" 1 & X_{21} & \\dots & X_{2k} \\\\\n",
" \\vdots & \\vdots & \\ddots & \\vdots \\\\\n",
" 1 & X_{n1} & \\dots & X_{nk}\n",
" \\end{pmatrix}\n",
" \\begin{pmatrix}\n",
" \\beta_{1} \\\\\n",
" \\beta_{2} \\\\\n",
" \\vdots \\\\\n",
" \\beta_{k}\n",
" \\end{pmatrix}\n",
" +\n",
" \\begin{pmatrix}\n",
" \\epsilon_{1} \\\\\n",
" \\epsilon_{2} \\\\\n",
" \\vdots \\\\\n",
" \\epsilon_{n}\n",
" \\end{pmatrix}\n",
"\\end{equation}\n",
"\n",
"といった形で行列とベクトルを用いて$\\mathbf{Y}=\\mathbf{X}\\boldsymbol{\\beta}+\\boldsymbol{\\epsilon}$と表す事が出来ます。\n",
"\n",
"誤差ベクトルの平方和$\\boldsymbol{\\epsilon}'\\boldsymbol{\\epsilon}$を最小にするには、\n",
"\n",
"$||\\boldsymbol{X\\beta-Y}||^2$を最小にすることになるので、\n",
"\n",
"$||\\boldsymbol{X\\beta-Y}||^2 = \\boldsymbol{(X\\beta-Y)'(X\\beta-Y)} = \\boldsymbol{(\\beta'X'-Y')(X\\beta-Y)} = \\boldsymbol{\\beta'X'X\\beta-2\\beta'X'Y+Y'Y}$\n",
"\n",
"この式を$\\boldsymbol{\\beta}$で微分して0と置いた式を解く。\n",
"\n",
"微分すると$\\boldsymbol{2X'X \\beta-2X'Y}$となるので、整理すると$\\boldsymbol{X'X \\beta = X'Y}$となる。\n",
"\n",
"ここで、$\\boldsymbol{X'X}$の逆行列$\\boldsymbol{(X'X)^{-1}}$が存在すれば、\n",
"\n",
"$\\boldsymbol{\\hat{\\beta} = (X'X)^{-1}X'Y}$から標本偏回帰係数を算出できます。"
],
"metadata": {
"id": "0WlfbTwEsVFV"
}
},
{
"cell_type": "markdown",
"source": [
"本講義ではRでの行列計算についてはあまり触れていませんが、\n",
"\n",
"`t(X)`で行列の転置、`solve(X)`で逆行列の計算、`X %*% Y`で行列XとYの積が求まります。\n",
"\n",
"実際に先ほどのデータで計算してみると…"
],
"metadata": {
"id": "0SP6960Nt880"
}
},
{
"cell_type": "code",
"source": [
"# 行列計算で偏回帰係数を求める\n",
"y <- c(75, 67, 65, 71, 78, 60, 57, 72)\n",
"x2 <- c(158, 149, 143, 153, 153, 140, 133, 152)\n",
"x3 <- c(100, 80, 90, 100, 100, 90, 80, 90)\n",
"x4 <- c(1.5, 1.4, 1.4, 1.5, 1.6, 1.4, 1.4, 1.6)\n",
"\n",
"X <- matrix(c(rep(1, 8), x2, x3, x4), ncol=4)\n",
"solve(t(X) %*% X) %*% t(X) %*% y"
],
"metadata": {
"id": "2_qKAIW3scG9",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 177
},
"outputId": "a93ce633-85aa-455e-a438-0b5cd379828c"
},
"execution_count": null,
"outputs": [
{
"output_type": "display_data",
"data": {
"text/html": [
"\n",
"A matrix: 4 × 1 of type dbl\n",
"\n",
"\t| -62.61384868 |
\n",
"\t| 0.57551822 |
\n",
"\t| 0.06999318 |
\n",
"\t| 26.70582575 |
\n",
"\n",
"
\n"
],
"text/markdown": "\nA matrix: 4 × 1 of type dbl\n\n| -62.61384868 |\n| 0.57551822 |\n| 0.06999318 |\n| 26.70582575 |\n\n",
"text/latex": "A matrix: 4 × 1 of type dbl\n\\begin{tabular}{l}\n\t -62.61384868\\\\\n\t 0.57551822\\\\\n\t 0.06999318\\\\\n\t 26.70582575\\\\\n\\end{tabular}\n",
"text/plain": [
" [,1] \n",
"[1,] -62.61384868\n",
"[2,] 0.57551822\n",
"[3,] 0.06999318\n",
"[4,] 26.70582575"
]
},
"metadata": {}
}
]
},
{
"cell_type": "markdown",
"source": [
"### 多重共線性\n",
"\n",
"重回帰分析を実施する際に、説明変数間に非常に高い相関関係がある場合、**多重共線性**の問題が生じる場合があります。\n",
"\n",
"極端な例ですが、先ほどのデータに施肥量Bという施肥量Aとほとんど同じ(相関が非常に強い)説明変数があったとします。\n",
"\n",
"\\begin{array}{ccccc} \\hline\n",
" 個体 & 収穫量 & 草丈 & 施肥量A & 施肥量B & 葉身幅 \\\\ \\hline\n",
" 1 & 75 & 158 & 100 & 100 & 1.5 \\\\\n",
" 2 & 67 & 149 & 80 & 80 & 1.4 \\\\\n",
" 3 & 65 & 143 & 90 & 90 & 1.4 \\\\\n",
" 4 & 71 & 153 & 100 & 100 & 1.5 \\\\\n",
" 5 & 78 & 153 & 100 & 100 & 1.6 \\\\\n",
" 6 & 60 & 140 & 90 & 90 & 1.4 \\\\\n",
" 7 & 57 & 133 & 80 & 80 & 1.4 \\\\\n",
" 8 & 72 & 152 & 90 & 89.999 & 1.6 \\\\ \\hline\n",
"\\end{array}\n",
"\n",
"このデータを用いて重回帰分析を行うと"
],
"metadata": {
"id": "0IAF_OnTRd7d"
}
},
{
"cell_type": "code",
"source": [
"# 多重共線性が生じた場合\n",
"y <- c(75, 67, 65, 71, 78, 60, 57, 72)\n",
"x2 <- c(158, 149, 143, 153, 153, 140, 133, 152)\n",
"x3 <- c(100, 80, 90, 100, 100, 90, 80, 90)\n",
"x4 <- c(100, 80, 90, 100, 100, 90, 80, 89.999)\n",
"x5 <- c(1.5, 1.4, 1.4, 1.5, 1.6, 1.4, 1.4, 1.6)\n",
"df <- data.frame(Yield=y, Height=x2, Fertilizer=x3, FertilizerB=x4, Leafwidth=x5)\n",
"\n",
"result <- lm(Yield~Height+Fertilizer+FertilizerB+Leafwidth, data=df)\n",
"summary(result)"
],
"metadata": {
"id": "hHf5Xkz9SVtT",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 466
},
"outputId": "28c49086-d219-4bce-a2d5-e6796f502bb2"
},
"execution_count": null,
"outputs": [
{
"output_type": "display_data",
"data": {
"text/plain": [
"\n",
"Call:\n",
"lm(formula = Yield ~ Height + Fertilizer + FertilizerB + Leafwidth, \n",
" data = df)\n",
"\n",
"Residuals:\n",
" 1 2 3 4 5 6 7 \n",
"-2.550e-01 -7.594e-02 2.415e+00 -1.330e+00 7.926e-01 -8.300e-01 -7.167e-01 \n",
" 8 \n",
" 2.981e-12 \n",
"\n",
"Coefficients:\n",
" Estimate Std. Error t value Pr(>|t|) \n",
"(Intercept) -80.5121 16.2739 -4.947 0.0158 *\n",
"Height 0.5850 0.1286 4.548 0.0199 *\n",
"Fertilizer -5603.9187 3061.9518 -1.830 0.1646 \n",
"FertilizerB 5603.8206 3061.8600 1.830 0.1646 \n",
"Leafwidth 48.7720 16.2175 3.007 0.0573 .\n",
"---\n",
"Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1\n",
"\n",
"Residual standard error: 1.78 on 3 degrees of freedom\n",
"Multiple R-squared: 0.9742,\tAdjusted R-squared: 0.9399 \n",
"F-statistic: 28.36 on 4 and 3 DF, p-value: 0.01018\n"
]
},
"metadata": {}
}
]
},
{
"cell_type": "markdown",
"source": [
"このように、多重共線性が生じると、施肥量の$\\hat{\\beta}$の推定値が極端な値になってしまうことが分かります。\n",
"\n",
"この様な場合を避けるために、相関の強い説明変数が混じっていた場合には、どちらか一方のみを採用する等する必要があります。\n",
"\n",
"特に遺伝子型データは連鎖の影響から多重共線性が非常に発生しやすいデータとして有名です。"
],
"metadata": {
"id": "5633ppu4Tia_"
}
},
{
"cell_type": "markdown",
"source": [
"## 相関・因果関係・擬似相関\n",
"\n",
"相関と回帰はいずれも2つの変数の関係を示す統計量でしたが、\n",
"\n",
"その関係性には相関関係・因果関係・擬似相関という3つのパターンがあります。\n",
"\n",
"![\"title\"](\"https://github.com/slt666666/biostatistics_text_wed/blob/main/source/_static/images/chapter8/soukan.png?raw=true\")
\n",
"\n",
"* 相関関係は2変数の間に方向性が無いパターン\n",
"* 因果関係は片方の変数がもう片方に影響を与えるパターン\n",
"* 擬似相関は第3の因子により2変数に関連が生じているパターン\n",
"\n",
"2変数のデータがあれば相関係数や回帰係数が算出できますが、それがどの様な関係性によって生じているのかは注意が必要です。\n",
"\n",
"ただ「相関がある」という結果から「因果関係がある」と断定することは通常難しく、\n",
"\n",
"また、一見因果関係がありそうでも、擬似相関による場合なども含まれています。\n",
"\n",
"例えば回帰分析によって「草丈が伸びれば収穫量が増える」という結果が分かったとしても、草丈が原因となって収穫量が増えたとは限りません。\n",
"\n",
"第3の要因(施肥量・品種の特性など)によって植物体が大きくなった結果、草丈・収穫量の両者が伸び、その間に擬似的な相関が生じたという可能性も十分あります。\n",
"\n",
"よって2変数の関係性について、結果を述べる際には表現に注意する必要があります。\n"
],
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