{"id":2119,"date":"2023-07-23T15:01:59","date_gmt":"2023-07-23T15:01:59","guid":{"rendered":"https:\/\/statorials.org\/cn\/%e5%ae%8c%e7%be%8e%e5%a4%9a%e9%87%8d%e5%85%b1%e7%ba%bf%e6%80%a7\/"},"modified":"2023-07-23T15:01:59","modified_gmt":"2023-07-23T15:01:59","slug":"%e5%ae%8c%e7%be%8e%e5%a4%9a%e9%87%8d%e5%85%b1%e7%ba%bf%e6%80%a7","status":"publish","type":"post","link":"https:\/\/statorials.org\/cn\/%e5%ae%8c%e7%be%8e%e5%a4%9a%e9%87%8d%e5%85%b1%e7%ba%bf%e6%80%a7\/","title":{"rendered":"\u4ec0\u4e48\u662f\u5b8c\u7f8e\u591a\u91cd\u5171\u7ebf\u6027\uff1f \uff08\u5b9a\u4e49\u548c\u793a\u4f8b\uff09"},"content":{"rendered":"

<\/p>\n

\n

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\"\"<\/p>\n

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\"\u5b8c\u7f8e\u591a\u91cd\u5171\u7ebf\u6027\u7684\u4f8b\u5b50\"<\/p>\n

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\u5b8c\u7f8e\u591a\u91cd\u5171\u7ebf\u6027\u95ee\u9898<\/strong><\/span><\/h2>\n

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\u5982\u4f55\u5904\u7406\u5b8c\u7f8e\u591a\u91cd\u5171\u7ebf\u6027<\/strong><\/span><\/h2>\n

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\"\"<\/p>\n

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\u5b8c\u7f8e\u591a\u91cd\u5171\u7ebf\u6027\u7684\u793a\u4f8b<\/strong><\/span><\/h2>\n

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1. \u9884\u6d4b\u53d8\u91cf\u662f\u53e6\u4e00\u4e2a\u53d8\u91cf\u7684\u500d\u6570<\/strong><\/span><\/h3>\n

\u5047\u8bbe\u6211\u4eec\u60f3\u4f7f\u7528\u201c\u8eab\u9ad8\uff08\u5398\u7c73\uff09\u201d\u548c\u201c\u8eab\u9ad8\uff08\u7c73\uff09\u201d\u6765\u9884\u6d4b\u67d0\u79cd\u6d77\u8c5a\u7684\u4f53\u91cd\u3002<\/span><\/p>\n

\u6211\u4eec\u7684\u6570\u636e\u96c6\u53ef\u80fd\u5982\u4e0b\u6240\u793a\uff1a<\/span> <\/p>\n

\"\"<\/p>\n

\u8bf7\u6ce8\u610f\uff0c\u201c\u4ee5\u5398\u7c73\u4e3a\u5355\u4f4d\u7684\u8eab\u9ad8\u201d\u7684\u503c\u4ec5\u7b49\u4e8e\u201c\u4ee5\u7c73\u4e3a\u5355\u4f4d\u7684\u8eab\u9ad8\u201d\u4e58\u4ee5 100\u3002\u8fd9\u662f\u5b8c\u7f8e\u591a\u91cd\u5171\u7ebf\u6027\u7684\u60c5\u51b5\u3002<\/span><\/p>\n

\u5982\u679c\u6211\u4eec\u5c1d\u8bd5\u4f7f\u7528\u6b64\u6570\u636e\u96c6\u5728 R \u4e2d\u62df\u5408\u591a\u5143\u7ebf\u6027\u56de\u5f52\u6a21\u578b\uff0c\u6211\u4eec\u5c06\u65e0\u6cd5\u751f\u6210\u9884\u6d4b\u53d8\u91cf\u201c\u7c73\u201d\u7684\u7cfb\u6570\u4f30\u8ba1\uff1a<\/span><\/p>\n

 #define data\n<\/span>df <- data. frame<\/span> (weight=c(400, 460, 470, 475, 490, 440, 430, 490, 500, 540),\n                 m=c(1.3, .7, .6, 1.3, 1.2, 1.5, 1.2, 1.6, 1.1, 1.4),\n                 cm=c(130, 70, 60, 130, 120, 150, 120, 160, 110, 140))\n\n#fit multiple linear regression model\n<\/span>model <- lm(weight~m+cm, data=df)\n\n#view summary of model\n<\/span>summary(model)\n\nCall:\nlm(formula = weight ~ m + cm, data = df)\n\nResiduals:\n    Min 1Q Median 3Q Max \n-70,501 -25,501 5,183 19,499 68,590 \n\nCoefficients: (1 not defined because of singularities)\n            Estimate Std. Error t value Pr(>|t|)    \n(Intercept) 458,676 53,403 8,589 2.61e-05 ***\nm 9.096 43.473 0.209 0.839    \ncm NA NA NA NA    \n---\nSignificant. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n\nResidual standard error: 41.9 on 8 degrees of freedom\nMultiple R-squared: 0.005442, Adjusted R-squared: -0.1189 \nF-statistic: 0.04378 on 1 and 8 DF, p-value: 0.8395<\/strong><\/pre>\n
 2. \u9884\u6d4b\u53d8\u91cf\u662f\u53e6\u4e00\u4e2a\u53d8\u91cf\u7684\u53d8\u6362\u7248\u672c<\/strong><\/span><\/h3>\n
\u5047\u8bbe\u6211\u4eec\u60f3\u4f7f\u7528\u201c\u5206\u6570\u201d\u548c\u201c\u7f29\u653e\u5206\u6570\u201d\u6765\u9884\u6d4b\u7bee\u7403\u8fd0\u52a8\u5458\u7684\u8bc4\u5206\u3002<\/span><\/p>\n
\u5047\u8bbe\u53d8\u91cf\u201c\u7f29\u653e\u70b9\u201d\u8ba1\u7b97\u5982\u4e0b\uff1a<\/span><\/p>\n
\u7f29\u653e\u70b9 = ( \u70b9 \u2013 \u03bc\u70b9<\/sub>) \/ \u03c3\u70b9<\/sub><\/span><\/p>\n
\u6211\u4eec\u7684\u6570\u636e\u96c6\u53ef\u80fd\u5982\u4e0b\u6240\u793a\uff1a<\/span> <\/p>\n
\"\"<\/p>\n
\u8bf7\u6ce8\u610f\uff0c\u6bcf\u4e2a\u201c\u7f29\u653e\u70b9\u201d\u503c\u53ea\u662f\u201c\u70b9\u201d\u7684\u6807\u51c6\u5316\u7248\u672c\u3002\u8fd9\u662f\u5b8c\u5168\u591a\u91cd\u5171\u7ebf\u6027\u7684\u60c5\u51b5\u3002<\/span><\/p>\n
\u5982\u679c\u6211\u4eec\u5c1d\u8bd5\u4f7f\u7528\u6b64\u6570\u636e\u96c6\u5728 R \u4e2d\u62df\u5408\u591a\u5143\u7ebf\u6027\u56de\u5f52\u6a21\u578b\uff0c\u6211\u4eec\u5c06\u65e0\u6cd5\u751f\u6210\u201c\u7f29\u653e\u70b9\u201d\u9884\u6d4b\u53d8\u91cf\u7684\u7cfb\u6570\u4f30\u8ba1\uff1a<\/span><\/p>\n
 #define data\n<\/span>df <- data. frame<\/span> (rating=c(88, 83, 90, 94, 96, 78, 79, 91, 90, 82),\n                 pts=c(17, 19, 24, 29, 33, 15, 14, 29, 25, 22))\n\ndf$scaled_pts <- (df$pts - mean(df$pts)) \/ sd(df$pts)\n\n#fit multiple linear regression model\n<\/span>model <- lm(rating~pts+scaled_pts, data=df)\n\n#view summary of model\n<\/span>summary(model)\n\nCall:\nlm(formula = rating ~ pts + scaled_pts, data = df)\n\nResiduals:\n    Min 1Q Median 3Q Max \n-4.4932 -1.3941 -0.2935 1.3055 5.8412 \n\nCoefficients: (1 not defined because of singularities)\n            Estimate Std. Error t value Pr(>|t|)    \n(Intercept) 67.4218 3.5896 18.783 6.67e-08 ***\npts 0.8669 0.1527 5.678 0.000466 ***\nscaled_pts NA NA NA NA    \n---\nSignificant. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n\nResidual standard error: 2.953 on 8 degrees of freedom\nMultiple R-squared: 0.8012, Adjusted R-squared: 0.7763 \nF-statistic: 32.23 on 1 and 8 DF, p-value: 0.0004663\n<\/strong><\/pre>\n
 3. \u865a\u62df\u53d8\u91cf\u9677\u9631<\/strong><\/span><\/h3>\n
\u53e6\u4e00\u79cd\u53ef\u80fd\u53d1\u751f\u5b8c\u7f8e\u591a\u91cd\u5171\u7ebf\u6027\u7684\u60c5\u51b5\u79f0\u4e3a\u865a\u62df\u53d8\u91cf\u9677\u9631<\/a>\u3002\u8fd9\u662f\u5f53\u6211\u4eec\u60f3\u8981\u5728\u56de\u5f52\u6a21\u578b\u4e2d\u83b7\u53d6\u5206\u7c7b\u53d8\u91cf\u5e76\u5c06\u5176\u8f6c\u6362\u4e3a\u5177\u6709 0\u30011\u30012 \u7b49\u503c\u7684\u201c\u865a\u62df\u53d8\u91cf\u201d\u65f6\u3002<\/span><\/p>\n
\u4f8b\u5982\uff0c\u5047\u8bbe\u6211\u4eec\u8981\u4f7f\u7528\u9884\u6d4b\u53d8\u91cf\u201c\u5e74\u9f84\u201d\u548c\u201c\u5a5a\u59fb\u72b6\u51b5\u201d\u6765\u9884\u6d4b\u6536\u5165\uff1a<\/span> <\/p>\n
\"\"<\/p>\n
\u8981\u4f7f\u7528\u201c\u5a5a\u59fb\u72b6\u51b5\u201d\u4f5c\u4e3a\u9884\u6d4b\u53d8\u91cf\uff0c\u6211\u4eec\u5fc5\u987b\u9996\u5148\u5c06\u5176\u8f6c\u6362\u4e3a\u865a\u62df\u53d8\u91cf\u3002<\/span><\/p>\n
\u4e3a\u6b64\uff0c\u6211\u4eec\u53ef\u4ee5\u5c06\u201c\u5355\u8eab\u201d\u4fdd\u7559\u4e3a\u57fa\u503c\uff0c\u56e0\u4e3a\u8fd9\u79cd\u60c5\u51b5\u6700\u5e38\u53d1\u751f\uff0c\u5e76\u5c06\u503c 0 \u6216 1 \u5206\u914d\u7ed9\u201c\u5df2\u5a5a\u201d\u548c\u201c\u79bb\u5a5a\u201d\uff0c\u5982\u4e0b\u6240\u793a\uff1a<\/span> <\/p>\n
\"\"<\/p>\n
\u9519\u8bef\u7684\u505a\u6cd5\u662f\u521b\u5efa\u4e09\u4e2a\u65b0\u7684\u865a\u62df\u53d8\u91cf\uff0c\u5982\u4e0b\u6240\u793a\uff1a<\/span> <\/p>\n
\"\"<\/p>\n
\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u201c\u5355\u8eab\u201d\u53d8\u91cf\u662f\u201c\u5df2\u5a5a\u201d\u548c\u201c\u79bb\u5a5a\u201d\u53d8\u91cf\u7684\u5b8c\u7f8e\u7ebf\u6027\u7ec4\u5408\u3002\u8fd9\u662f\u5b8c\u7f8e\u591a\u91cd\u5171\u7ebf\u6027\u7684\u4e00\u4e2a\u4f8b\u5b50\u3002<\/span><\/p>\n
\u5982\u679c\u6211\u4eec\u5c1d\u8bd5\u4f7f\u7528\u6b64\u6570\u636e\u96c6\u5728 R \u4e2d\u62df\u5408\u591a\u5143\u7ebf\u6027\u56de\u5f52\u6a21\u578b\uff0c\u6211\u4eec\u5c06\u65e0\u6cd5\u4e3a\u6bcf\u4e2a\u9884\u6d4b\u53d8\u91cf\u751f\u6210\u7cfb\u6570\u4f30\u8ba1\uff1a<\/span><\/p>\n
 #define data\n<\/span>df <- data. frame<\/span> (income=c(45, 48, 54, 57, 65, 69, 78, 83, 98, 104, 107),\n                 age=c(23, 25, 24, 29, 38, 36, 40, 59, 56, 64, 53),\n                 single=c(1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 0),\n                 married=c(0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 1),\n                 divorced=c(0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0))\n\n#fit multiple linear regression model\n<\/span>model <- lm(income~age+single+married+divorced, data=df)\n\n#view summary of model\n<\/span>summary(model)\n\nCall:\nlm(formula = income ~ age + single + married + divorced, data = df)\n\nResiduals:\n    Min 1Q Median 3Q Max \n-9.7075 -5.0338 0.0453 3.3904 12.2454 \n\nCoefficients: (1 not defined because of singularities)\n            Estimate Std. Error t value Pr(>|t|)   \n(Intercept) 16.7559 17.7811 0.942 0.37739   \nage 1.4717 0.3544 4.152 0.00428 **\nsingle -2.4797 9.4313 -0.263 0.80018   \nmarried NA NA NA NA   \ndivorced -8.3974 12.7714 -0.658 0.53187   \n---\nSignificant. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n\nResidual standard error: 8.391 on 7 degrees of freedom\nMultiple R-squared: 0.9008, Adjusted R-squared: 0.8584 \nF-statistic: 21.2 on 3 and 7 DF, p-value: 0.0006865\n<\/strong><\/pre>\n
\u5176\u4ed6\u8d44\u6e90<\/strong><\/span><\/h3>\n
\u56de\u5f52\u4e2d\u7684\u591a\u91cd\u5171\u7ebf\u6027\u548c VIF \u6307\u5357<\/a>
\u5982\u4f55\u5728R\u4e2d\u8ba1\u7b97VIF<\/a>
\u5982\u4f55\u7528Python\u8ba1\u7b97VIF<\/a>
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