{"id":1330,"date":"2024-01-07T18:15:57","date_gmt":"2024-01-07T10:15:57","guid":{"rendered":"https:\/\/edu.secda.info\/scu12354014\/?p=1330"},"modified":"2024-01-07T20:50:37","modified_gmt":"2024-01-07T12:50:37","slug":"%e8%a8%88%e9%87%8f%e7%b6%93%e6%bf%9f%e5%ad%b8%e4%bd%9c%e6%a5%ad-u4-%e5%96%ae%e4%b8%80%e8%bf%b4%e6%ad%b8%e8%ae%8a%e6%95%b8%e7%9a%84%e7%b7%9a%e6%80%a7%e8%bf%b4%e6%ad%b8","status":"publish","type":"post","link":"https:\/\/edu.secda.info\/scu12354014\/?p=1330","title":{"rendered":"\u8a08\u91cf\u7d93\u6fdf\u5b78\u4f5c\u696d U4 \u55ae\u4e00\u8ff4\u6b78\u8b8a\u6578\u7684\u7dda\u6027\u8ff4\u6b78"},"content":{"rendered":"<p><span style=\"color: #0000ff;\"><strong>4.1 \u7c21\u55ae\u7dda\u6027\u8ff4\u6b78<\/strong><\/span><\/p>\n<p>\u7dda\u6027\u56de\u6b78\u6a21\u578b\u662f<span id=\"MJXc-Node-94\" class=\"mjx-msubsup\"><span class=\"mjx-base\"><span id=\"MJXc-Node-95\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\">Y<\/span><\/span><\/span><span class=\"mjx-sub\"><span id=\"MJXc-Node-96\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\">i<\/span><\/span><\/span><\/span><span id=\"MJXc-Node-97\" class=\"mjx-mo MJXc-space3\"><span class=\"mjx-char MJXc-TeX-main-R\">=<\/span><\/span><span id=\"MJXc-Node-98\" class=\"mjx-msubsup MJXc-space3\"><span class=\"mjx-base\"><span id=\"MJXc-Node-99\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\">\u03b2<\/span><\/span><\/span><span class=\"mjx-sub\"><span id=\"MJXc-Node-100\" class=\"mjx-mn\"><span class=\"mjx-char MJXc-TeX-main-R\">0<\/span><\/span><\/span><\/span><span id=\"MJXc-Node-101\" class=\"mjx-mo MJXc-space2\"><span class=\"mjx-char MJXc-TeX-main-R\">+<\/span><\/span><span id=\"MJXc-Node-102\" class=\"mjx-msubsup MJXc-space2\"><span class=\"mjx-base\"><span id=\"MJXc-Node-103\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\">\u03b2<\/span><\/span><\/span><span class=\"mjx-sub\"><span id=\"MJXc-Node-104\" class=\"mjx-mn\"><span class=\"mjx-char MJXc-TeX-main-R\">1<\/span><\/span><\/span><\/span><span id=\"MJXc-Node-105\" class=\"mjx-msubsup\"><span class=\"mjx-base\"><span id=\"MJXc-Node-106\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\">X<\/span><\/span><\/span><span class=\"mjx-sub\"><span id=\"MJXc-Node-107\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\">i<\/span><\/span><\/span><\/span><span id=\"MJXc-Node-108\" class=\"mjx-mo MJXc-space2\"><span class=\"mjx-char MJXc-TeX-main-R\">+<\/span><\/span><span id=\"MJXc-Node-109\" class=\"mjx-msubsup MJXc-space2\"><span class=\"mjx-base\"><span id=\"MJXc-Node-110\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\">u<\/span><\/span><\/span><span class=\"mjx-sub\"><span id=\"MJXc-Node-111\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\">i<\/span><\/span><\/span><\/span><\/p>\n<blockquote><p>STR &lt;- c(15, 17, 19, 20, 22, 23.5, 25)<br \/>\nTestScore &lt;- c(680, 640, 670, 660, 630, 660, 635)<\/p>\n<p>plot(TestScore ~ STR,ylab=&#8221;Test Score&#8221;,pch=20)<\/p>\n<p>abline(a = 713, b = -3)<\/p><\/blockquote>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"\" src=\"https:\/\/www.econometrics-with-r.org\/ITER_files\/figure-html\/unnamed-chunk-145-1.png\" width=\"778\" height=\"556\" \/><\/p>\n<hr \/>\n<p><strong><span style=\"color: #0000ff;\">4.2 \u4f30\u8a08\u7dda\u6027\u8ff4\u6b78\u6a21\u578b\u7684\u4fc2\u6578<\/span><\/strong><\/p>\n<blockquote><p>plot(score ~ STR,data = CASchools,main = &#8220;Scatterplot of Test Score and STR&#8221;,xlab = &#8220;STR (X)&#8221;,ylab = &#8220;Test Score (Y)&#8221;)<\/p><\/blockquote>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"\" src=\"https:\/\/www.econometrics-with-r.org\/ITER_files\/figure-html\/unnamed-chunk-152-1.png\" width=\"688\" height=\"492\" \/><\/p>\n<p>\u89c0\u5bdf\u503c\u5728\u5e2b\u751f\u6bd4\u548c\u8003\u8a66\u6210\u7e3e\u7684\u6563\u4f48\u5716\u3002\u6211\u5011\u770b\u5230\u9019\u4e9b\u9ede\u5f37\u70c8\u5730\u5206\u6563\uff0c\u800c\u4e14\u9019\u4e9b\u8b8a\u6578\u5448\u8ca0\u76f8\u95dc\u3002\u4e5f\u5c31\u662f\u8aaa\uff0c\u6211\u5011\u9810\u671f\u5728\u8f03\u5927\u7684\u73ed\u7d1a\u4e2d\u89c0\u5bdf\u5230\u8f03\u4f4e\u7684\u5206\u6578\u3002<\/p>\n<blockquote><p>linear_model &lt;- lm(score ~ STR, data = CASchools)<\/p><\/blockquote>\n<p>Coefficients:<br \/>\n(Intercept)\u00a0 \u00a0STR<br \/>\n698.93\u00a0 \u00a0 \u00a0 \u00a0 \u00a0-2.28<\/p>\n<blockquote><p>plot(score ~ STR,data = CASchools,main = &#8220;Scatterplot of Test Score and STR&#8221;,xlab = &#8220;STR (X)&#8221;,ylab = &#8220;Test Score (Y)&#8221;,xlim = c(10, 30),ylim = c(600, 720))<\/p>\n<p>abline(linear_model)<\/p><\/blockquote>\n<p>&nbsp;<\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"\" src=\"https:\/\/www.econometrics-with-r.org\/ITER_files\/figure-html\/unnamed-chunk-158-1.png\" width=\"729\" height=\"520\" \/><\/p>\n<hr \/>\n<p><strong><span style=\"color: #0000ff;\">4.3 \u64ec\u5408\u5ea6\u91cf<\/span><\/strong><\/p>\n<blockquote><p>summary(linear_model)<\/p><\/blockquote>\n<p>lm(formula = score ~ STR, data = CASchools)<\/p>\n<p>Residuals:<br \/>\nMin\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 1Q\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 Median\u00a0 \u00a0 \u00a0 3Q\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 Max<br \/>\n-47.727\u00a0 \u00a0 \u00a0 \u00a0 -14.251\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 0.483\u00a0 \u00a0 12.822\u00a0 \u00a0 \u00a0 \u00a048.540<\/p>\n<p>Coefficients:<br \/>\nEstimate\u00a0 \u00a0 \u00a0 \u00a0 \u00a0Std. Error\u00a0 \u00a0 \u00a0t value\u00a0 \u00a0 \u00a0 Pr(&gt;|t|)<br \/>\n(Intercept)\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 698.9329\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 9.4675\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 73.825\u00a0 \u00a0 &lt; 2e-16 ***<br \/>\nSTR\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 -2.2798\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a00.4798\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 -4.751\u00a0 \u00a0 \u00a0 2.78e-06 ***<br \/>\n&#8212;<br \/>\nSignif. codes: 0 &#8216;***&#8217; 0.001 &#8216;**&#8217; 0.01 &#8216;*&#8217; 0.05 &#8216;.&#8217; 0.1 &#8216; &#8216; 1<\/p>\n<p>Residual standard error: 18.58 on 418 degrees of freedom<br \/>\nMultiple R-squared: <strong><span style=\"color: #ff0000;\">0.05124,<\/span><\/strong> Adjusted R-squared: 0.04897<br \/>\nF-statistic: 22.58 on 1 and 418 DF, p-value: 2.783e-06<\/p>\n<p>R^2\uff1a\u89e3\u91cb\u8b8a\u6578 <span class=\"math inline\" data-immersive-translate-walked=\"d7dfdb8a-87f2-45d9-a1cb-5d592097d16a\"><span id=\"MathJax-Element-39-Frame\" class=\"mjx-chtml MathJax_CHTML\" style=\"-webkit-font-smoothing: antialiased; box-sizing: border-box; -webkit-tap-highlight-color: transparent; text-size-adjust: none; display: inline-table; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 17.6px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; margin: 0px; padding: 1px 0px; position: relative;\" tabindex=\"0\" role=\"presentation\" data-mathml=\"&lt;math xmlns=&quot;http:\/\/www.w3.org\/1998\/Math\/MathML&quot;&gt;&lt;mi&gt;S&lt;\/mi&gt;&lt;mi&gt;T&lt;\/mi&gt;&lt;mi&gt;R&lt;\/mi&gt;&lt;\/math&gt;\"><span id=\"MJXc-Node-395\" class=\"mjx-math\" aria-hidden=\"true\"><span id=\"MJXc-Node-396\" class=\"mjx-mrow\"><span id=\"MJXc-Node-397\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\">S<\/span><\/span><span id=\"MJXc-Node-398\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\">T<\/span><\/span><span id=\"MJXc-Node-399\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\">R<\/span><\/span><\/span><\/span><\/span><\/span>\u00a0\u89e3\u91cb\u4e86\u4f9d\u8b8a\u6578\u00a0<span class=\"math inline\" data-immersive-translate-walked=\"d7dfdb8a-87f2-45d9-a1cb-5d592097d16a\"><span id=\"MathJax-Element-38-Frame\" class=\"mjx-chtml MathJax_CHTML\" style=\"-webkit-font-smoothing: antialiased; box-sizing: border-box; -webkit-tap-highlight-color: transparent; text-size-adjust: none; display: inline-table; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 17.6px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; margin: 0px; padding: 1px 0px; position: relative;\" tabindex=\"0\" role=\"presentation\" data-mathml=\"&lt;math xmlns=&quot;http:\/\/www.w3.org\/1998\/Math\/MathML&quot;&gt;&lt;mi&gt;s&lt;\/mi&gt;&lt;mi&gt;c&lt;\/mi&gt;&lt;mi&gt;o&lt;\/mi&gt;&lt;mi&gt;r&lt;\/mi&gt;&lt;mi&gt;e&lt;\/mi&gt;&lt;\/math&gt;\"><span id=\"MJXc-Node-388\" class=\"mjx-math\" aria-hidden=\"true\"><span id=\"MJXc-Node-389\" class=\"mjx-mrow\"><span id=\"MJXc-Node-390\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\">s<\/span><\/span><span id=\"MJXc-Node-391\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\">c<\/span><\/span><span id=\"MJXc-Node-392\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\">o<\/span><\/span><span id=\"MJXc-Node-393\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\">r<\/span><\/span><span id=\"MJXc-Node-394\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\">e<\/span><\/span><\/span><\/span><\/span><\/span>\u00a0\u7684\u8b8a\u7570\u6578\u7684\u00a0<span class=\"math inline\" data-immersive-translate-walked=\"d7dfdb8a-87f2-45d9-a1cb-5d592097d16a\"><span id=\"MathJax-Element-37-Frame\" class=\"mjx-chtml MathJax_CHTML\" style=\"-webkit-font-smoothing: antialiased; box-sizing: border-box; -webkit-tap-highlight-color: transparent; text-size-adjust: none; display: inline-table; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 17.6px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; margin: 0px; padding: 1px 0px; position: relative;\" tabindex=\"0\" role=\"presentation\" data-mathml=\"&lt;math xmlns=&quot;http:\/\/www.w3.org\/1998\/Math\/MathML&quot;&gt;&lt;mn&gt;5.1&lt;\/mn&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;&amp;#x0025;&lt;\/mi&gt;&lt;\/math&gt;\"><span id=\"MJXc-Node-384\" class=\"mjx-math\" aria-hidden=\"true\"><span id=\"MJXc-Node-385\" class=\"mjx-mrow\"><span id=\"MJXc-Node-386\" class=\"mjx-mn\"><span class=\"mjx-char MJXc-TeX-main-R\">5.1<\/span><\/span><span id=\"MJXc-Node-387\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-main-R\">%\u3002<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u6b98\u5dee\u6a19\u6e96\u8aa4\u5dee\u7a31\u70ba\u00a0<span class=\"math inline\" data-immersive-translate-walked=\"d7dfdb8a-87f2-45d9-a1cb-5d592097d16a\"><span id=\"MathJax-Element-41-Frame\" class=\"mjx-chtml MathJax_CHTML\" style=\"-webkit-font-smoothing: antialiased; box-sizing: border-box; -webkit-tap-highlight-color: transparent; text-size-adjust: none; display: inline-table; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 17.6px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; margin: 0px; padding: 1px 0px; position: relative;\" tabindex=\"0\" role=\"presentation\" data-mathml=\"&lt;math xmlns=&quot;http:\/\/www.w3.org\/1998\/Math\/MathML&quot;&gt;&lt;mi&gt;S&lt;\/mi&gt;&lt;mi&gt;E&lt;\/mi&gt;&lt;mi&gt;R&lt;\/mi&gt;&lt;\/math&gt;\"><span id=\"MJXc-Node-407\" class=\"mjx-math\" aria-hidden=\"true\"><span id=\"MJXc-Node-408\" class=\"mjx-mrow\"><span id=\"MJXc-Node-409\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\">S<\/span><\/span><span id=\"MJXc-Node-410\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\">E<\/span><\/span><span id=\"MJXc-Node-411\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\">R<\/span><\/span><\/span><\/span><\/span><\/span>\u00a0<span class=\"math inline\" data-immersive-translate-walked=\"d7dfdb8a-87f2-45d9-a1cb-5d592097d16a\"><span id=\"MathJax-Element-42-Frame\" class=\"mjx-chtml MathJax_CHTML\" style=\"-webkit-font-smoothing: antialiased; box-sizing: border-box; -webkit-tap-highlight-color: transparent; text-size-adjust: none; display: inline-table; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 17.6px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; margin: 0px; padding: 1px 0px; position: relative;\" tabindex=\"0\" role=\"presentation\" data-mathml=\"&lt;math xmlns=&quot;http:\/\/www.w3.org\/1998\/Math\/MathML&quot;&gt;&lt;mn&gt;18.58&lt;\/mn&gt;&lt;\/math&gt;\"><span id=\"MJXc-Node-412\" class=\"mjx-math\" aria-hidden=\"true\"><span id=\"MJXc-Node-413\" class=\"mjx-mrow\"><span id=\"MJXc-Node-414\" class=\"mjx-mn\"><span class=\"mjx-char MJXc-TeX-main-R\">18.58 \uff0c\u5be6\u969b\u7372\u5f97\u7684\u6e2c\u9a57\u5206\u6578\u8207\u8ff4\u6b78\u7dda\u7684\u5e73\u5747\u504f\u5dee\u70ba\u00a0<span id=\"MathJax-Element-44-Frame\" class=\"mjx-chtml MathJax_CHTML\" style=\"-webkit-font-smoothing: antialiased; box-sizing: border-box; -webkit-tap-highlight-color: transparent; text-size-adjust: none; display: inline-table; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 17.6px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; margin: 0px; padding: 1px 0px; position: relative;\" tabindex=\"0\" role=\"presentation\" data-mathml=\"&lt;math xmlns=&quot;http:\/\/www.w3.org\/1998\/Math\/MathML&quot;&gt;&lt;mn&gt;18.58&lt;\/mn&gt;&lt;\/math&gt;\"><span id=\"MJXc-Node-420\" class=\"mjx-math\" aria-hidden=\"true\"><span id=\"MJXc-Node-421\" class=\"mjx-mrow\"><span id=\"MJXc-Node-422\" class=\"mjx-mn\">18.58<\/span><\/span><\/span><\/span>\u9ede<\/span><\/span><\/span><\/span><\/span><\/span>\u00a0\u3002<\/p>\n<hr \/>\n<p><strong><span style=\"color: #0000ff;\">4.4 \u6700\u5c0f\u5e73\u65b9\u5047\u8a2d<\/span><\/strong><\/p>\n<p>\u5047\u8a2d 1\uff1a\u8aa4\u5dee\u9805\u7684\u689d\u4ef6\u5e73\u5747\u503c\u70ba\u96f6<\/p>\n<blockquote><p>set.seed(321)<\/p>\n<p># simulate the data<br \/>\nX &lt;- runif(50, min = -5, max = 5)<br \/>\nu &lt;- rnorm(50, sd = 1)<\/p>\n<p># the true relation<br \/>\nY &lt;- X^2 + 2 * X + u<\/p>\n<p># estimate a simple regression model<br \/>\nmod_simple &lt;- lm(Y ~ X)<\/p>\n<p># estimate a quadratic regression model<br \/>\nmod_quadratic &lt;- lm( Y ~ X + I(X^2))<\/p>\n<p># predict using a quadratic model<br \/>\nprediction &lt;- predict(mod_quadratic, data.frame(X = sort(X)))<\/p>\n<p># plot the results<br \/>\nplot( Y ~ X, col = &#8220;black&#8221;, pch = 20, xlab = &#8220;X&#8221;, ylab = &#8220;Y&#8221;)<br \/>\nabline( mod_simple, col = &#8220;blue&#8221;,lwd=2)<br \/>\n#red line = incorrect linear regression (this violates the first OLS assumption)<br \/>\nlines( sort(X), prediction,col=&#8221;red&#8221;,lwd=2)<br \/>\nlegend(&#8220;topleft&#8221;,legend = c(&#8220;Simple Regression Model&#8221;,&#8221;Quadratic Model&#8221;),cex = 1,lty = 1,col = c(&#8220;blue&#8221;,&#8221;red&#8221;))<\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"\" src=\"https:\/\/www.econometrics-with-r.org\/ITER_files\/figure-html\/unnamed-chunk-163-1.png\" width=\"716\" height=\"512\" \/><\/p><\/blockquote>\n<p><strong><span style=\"color: #0000ff;\">\u5047\u8a2d 2\uff1a\u7368\u7acb\u540c\u5206\u5e03\u8cc7\u6599<\/span><\/strong><\/p>\n<p>\u9019\u500b\u4f8b\u5b50\u4e2d\uff0c\u5c0d\u54e1\u5de5\u6578\u91cf\u7684\u89c0\u5bdf\u4e0d\u53ef\u80fd\u662f\u7368\u7acb\u7684\uff1a\u4eca\u5929\u7684\u5c31\u696d\u6c34\u5e73\u8207\u660e\u5929\u7684\u5c31\u696d\u6c34\u5e73\u76f8\u95dc\u3002\u9055\u53cd i.i.d. \u5047\u8a2d\u3002<\/p>\n<blockquote><p>set.seed(123)<\/p>\n<p># generate a date vector<br \/>\nDate &lt;- seq(as.Date(&#8220;1951\/1\/1&#8221;), as.Date(&#8220;2000\/1\/1&#8221;), &#8220;years&#8221;)<\/p>\n<p># initialize the employment vector<br \/>\nX &lt;- c(5000, rep(NA, length(Date)-1))<\/p>\n<p># generate time series observations with random influences<br \/>\nfor (t in 2:length(Date)) {<br \/>\nX[t] &lt;- -50 + 0.98 * X[t-1] + rnorm(n = 1, sd = 200)<br \/>\n}<\/p>\n<p>#plot the results<br \/>\nplot(x = Date,y = X,type = &#8220;l&#8221;,col = &#8220;steelblue&#8221;,ylab = &#8220;Workers&#8221;,xlab = &#8220;Time&#8221;,lwd=2)<\/p><\/blockquote>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"\" src=\"https:\/\/www.econometrics-with-r.org\/ITER_files\/figure-html\/unnamed-chunk-164-1.png\" width=\"707\" height=\"505\" \/><\/p>\n<p><strong><span style=\"color: #0000ff;\">\u5047\u8a2d 3\uff1a\u6975\u7aef\u96e2\u7fa4\u503c\u4e0d\u592a\u53ef\u80fd\u767c\u751f<\/span><\/strong><\/p>\n<p>\u6975\u7aef\u89c0\u5bdf\u503c\u5728\u672a\u77e5\u8ff4\u6b78\u4fc2\u6578\u7684\u4f30\u8a08\u4e2d\u6703\u53d7\u5230\u5f88\u5927\u7684\u6b0a\u91cd\u3002\u56e0\u6b64\uff0c\u7570\u5e38\u503c\u53ef\u80fd\u5c0e\u81f4\u8ff4\u6b78\u4fc2\u6578\u7684\u4f30\u8a08\u503c\u56b4\u91cd\u5931\u771f\u3002<\/p>\n<p>(\u7d05\u7dda\uff1a\u7121\u96e2\u7fa4\u503c\uff1b\u85cd\u7dda\uff1a\u52a0\u5165\u96e2\u7fa4\u503c)<\/p>\n<blockquote><p>X &lt;- sort(runif(10, min = 30, max = 70))<br \/>\nY &lt;- rnorm(10 , mean = 200, sd = 50)<br \/>\nY[9] &lt;- 2000<\/p>\n<p># fit model with outlier<br \/>\nfit &lt;- lm(Y ~ X)<\/p>\n<p># fit model without outlier<br \/>\nfitWithoutOutlier &lt;- lm(Y[-9] ~ X[-9])<\/p>\n<p># plot the results<br \/>\nplot(Y ~ X,pch=20)<br \/>\nabline(fit,lwd=2,col=&#8221;blue&#8221;)<br \/>\nabline(fitWithoutOutlier, col = &#8220;red&#8221;,lwd=2)<br \/>\nlegend(&#8220;topleft&#8221;,legend = c(&#8220;Model with Outlier&#8221;,&#8221;Model without Outlier&#8221;),cex = 1,lty = 1,col = c(&#8220;blue&#8221;,&#8221;red&#8221;))<\/p><\/blockquote>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"\" src=\"https:\/\/www.econometrics-with-r.org\/ITER_files\/figure-html\/unnamed-chunk-165-1.png\" width=\"732\" height=\"523\" \/><\/p>\n<hr \/>\n<p><span style=\"color: #0000ff;\"><strong>4.5 OLS \u4f30\u8a08\u91cf\u7684\u62bd\u6a23\u5206\u914d<\/strong><\/span><\/p>\n<p>\u4f30\u8a08\u91cf\u7684\u5206\u4f48\u53ef\u4ee5\u5f88\u597d\u5730\u8fd1\u4f3c\u65bc\u95dc\u9375\u6982\u5ff5 4.4 \u4e2d\u6240\u8ff0\u7684\u5404\u81ea\u7406\u8ad6\u5e38\u614b\u5206\u4f48\u3002<\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"\" src=\"https:\/\/www.econometrics-with-r.org\/ITER_files\/figure-html\/unnamed-chunk-172-1.png\" width=\"712\" height=\"509\" \/><\/p>\n<p>\u6211\u5011\u767c\u73fe\uff0c\u96a8\u8457\u00a0<span class=\"math inline\" data-immersive-translate-walked=\"1e4d12aa-748e-4ad0-8f53-65031b0b43ec\"><span id=\"MathJax-Element-70-Frame\" class=\"mjx-chtml MathJax_CHTML\" style=\"-webkit-font-smoothing: antialiased; box-sizing: border-box; -webkit-tap-highlight-color: transparent; text-size-adjust: none; display: inline-table; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 17.6px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; margin: 0px; padding: 1px 0px; position: relative;\" tabindex=\"0\" role=\"presentation\" data-mathml=\"&lt;math xmlns=&quot;http:\/\/www.w3.org\/1998\/Math\/MathML&quot;&gt;&lt;mi&gt;n&lt;\/mi&gt;&lt;\/math&gt;\"><span id=\"MJXc-Node-636\" class=\"mjx-math\" aria-hidden=\"true\"><span id=\"MJXc-Node-637\" class=\"mjx-mrow\"><span id=\"MJXc-Node-638\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\">n<\/span><\/span><\/span><\/span><\/span><\/span>\u00a0\u589e\u52a0\uff0c\u00a0<span class=\"math inline\" data-immersive-translate-walked=\"1e4d12aa-748e-4ad0-8f53-65031b0b43ec\"><span id=\"MathJax-Element-71-Frame\" class=\"mjx-chtml MathJax_CHTML\" style=\"-webkit-font-smoothing: antialiased; box-sizing: border-box; -webkit-tap-highlight-color: transparent; text-size-adjust: none; display: inline-table; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 17.6px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; margin: 0px; padding: 1px 0px; position: relative;\" tabindex=\"0\" role=\"presentation\" data-mathml=\"&lt;math xmlns=&quot;http:\/\/www.w3.org\/1998\/Math\/MathML&quot;&gt;&lt;msub&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;&amp;#x03B2;&lt;\/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x005E;&lt;\/mo&gt;&lt;\/mover&gt;&lt;\/mrow&gt;&lt;mn&gt;1&lt;\/mn&gt;&lt;\/msub&gt;&lt;\/math&gt;\"><span id=\"MJXc-Node-639\" class=\"mjx-math\" aria-hidden=\"true\"><span id=\"MJXc-Node-640\" class=\"mjx-mrow\"><span id=\"MJXc-Node-641\" class=\"mjx-msubsup\"><span class=\"mjx-base\"><span id=\"MJXc-Node-642\" class=\"mjx-texatom\"><span id=\"MJXc-Node-643\" class=\"mjx-mrow\"><span id=\"MJXc-Node-644\" class=\"mjx-munderover\"><span class=\"mjx-stack\"><span class=\"mjx-over\"><span id=\"MJXc-Node-646\" class=\"mjx-mo\"><span class=\"mjx-char MJXc-TeX-main-R\">^<\/span><\/span><\/span><span class=\"mjx-op\"><span id=\"MJXc-Node-645\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\">\u03b2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mjx-sub\"><span id=\"MJXc-Node-647\" class=\"mjx-mn\"><span class=\"mjx-char MJXc-TeX-main-R\">1<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u7684\u5206\u4f48\u96c6\u4e2d\u5728\u5176\u5e73\u5747\u503c\u9644\u8fd1\uff0c\u5373\u5176\u8b8a\u7570\u6578\u6e1b\u5c11\u3002<\/p>\n<p>\u589e\u52a0\u6a23\u672c\u91cf\uff0c\u89c0\u5bdf\u5230\u63a5\u8fd1 <span class=\"math inline\" data-immersive-translate-walked=\"1e4d12aa-748e-4ad0-8f53-65031b0b43ec\"><span id=\"MathJax-Element-72-Frame\" class=\"mjx-chtml MathJax_CHTML\" style=\"-webkit-font-smoothing: antialiased; box-sizing: border-box; -webkit-tap-highlight-color: transparent; text-size-adjust: none; display: inline-table; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 17.6px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; margin: 0px; padding: 1px 0px; position: relative;\" tabindex=\"0\" role=\"presentation\" data-mathml=\"&lt;math xmlns=&quot;http:\/\/www.w3.org\/1998\/Math\/MathML&quot;&gt;&lt;msub&gt;&lt;mi&gt;&amp;#x03B2;&lt;\/mi&gt;&lt;mn&gt;1&lt;\/mn&gt;&lt;\/msub&gt;&lt;mo&gt;=&lt;\/mo&gt;&lt;mn&gt;3.5&lt;\/mn&gt;&lt;\/math&gt;\"><span id=\"MJXc-Node-648\" class=\"mjx-math\" aria-hidden=\"true\"><span id=\"MJXc-Node-649\" class=\"mjx-mrow\"><span id=\"MJXc-Node-650\" class=\"mjx-msubsup\"><span class=\"mjx-base\"><span id=\"MJXc-Node-651\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\">\u03b2<\/span><\/span><\/span><span class=\"mjx-sub\"><span id=\"MJXc-Node-652\" class=\"mjx-mn\"><span class=\"mjx-char MJXc-TeX-main-R\">1<\/span><\/span><\/span><\/span><span id=\"MJXc-Node-653\" class=\"mjx-mo MJXc-space3\"><span class=\"mjx-char MJXc-TeX-main-R\">=<\/span><\/span><span id=\"MJXc-Node-654\" class=\"mjx-mn MJXc-space3\"><span class=\"mjx-char MJXc-TeX-main-R\">3.5<\/span><\/span><\/span><\/span><\/span><\/span>\u771f\u5be6\u503c\u7684\u4f30\u8a08\u503c\u7684\u53ef\u80fd\u6027\u6703\u589e\u52a0\u3002<\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"\" src=\"https:\/\/www.econometrics-with-r.org\/ITER_files\/figure-html\/unnamed-chunk-173-1.png\" width=\"904\" height=\"904\" \/><\/p>\n<p>\u5f88\u660e\u986f\u5730\uff0c\u63a5\u8fd1\u6a23\u672c\u5e73\u5747\u503c\u7684\u89c0\u5bdf\u503c\uff0c\u5176\u8b8a\u7570\u6027\u5c0f\u65bc\u90a3\u4e9b\u8ddd\u96e2\u8f03\u9060\u7684\u89c0\u5bdf\u503c\u3002<\/p>\n<p>\u5373\u4f7f\u7528\u8b8a\u7570\u6027\u5927\u65bc\u85cd\u8272\u89c0\u5bdf\u503c\u7684\u89c0\u5bdf\u503c\u96c6\uff0c\u5c07\u6703\u7522\u751f\u4e00\u689d\u66f4\u7cbe\u78ba\u7684\u7dda\u3002<\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"\" src=\"https:\/\/www.econometrics-with-r.org\/ITER_files\/figure-html\/unnamed-chunk-174-1.png\" width=\"758\" height=\"542\" \/><\/p>\n<p><span class=\"math inline\" data-immersive-translate-walked=\"75476a67-9da1-44c0-ae8a-6c874f7e221e\"><span id=\"MathJax-Element-88-Frame\" class=\"mjx-chtml MathJax_CHTML\" style=\"-webkit-font-smoothing: antialiased; box-sizing: border-box; -webkit-tap-highlight-color: transparent; text-size-adjust: none; display: inline-table; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 17.6px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; margin: 0px; padding: 1px 0px; position: relative;\" tabindex=\"0\" role=\"presentation\" data-mathml=\"&lt;math xmlns=&quot;http:\/\/www.w3.org\/1998\/Math\/MathML&quot;&gt;&lt;msub&gt;&lt;mi&gt;X&lt;\/mi&gt;&lt;mi&gt;i&lt;\/mi&gt;&lt;\/msub&gt;&lt;\/math&gt;\"><span id=\"MJXc-Node-852\" class=\"mjx-math\" aria-hidden=\"true\"><span id=\"MJXc-Node-853\" class=\"mjx-mrow\"><span id=\"MJXc-Node-854\" class=\"mjx-msubsup\"><span class=\"mjx-base\"><span id=\"MJXc-Node-855\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\">X<\/span><\/span><\/span><span class=\"mjx-sub\"><span id=\"MJXc-Node-856\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\">i<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u00a0\u4e2d\u7684\u8b8a\u7570\u6578\u8d8a\u5927\uff0c\u53ef\u4f9b\u4f30\u8a08\u7cbe\u78ba\u5ea6\u53d7\u76ca\u7684\u8cc7\u8a0a\u5c31\u8d8a\u591a\u3002<\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"\" src=\"https:\/\/www.econometrics-with-r.org\/ITER_files\/figure-html\/unnamed-chunk-175-1.png\" width=\"763\" height=\"545\" \/><\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>4.1 \u7c21\u55ae\u7dda\u6027\u8ff4\u6b78 \u7dda\u6027\u56de\u6b78\u6a21\u578b\u662fYi=\u03b20+\u03b21Xi+ui STR &lt;<\/p>\n","protected":false},"author":16,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1,27],"tags":[],"_links":{"self":[{"href":"https:\/\/edu.secda.info\/scu12354014\/index.php?rest_route=\/wp\/v2\/posts\/1330"}],"collection":[{"href":"https:\/\/edu.secda.info\/scu12354014\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/edu.secda.info\/scu12354014\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/edu.secda.info\/scu12354014\/index.php?rest_route=\/wp\/v2\/users\/16"}],"replies":[{"embeddable":true,"href":"https:\/\/edu.secda.info\/scu12354014\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=1330"}],"version-history":[{"count":4,"href":"https:\/\/edu.secda.info\/scu12354014\/index.php?rest_route=\/wp\/v2\/posts\/1330\/revisions"}],"predecessor-version":[{"id":1334,"href":"https:\/\/edu.secda.info\/scu12354014\/index.php?rest_route=\/wp\/v2\/posts\/1330\/revisions\/1334"}],"wp:attachment":[{"href":"https:\/\/edu.secda.info\/scu12354014\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1330"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/edu.secda.info\/scu12354014\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1330"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/edu.secda.info\/scu12354014\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1330"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}