什么是分层逐步多元回归分析？ 什么是分层逐步多元回归分析？
\u4ec0\u4e48\u662f\u5206\u5c42\u9010\u6b65\u591a\u5143\u56de\u5f52\u5206\u6790\uff1f\u6240\u8c13\u56de\u5f52\u5206\u6790\u6cd5\uff0c\u662f\u5728\u638c\u63e1\u5927\u91cf\u89c2\u5bdf\u6570\u636e\u7684\u57fa\u7840\u4e0a\uff0c\u5229\u7528\u6570\u7406\u7edf\u8ba1\u65b9\u6cd5\u5efa\u7acb\u56e0\u53d8\u91cf\u4e0e\u81ea\u53d8\u91cf\u4e4b\u95f4\u7684\u56de\u5f52\u5173\u7cfb\u51fd\u6570\u8868\u8fbe\u5f0f(\u79f0\u56de\u5f52\u65b9\u7a0b\u5f0f)\u3002\u56de\u5f52\u5206\u6790\u4e2d\uff0c\u5f53\u7814\u7a76\u7684\u56e0\u679c\u5173\u7cfb\u53ea\u6d89\u53ca\u56e0\u53d8\u91cf\u548c\u4e00\u4e2a\u81ea\u53d8\u91cf\u65f6\uff0c\u53eb\u505a\u4e00\u5143\u56de\u5f52\u5206\u6790;\u5f53\u7814\u7a76\u7684\u56e0\u679c\u5173\u7cfb\u6d89\u53ca\u56e0\u53d8\u91cf\u548c\u4e24\u4e2a\u6216\u4e24\u4e2a\u4ee5\u4e0a\u81ea\u53d8\u91cf\u65f6\uff0c\u53eb\u505a\u591a\u5143\u56de\u5f52\u5206\u6790\u3002\u6b64\u5916\uff0c\u56de\u5f52\u5206\u6790\u4e2d\uff0c\u53c8\u4f9d\u636e\u63cf\u8ff0\u81ea\u53d8\u91cf\u4e0e\u56e0\u53d8\u91cf\u4e4b\u95f4\u56e0\u679c\u5173\u7cfb\u7684\u51fd\u6570\u8868\u8fbe\u5f0f\u662f\u7ebf\u6027\u7684\u8fd8\u662f\u975e\u7ebf\u6027\u7684\uff0c\u5206\u4e3a\u7ebf\u6027\u56de\u5f52\u5206\u6790\u548c\u975e\u7ebf\u6027\u56de\u5f52\u5206\u6790\u3002\u901a\u5e38\u7ebf\u6027\u56de\u5f52\u5206\u6790\u6cd5\u662f\u6700\u57fa\u672c\u7684\u5206\u6790\u65b9\u6cd5\uff0c\u9047\u5230\u975e\u7ebf\u6027\u56de\u5f52\u95ee\u9898\u53ef\u4ee5\u501f\u52a9\u6570\u5b66\u624b\u6bb5\u5316\u4e3a\u7ebf\u6027\u56de\u5f52\u95ee\u9898\u5904\u7406\u3002
\u5206\u5c42\u56de\u5f52\u5176\u5b9e\u662f\u5bf9\u4e24\u4e2a\u6216\u591a\u4e2a\u56de\u5f52\u6a21\u578b\u8fdb\u884c\u6bd4\u8f83\u3002\u6211\u4eec\u53ef\u4ee5\u6839\u636e\u4e24\u4e2a\u6a21\u578b\u6240\u89e3\u91ca\u7684\u53d8\u5f02\u91cf\u7684\u5dee\u5f02\u6765\u6bd4\u8f83\u6240\u5efa\u7acb\u7684\u4e24\u4e2a\u6a21\u578b\u3002\u4e00\u4e2a\u6a21\u578b\u89e3\u91ca\u4e86\u8d8a\u591a\u7684\u53d8\u5f02\uff0c\u5219\u5b83\u5bf9\u6570\u636e\u7684\u62df\u5408\u5c31\u8d8a\u597d\u3002\u5047\u5982\u5728\u5176\u4ed6\u6761\u4ef6\u76f8\u7b49\u7684\u60c5\u51b5\u4e0b\uff0c\u4e00\u4e2a\u6a21\u578b\u6bd4\u53e6\u4e00\u4e2a\u6a21\u578b\u89e3\u91ca\u4e86\u66f4\u591a\u7684\u53d8\u5f02\uff0c\u5219\u8fd9\u4e2a\u6a21\u578b\u662f\u4e00\u4e2a\u66f4\u597d\u7684\u6a21\u578b\u3002\u4e24\u4e2a\u6a21\u578b\u6240\u89e3\u91ca\u7684\u53d8\u5f02\u91cf\u4e4b\u95f4\u7684\u5dee\u5f02\u53ef\u4ee5\u7528\u7edf\u8ba1\u663e\u8457\u6027\u6765\u4f30\u8ba1\u548c\u68c0\u9a8c\u3002
\u6a21\u578b\u6bd4\u8f83\u53ef\u4ee5\u7528\u6765\u8bc4\u4f30\u4e2a\u4f53\u9884\u6d4b\u53d8\u91cf\u3002\u68c0\u9a8c\u4e00\u4e2a\u9884\u6d4b\u53d8\u91cf\u662f\u5426\u663e\u8457\u7684\u65b9\u6cd5\u662f\u6bd4\u8f83\u4e24\u4e2a\u6a21\u578b\uff0c\u5176\u4e2d\u7b2c\u4e00\u4e2a\u6a21\u578b\u4e0d\u5305\u62ec\u8fd9\u4e2a\u9884\u6d4b\u53d8\u91cf\uff0c\u800c\u7b2c\u4e8c\u4e2a\u6a21\u578b\u5305\u62ec\u8be5\u53d8\u91cf\u3002\u5047\u5982\u8be5\u9884\u6d4b\u53d8\u91cf\u89e3\u91ca\u4e86\u663e\u8457\u7684\u989d\u5916\u53d8\u5f02\uff0c\u90a3\u7b2c\u4e8c\u4e2a\u6a21\u578b\u5c31\u663e\u8457\u5730\u89e3\u91ca\u4e86\u6bd4\u7b2c\u4e00\u4e2a\u6a21\u578b\u66f4\u591a\u7684\u53d8\u5f02\u3002\u8fd9\u79cd\u89c2\u70b9\u7b80\u5355\u800c\u6709\u529b\u3002\u4f46\u662f\uff0c\u8981\u7406\u89e3\u8fd9\u79cd\u5206\u6790\uff0c\u4f60\u5fc5\u987b\u7406\u89e3\u8be5\u9884\u6d4b\u53d8\u91cf\u6240\u89e3\u91ca\u7684\u72ec\u7279\u53d8\u5f02\u548c\u603b\u4f53\u53d8\u5f02\u4e4b\u95f4\u7684\u5dee\u5f02\u3002
\u4e00\u4e2a\u9884\u6d4b\u53d8\u91cf\u6240\u89e3\u91ca\u7684\u603b\u4f53\u53d8\u5f02\u662f\u8be5\u9884\u6d4b\u53d8\u91cf\u548c\u7ed3\u679c\u53d8\u91cf\u4e4b\u95f4\u76f8\u5173\u7684\u5e73\u65b9\u3002\u5b83\u5305\u62ec\u8be5\u9884\u6d4b\u53d8\u91cf\u548c\u7ed3\u679c\u53d8\u91cf\u4e4b\u95f4\u7684\u6240\u6709\u5173\u7cfb\u3002
\u9884\u6d4b\u53d8\u91cf\u7684\u72ec\u7279\u53d8\u5f02\u662f\u6307\u5728\u63a7\u5236\u4e86\u5176\u4ed6\u53d8\u91cf\u4ee5\u540e\uff0c\u9884\u6d4b\u53d8\u91cf\u5bf9\u7ed3\u679c\u53d8\u91cf\u7684\u5f71\u54cd\u3002\u8fd9\u6837\uff0c\u9884\u6d4b\u53d8\u91cf\u7684\u72ec\u7279\u53d8\u5f02\u4f9d\u8d56\u4e8e\u5176\u4ed6\u9884\u6d4b\u53d8\u91cf\u3002\u5728\u6807\u51c6\u591a\u91cd\u56de\u5f52\u5206\u6790\u4e2d\uff0c\u53ef\u4ee5\u5bf9\u72ec\u7279\u53d8\u5f02\u8fdb\u884c\u68c0\u9a8c\uff0c\u6bcf\u4e2a\u9884\u6d4b\u53d8\u91cf\u7684\u56de\u5f52\u7cfb\u6570\u5927\u5c0f\u4f9d\u8d56\u4e8e\u6a21\u578b\u4e2d\u7684\u5176\u4ed6\u9884\u6d4b\u53d8\u91cf\u3002
\u5728\u6807\u51c6\u591a\u91cd\u56de\u5f52\u5206\u6790\u4e2d\uff0c\u56de\u5f52\u7cfb\u6570\u7528\u6765\u68c0\u9a8c\u6bcf\u4e2a\u9884\u6d4b\u53d8\u91cf\u6240\u89e3\u91ca\u7684\u72ec\u7279\u53d8\u5f02\u3002\u8fd9\u4e2a\u72ec\u7279\u53d8\u5f02\u5c31\u662f\u504f\u76f8\u5173\u7684\u5e73\u65b9\uff08Squared semi-partial correlation\uff09-sr2\uff08\u504f\u786e\u5b9a\u7cfb\u6570\uff09\u3002\u5b83\u8868\u793a\u4e86\u7ed3\u679c\u53d8\u91cf\u4e2d\u7531\u7279\u5b9a\u9884\u6d4b\u53d8\u91cf\u6240\u5355\u72ec\u89e3\u91ca\u7684\u53d8\u5f02\u3002\u6b63\u5982\u6211\u4eec\u770b\u5230\u7684\uff0c\u5b83\u4f9d\u8d56\u4e8e\u6a21\u578b\u4e2d\u7684\u5176\u4ed6\u53d8\u91cf\u3002\u5047\u5982\u9884\u6d4b\u53d8\u91cf\u4e4b\u95f4\u5b58\u5728\u91cd\u53e0\uff0c\u90a3\u4e48\u5b83\u4eec\u5171\u6709\u7684\u53d8\u5f02\u5c31\u4f1a\u524a\u5f31\u72ec\u7279\u53d8\u5f02\u3002\u9884\u6d4b\u53d8\u91cf\u7684\u72ec\u7279\u6548\u5e94\u6307\u7684\u662f\u53bb\u9664\u91cd\u53e0\u6548\u5e94\u540e\u8be5\u9884\u6d4b\u53d8\u91cf\u4e0e\u7ed3\u679c\u53d8\u91cf\u7684\u76f8\u5173\u3002\u8fd9\u6837\uff0c\u67d0\u4e2a\u9884\u6d4b\u53d8\u91cf\u7684\u7279\u5b9a\u6548\u5e94\u5c31\u4f9d\u8d56\u4e8e\u6a21\u578b\u4e2d\u7684\u5176\u4ed6\u9884\u6d4b\u53d8\u91cf\u3002
\u6807\u51c6\u591a\u91cd\u56de\u5f52\u7684\u5c40\u9650\u6027\u5728\u4e8e\u4e0d\u80fd\u5c06\u91cd\u53e0\uff08\u5171\u540c\uff09\u53d8\u5f02\u5f52\u56e0\u4e8e\u6a21\u578b\u4e2d\u7684\u4efb\u4f55\u4e00\u4e2a\u9884\u6d4b\u53d8\u91cf\u3002\u8fd9\u5c31\u610f\u5473\u7740\u6a21\u578b\u4e2d\u6240\u6709\u9884\u6d4b\u53d8\u91cf\u7684\u504f\u51b3\u5b9a\u7cfb\u6570\u4e4b\u548c\u8981\u5c0f\u4e8e\u6574\u4e2a\u6a21\u578b\u7684\u51b3\u5b9a\u7cfb\u6570\uff08R2\uff09\u3002\u603b\u51b3\u5b9a\u7cfb\u6570\u5305\u62ec\u504f\u51b3\u5b9a\u7cfb\u6570\u4e4b\u548c\u4e0e\u5171\u540c\u53d8\u5f02\u3002\u5206\u5c42\u56de\u5f52\u63d0\u4f9b\u4e86\u4e00\u79cd\u53ef\u4ee5\u5c06\u5171\u540c\u53d8\u5f02\u5206\u914d\u7ed9\u7279\u5b9a\u9884\u6d4b\u53d8\u91cf\u7684\u65b9\u6cd5\u3002
\u5206\u5c42\u56de\u5f52
\u6807\u51c6\u591a\u91cd\u56de\u5f52\u53ef\u4ee5\u6d4b\u91cf\u6a21\u578b\u6240\u89e3\u91ca\u7684\u53d8\u5f02\u91cf\u7684\u5927\u5c0f\uff0c\u5b83\u7531\u590d\u76f8\u5173\u7cfb\u6570\u7684\u5e73\u65b9\uff08R2\uff0c\u5373\u51b3\u5b9a\u7cfb\u6570\uff09\u6765\u8868\u793a\uff0c\u4ee3\u8868\u4e86\u9884\u6d4b\u53d8\u91cf\u6240\u89e3\u91ca\u7684\u56e0\u53d8\u91cf\u7684\u53d8\u5f02\u91cf\u3002\u6a21\u578b\u7684\u663e\u8457\u6027\u68c0\u9a8c\u662f\u5c06\u9884\u6d4b\u53d8\u91cf\u6240\u89e3\u91ca\u7684\u53d8\u5f02\u4e0e\u8bef\u5dee\u53d8\u5f02\u8fdb\u884c\u6bd4\u8f83\uff08\u5373F\u503c\uff09\u3002
\u4f46\u662f\uff0c\u4e5f\u53ef\u4ee5\u91c7\u7528\u76f8\u540c\u7684\u65b9\u5f0f\u6765\u6bd4\u8f83\u4e24\u4e2a\u6a21\u578b\u3002\u53ef\u4ee5\u5c06\u4e24\u4e2a\u6a21\u578b\u6240\u89e3\u91ca\u7684\u53d8\u5f02\u4e4b\u5dee\u4f5c\u4e3aF\u503c\u7684\u5206\u5b50\u3002\u5047\u5982\u4e0e\u8bef\u5dee\u53d8\u5f02\u76f8\u6bd4\uff0c\u4e24\u4e2a\u6a21\u578b\u6240\u89e3\u91ca\u7684\u53d8\u5f02\u5dee\u522b\u8db3\u591f\u5927\uff0c\u90a3\u4e48\u5c31\u53ef\u4ee5\u8bf4\u8fd9\u79cd\u5dee\u522b\u8fbe\u5230\u4e86\u7edf\u8ba1\u7684\u663e\u8457\u6027\u3002\u76f8\u5e94\u7684\u65b9\u7a0b\u5f0f\u5c06\u5728\u4e0b\u9762\u8be6\u7ec6\u9610\u8ff0\u3002
\u5206\u5c42\u56de\u5f52\u5c31\u662f\u91c7\u7528\u7684\u8fd9\u79cd\u65b9\u5f0f\u3002\u5206\u5c42\u56de\u5f52\u5305\u62ec\u5efa\u7acb\u4e00\u7cfb\u5217\u6a21\u578b\uff0c\u5904\u4e8e\u7cfb\u5217\u4e2d\u67d0\u4e2a\u4f4d\u7f6e\u7684\u6a21\u578b\u5c06\u4f1a\u5305\u62ec\u524d\u4e00\u6a21\u578b\u6240\u6ca1\u6709\u7684\u989d\u5916\u9884\u6d4b\u53d8\u91cf\u3002\u5047\u5982\u52a0\u5165\u6a21\u578b\u7684\u989d\u5916\u89e3\u91ca\u53d8\u91cf\u5bf9\u89e3\u91ca\u5206\u6570\u5dee\u5f02\u5177\u6709\u663e\u8457\u7684\u989d\u5916\u8d21\u732e\uff0c\u90a3\u4e48\u5b83\u5c06\u4f1a\u663e\u8457\u5730\u63d0\u9ad8\u51b3\u5b9a\u7cfb\u6570\u3002
\u8fd9\u4e2a\u6a21\u578b\u4e0e\u6807\u51c6\u591a\u91cd\u56de\u5f52\u7684\u5dee\u5f02\u5728\u4e8e\u5b83\u53ef\u4ee5\u5c06\u5171\u540c\u53d8\u5f02\u5206\u914d\u5230\u9884\u6d4b\u53d8\u91cf\u4e2d\u3002\u800c\u5728\u6807\u51c6\u591a\u91cd\u56de\u5f52\u4e2d\uff0c\u5171\u540c\u53d8\u5f02\u4e0d\u80fd\u5206\u914d\u5230\u4efb\u4f55\u9884\u6d4b\u53d8\u91cf\u4e2d\uff0c\u6bcf\u4e2a\u9884\u6d4b\u53d8\u91cf\u53ea\u80fd\u5206\u914d\u5230\u5b83\u6240\u89e3\u91ca\u7684\u72ec\u7279\u53d8\u5f02\uff0c\u5171\u540c\u53d8\u5f02\u5219\u88ab\u629b\u5f03\u4e86\u3002\u5728\u5206\u5c42\u56de\u5f52\u4e2d\uff0c\u5c06\u4f1a\u628a\u91cd\u53e0\uff08\u5171\u540c\uff09\u53d8\u5f02\u5206\u914d\u7ed9\u7b2c\u4e00\u4e2a\u6a21\u578b\u4e2d\u7684\u9884\u6d4b\u53d8\u91cf\u3002\u56e0\u6b64\uff0c\u5171\u540c\u53d8\u5f02\u5c06\u4f1a\u5206\u914d\u7ed9\u4f18\u5148\u8fdb\u5165\u6a21\u578b\u7684\u53d8\u91cf\u3002
\u91cd\u53e0\u7684\u9884\u6d4b\u53d8\u91cf(\u76f8\u5173\u7684\u9884\u6d4b\u53d8\u91cfPredictor variables that overlap)
\u7b80\u5355\u5730\u770b\u6765\uff0c\u7531\u4e00\u7cfb\u5217\u9884\u6d4b\u53d8\u91cf\u6240\u89e3\u91ca\u7684\u53d8\u5f02\u5c31\u50cf\u4e00\u5757\u5757\u86cb\u7cd5\u5806\u79ef\u5728\u4e00\u8d77\u3002\u6bcf\u4e2a\u9884\u6d4b\u53d8\u91cf\u90fd\u6709\u81ea\u5df1\u660e\u786e\u7684\u4e00\u5757\u3002\u5b83\u4eec\u5230\u8fbe\u684c\u5b50\u7684\u65f6\u95f4\u662f\u65e0\u5173\u7d27\u8981\u7684\uff0c\u56e0\u4e3a\u603b\u6709\u540c\u6837\u5927\u5c0f\u7684\u86cb\u7cd5\u5728\u7b49\u7740\u5b83\u4eec\u3002\u4e0d\u540c\u90e8\u5206\u53d8\u5f02\u7684\u7b80\u5355\u76f8\u52a0\u5c31\u6784\u6210\u4e86\u67d0\u4e2a\u6a21\u578b\u6240\u89e3\u91ca\u7684\u603b\u4f53\u53d8\u5f02\u3002
\u4f46\u662f\uff0c\u8fd9\u79cd\u52a0\u6cd5\u7684\u89c2\u70b9\u53ea\u6709\u5728\u6bcf\u4e2a\u9884\u6d4b\u53d8\u91cf\u4e92\u76f8\u72ec\u7acb\u7684\u60c5\u51b5\u4e0b\u624d\u662f\u6b63\u786e\u7684\u3002\u5bf9\u4e8e\u591a\u91cd\u56de\u5f52\u6765\u8bf4\uff0c\u5219\u5f80\u5f80\u4e0d\u6b63\u786e\u3002\u5047\u5982\u9884\u6d4b\u53d8\u91cf\u5f7c\u6b64\u76f8\u5173\uff0c\u5b83\u4eec\u5c31\u4f1a\u5728\u89e3\u91ca\u53d8\u5f02\u65f6\u5f7c\u6b64\u7ade\u4e89\u3002\u5f52\u56e0\u4e8e\u67d0\u4e2a\u9884\u6d4b\u53d8\u91cf\u7684\u53d8\u5f02\u6570\u91cf\u8fd8\u53d6\u51b3\u4e8e\u6a21\u578b\u4e2d\u6240\u5305\u542b\u7684\u5176\u4ed6\u53d8\u91cf\u3002\u8fd9\u5c31\u4f7f\u5f97\u6211\u4eec\u5bf9\u4e24\u4e2a\u6a21\u578b\u7684\u6bd4\u8f83\u8fdb\u884c\u89e3\u91ca\u65f6\uff0c\u60c5\u51b5\u53d8\u5f97\u66f4\u4e3a\u590d\u6742\u3002
\u65b9\u5dee\u5206\u6790\u6a21\u578b\u662f\u5efa\u7acb\u5728\u6a21\u578b\u4e2d\u7684\u56e0\u7d20\u76f8\u4e92\u72ec\u7acb\u7684\u57fa\u7840\u4e0a\u7684\u3002\u5728ANOVA\u4e2d\uff0c\u56e0\u7d20\u5bf9\u5e94\u4e8e\u591a\u91cd\u56de\u5f52\u4e2d\u7684\u9884\u6d4b\u53d8\u91cf\u3002\u8fd9\u4e9b\u56e0\u7d20\u5177\u6709\u52a0\u6cd5\u6548\u5e94\uff0c\u53d8\u5f02\uff08\u65b9\u5dee\uff09\u53ef\u4ee5\u88ab\u6574\u9f50\u5730\u5207\u5f00\u6216\u5206\u5272\u3002\u8fd9\u4e9b\u56e0\u7d20\u4e4b\u95f4\u662f\u6b63\u4ea4\u7684\u3002
\u4f46\u662f\uff0c\u5728\u591a\u91cd\u56de\u5f52\u4e2d\uff0c\u53d8\u91cf\u8fdb\u5165\u6a21\u578b\u7684\u987a\u5e8f\u4f1a\u5f71\u54cd\u8be5\u53d8\u91cf\u6240\u5206\u914d\u7684\u53d8\u5f02\u91cf\u3002\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u9884\u6d4b\u53d8\u91cf\u5c31\u50cf\u4e00\u5757\u5757\u6d78\u5728\u5496\u5561\u676f\u4e2d\u7684\u6d77\u7ef5\u3002\u6bcf\u4e00\u5757\u90fd\u5438\u6536\u4e86\u4e00\u4e9b\u53d8\u5f02\u3002\u5728\u5206\u5c42\u591a\u91cd\u56de\u5f52\u4e2d\uff0c\u7b2c\u4e00\u5757\u6d78\u5165\u5496\u5561\u676f\u7684\u6d77\u7ef5\u9996\u5148\u5438\u6536\u53d8\u5f02\uff0c\u5b83\u8d2a\u5a6a\u5730\u5438\u6536\u5c3d\u53ef\u80fd\u591a\u7684\u53d8\u5f02\u3002\u5047\u5982\u4e24\u4e2a\u9884\u6d4b\u53d8\u91cf\u76f8\u5173\uff0c\u90a3\u5b83\u4eec\u6240\u89e3\u91ca\u7684\u53d8\u5f02\u5c31\u5b58\u5728\u91cd\u53e0\u3002\u5982\u679c\u4e00\u4e2a\u53d8\u91cf\u9996\u5148\u8fdb\u5165\u6a21\u578b\uff0c\u90a3\u5b83\u5c31\u5c06\u91cd\u53e0\uff08\u5171\u540c\uff09\u53d8\u5f02\u5438\u6536\u636e\u4e3a\u5df1\u6709\uff0c\u4e0d\u518d\u4e0e\u53e6\u4e00\u4e2a\u53d8\u91cf\u5206\u4eab\u3002
\u5728\u6807\u51c6\u591a\u91cd\u56de\u5f52\u4e2d\uff0c\u6240\u6709\u9884\u6d4b\u53d8\u91cf\u540c\u65f6\u8fdb\u5165\u6a21\u578b\uff0c\u5c31\u50cf\u5c06\u6240\u6709\u6d77\u7ef5\u540c\u65f6\u6254\u8fdb\u5496\u5561\u676f\u4e00\u6837\uff0c\u5b83\u4eec\u4e92\u76f8\u5206\u4eab\u5171\u540c\u53d8\u5f02\u3002\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u504f\u76f8\u5173\u7684\u5e73\u65b9\uff08sr2\uff09\u4e0e\u56de\u5f52\u7cfb\u6570\u76f8\u7b49\uff0c\u5b83\u4eec\u68c0\u9a8c\u4e86\u76f8\u540c\u7684\u4e1c\u897f\uff1a\u6392\u9664\u4e86\u4efb\u4f55\u5171\u540c\u53d8\u5f02\u540e\u7684\u72ec\u7279\u53d8\u5f02\u3002\u8fd9\u6837\uff0c\u5728\u591a\u91cd\u56de\u5f52\u4e2d\uff0c\u5bf9\u56de\u5f52\u7cfb\u6570\u7684T\u68c0\u9a8c\u5c31\u662fsr2\u7684\u7edf\u8ba1\u663e\u8457\u6027\u68c0\u9a8c\u3002\u4f46\u662f\uff0c\u5728\u5206\u5c42\u56de\u5f52\u6216\u9010\u6b65\u56de\u5f52\u4e2d\uff0csr2\u4e0d\u518d\u4e0e\u56de\u5f52\u7cfb\u6570\u76f8\u7b49\u3002\u4f46T\u68c0\u9a8c\u4ecd\u7136\u662f\u5bf9\u56de\u5f52\u7cfb\u6570\u7684\u68c0\u9a8c\u3002\u8981\u4f30\u8ba1sr2\u662f\u5426\u663e\u8457\uff0c\u5fc5\u987b\u5bf9\u6a21\u578b\u8fdb\u884c\u6bd4\u8f83\u3002
\u6a21\u578b\u6bd4\u8f83\u5c31\u662f\u9996\u5148\u5efa\u7acb\u4e00\u4e2a\u6a21\u578b\uff08\u6a21\u578ba\uff09\uff0c\u4f7f\u5b83\u5305\u62ec\u9664\u4e86\u8981\u68c0\u9a8c\u7684\u53d8\u91cf\u4ee5\u5916\u7684\u6240\u6709\u53d8\u91cf\uff0c\u7136\u540e\u518d\u5c06\u60f3\u8981\u68c0\u9a8c\u7684\u53d8\u91cf\u52a0\u5165\u6a21\u578b(\u6a21\u578bb)\uff0c\u770b\u6240\u89e3\u91ca\u7684\u53d8\u5f02\u662f\u5426\u663e\u8457\u63d0\u9ad8\u3002\u8981\u68c0\u9a8c\u6a21\u578bb\u662f\u5426\u8981\u6bd4\u6a21\u578ba\u663e\u8457\u5730\u89e3\u91ca\u4e86\u66f4\u591a\u7684\u53d8\u5f02\uff0c\u5c31\u8981\u8003\u5bdf\u5404\u4e2a\u6a21\u578b\u6240\u89e3\u91ca\u7684\u53d8\u5f02\u4e4b\u5dee\u662f\u5426\u663e\u8457\u5927\u4e8e\u8bef\u5dee\u53d8\u5f02\u3002\u4e0b\u9762\u5c31\u662f\u68c0\u9a8c\u65b9\u7a0b\u5f0f\uff08Tabachnik and Fidell, 1989\uff09\u3002
(R2b-R2a)\uff0fM
F = \u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014
(1+ R2b) \uff0fdferror
\uff082\u4e3a\u5e73\u65b9\uff0ca,b\u4e3a\u4e0b\u6807\u3002\u4e0d\u77e5\u9053\u5728blog\u91cc\u5982\u4f55\u8bbe\u7f6e\u6587\u5b57\u683c\u5f0f\uff09
\u539f\u6587\uff08DATA ANALYSIS FOR PSYCHOLOGY, George Dunbar\uff09\u5982\u6b64\uff0c\u4f46\u53c2\u8003\u4e86\u5176\u4ed6\u4e66\u540e\uff0c\u89c9\u5f97\u8fd9\u662f\u8bef\u5370\uff0c\u771f\u6b63\u7684\u516c\u5f0f\u5e94\u8be5\u662f\u8fd9\u6837\u7684\uff1a
(R2b-R2a)\uff0fM
F = \u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014
(1- R2b) \uff0fdferror
\u6ce8\uff1a
M\u662f\u6307\u6a21\u578bb\u4e2d\u6dfb\u52a0\u7684\u9884\u6d4b\u53d8\u91cf\u6570\u91cf
R2b\u662f\u6307\u6a21\u578bb\uff08\u5305\u542b\u66f4\u591a\u9884\u6d4b\u53d8\u91cf\u7684\u6a21\u578b\uff09\u7684\u590d\u76f8\u5173\u7cfb\u6570\u7684\u5e73\u65b9\uff08\u51b3\u5b9a\u7cfb\u6570\uff09\u3002
R2a\u662f\u6307\u6a21\u578ba\uff08\u5305\u542b\u8f83\u5c11\u9884\u6d4b\u53d8\u91cf\u7684\u6a21\u578b\uff09\u7684\u590d\u76f8\u5173\u7cfb\u6570\u7684\u5e73\u65b9\uff08\u51b3\u5b9a\u7cfb\u6570\uff09\u3002
dferror\u662f\u6307\u6a21\u578bb\u8bef\u5dee\u53d8\u5f02\u7684\u81ea\u7531\u5ea6\u3002
\u5206\u5c42\u56de\u5f52\u4e0e\u5411\u524d\u56de\u5f52\u3001\u5411\u540e\u56de\u5f52\u548c\u9010\u6b65\u56de\u5f52\u7684\u533a\u522b
\u540e\u4e09\u8005\u90fd\u662f\u9009\u62e9\u53d8\u91cf\u7684\u65b9\u6cd5\u3002
\u5411\u524d\u56de\u5f52\uff1a\u6839\u636e\u81ea\u53d8\u91cf\u5bf9\u56e0\u53d8\u91cf\u7684\u8d21\u732e\u7387\uff0c\u9996\u5148\u9009\u62e9\u4e00\u4e2a\u8d21\u732e\u7387\u6700\u5927\u7684\u81ea\u53d8\u91cf\u8fdb\u5165\uff0c\u4e00\u6b21\u53ea\u52a0\u5165\u4e00\u4e2a\u8fdb\u5165\u6a21\u578b\u3002\u7136\u540e\uff0c\u518d\u9009\u62e9\u53e6\u4e00\u4e2a\u6700\u597d\u7684\u52a0\u5165\u6a21\u578b\uff0c\u76f4\u81f3\u9009\u62e9\u6240\u6709\u7b26\u5408\u6807\u51c6\u8005\u5168\u90e8\u8fdb\u5165\u56de\u5f52\u3002
\u5411\u540e\u56de\u5f52\uff1a\u5c06\u81ea\u53d8\u91cf\u4e00\u6b21\u7eb3\u5165\u56de\u5f52\uff0c\u7136\u540e\u6839\u636e\u6807\u51c6\u5220\u9664\u4e00\u4e2a\u6700\u4e0d\u663e\u8457\u8005\uff0c\u518d\u505a\u4e00\u6b21\u56de\u5f52\u5224\u65ad\u5176\u4f59\u53d8\u91cf\u7684\u53d6\u820d\uff0c\u76f4\u81f3\u4fdd\u7559\u8005\u90fd\u8fbe\u5230\u8981\u6c42\u3002
\u9010\u6b65\u56de\u5f52\u662f\u5411\u524d\u56de\u5f52\u6cd5\u548c\u5411\u540e\u56de\u5f52\u6cd5\u7684\u7ed3\u5408\u3002\u9996\u5148\u6309\u81ea\u53d8\u91cf\u5bf9\u56e0\u53d8\u91cf\u7684\u8d21\u732e\u7387\u8fdb\u884c\u6392\u5e8f\uff0c\u6309\u7167\u4ece\u5927\u5230\u5c0f\u7684\u987a\u5e8f\u9009\u62e9\u8fdb\u5165\u6a21\u578b\u7684\u53d8\u91cf\u3002\u6bcf\u5c06\u4e00\u4e2a\u53d8\u91cf\u52a0\u5165\u6a21\u578b\uff0c\u5c31\u8981\u5bf9\u6a21\u578b\u4e2d\u7684\u6bcf\u4e2a\u53d8\u91cf\u8fdb\u884c\u68c0\u9a8c\uff0c\u5254\u9664\u4e0d\u663e\u8457\u7684\u53d8\u91cf\uff0c\u7136\u540e\u518d\u5bf9\u7559\u5728\u6a21\u578b\u4e2d\u7684\u53d8\u91cf\u8fdb\u884c\u68c0\u9a8c\u3002\u76f4\u5230\u6ca1\u6709\u53d8\u91cf\u53ef\u4ee5\u7eb3\u5165\uff0c\u4e5f\u6ca1\u6709\u53d8\u91cf\u53ef\u4ee5\u5254\u9664\u4e3a\u6b62\u3002
\u5411\u524d\u56de\u5f52\u3001\u5411\u540e\u56de\u5f52\u548c\u9010\u6b65\u56de\u5f52\u90fd\u8981\u6309\u7167\u4e00\u5b9a\u5224\u65ad\u6807\u51c6\u6267\u884c\u3002\u5373\u5728\u5c06\u81ea\u53d8\u91cf\u52a0\u5165\u6216\u5220\u9664\u6a21\u578b\u65f6\uff0c\u8981\u8fdb\u884c\u504fF\u68c0\u9a8c\uff0c\u8ba1\u7b97\u516c\u5f0f\u4e3a\uff1a
(R2b-R2a)\uff0fM
F = \u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014
(1- R2b) \uff0fdferror
SPSS\u56de\u5f52\u6240\u8bbe\u5b9a\u7684\u9ed8\u8ba4\u6807\u51c6\u662f\u9009\u62e9\u8fdb\u5165\u8005\u65f6\u504fF\u68c0\u9a8c\u503c\u4e3a3.84\uff0c\u9009\u62e9\u5220\u9664\u8005\u65f6\u7684F\u68c0\u9a8c\u503c\u4e3a2.71\u3002
\u4ece\u4e0a\u9762\u53ef\u4ee5\u770b\u51fa\uff0c\u5206\u5c42\u56de\u5f52\u548c\u5404\u79cd\u9009\u62e9\u81ea\u53d8\u91cf\u7684\u65b9\u6cd5\uff0c\u5176\u5b9e\u90fd\u6d89\u53ca\u6a21\u578b\u4e4b\u95f4\u7684\u6bd4\u8f83\u95ee\u9898\uff0c\u800c\u4e14F\u68c0\u9a8c\u7684\u516c\u5f0f\u4e5f\u76f8\u7b49\uff0c\u8bf4\u660e\u5b83\u4eec\u62e5\u6709\u76f8\u540c\u7684\u7edf\u8ba1\u5b66\u57fa\u7840\u3002\u4f46\u662f\uff0c\u5b83\u4eec\u53c8\u662f\u4e0d\u540c\u8303\u7574\u7684\u6982\u5ff5\u3002\u5206\u5c42\u56de\u5f52\u662f\u5bf9\u4e8e\u6a21\u578b\u6bd4\u8f83\u800c\u8a00\u7684\uff0c\u800c\u4e0a\u9762\u4e09\u79cd\u65b9\u6cd5\u5219\u662f\u9488\u5bf9\u81ea\u53d8\u91cf\u800c\u8a00\u7684\u3002\u4e0a\u9762\u4e09\u79cd\u9009\u62e9\u81ea\u53d8\u91cf\u7684\u65b9\u6cd5\uff0c\u90fd\u662f\u7531\u8f6f\u4ef6\u6839\u636e\u8bbe\u5b9a\u6807\u51c6\u6765\u81ea\u52a8\u9009\u62e9\u8fdb\u5165\u6a21\u578b\u7684\u53d8\u91cf\u3002\u800c\u5206\u5c42\u56de\u5f52\u5219\u662f\u7531\u7814\u7a76\u8005\u6839\u636e\u7ecf\u9a8c\u548c\u7406\u8bba\u601d\u8003\u6765\u5c06\u81ea\u53d8\u91cf\u5206\u6210\u4e0d\u540c\u7684\u7ec4\uff08block\uff09\uff0c\u7136\u540e\u518d\u5b89\u6392\u6bcf\u4e00\u7ec4\u53d8\u91cf\u8fdb\u5165\u6a21\u578b\u7684\u987a\u5e8f\uff0c\u8fdb\u5165\u7684\u987a\u5e8f\u4e0d\u662f\u6839\u636e\u8d21\u732e\u7387\uff0c\u800c\u662f\u6839\u636e\u76f8\u5e94\u7684\u7406\u8bba\u5047\u8bbe\u3002\u800c\u4e14\uff0c\u7814\u7a76\u8005\u8fd8\u53ef\u4ee5\u4e3a\u4e0d\u540c\u7ec4\u7684\u81ea\u53d8\u91cf\u9009\u7528\u4e0d\u540c\u7684\u7eb3\u5165\u53d8\u91cf\u7684\u65b9\u6cd5\u3002
\u5206\u5c42\u56de\u5f52\u5728SPSS\u4e0a\u7684\u5b9e\u73b0
\u5728\u7ebf\u6027\u56de\u5f52\u4e3b\u5bf9\u8bdd\u6846\u4e2d\uff0c\u5728\u5b9a\u4e49\u5b8c\u4e00\u7ec4\u81ea\u53d8\u91cf\u540e\uff0c\u5728\u56e0\u53d8\u91cf\u4e0d\u53d8\u7684\u60c5\u51b5\u4e0b\uff0c\u5229\u7528block\u524d\u540e\u7684previous\u548cnext\u6309\u94ae\uff0c\u7ee7\u7eed\u5c06\u5176\u4ed6\u53d8\u91cf\u7ec4\u52a0\u5165\u6a21\u578b\u3002
\u6240\u8c13\u56de\u5f52\u5206\u6790\u6cd5\uff0c\u662f\u5728\u638c\u63e1\u5927\u91cf\u89c2\u5bdf\u6570\u636e\u7684\u57fa\u7840\u4e0a\uff0c\u5229\u7528\u6570\u7406\u7edf\u8ba1\u65b9\u6cd5\u5efa\u7acb\u56e0\u53d8\u91cf\u4e0e\u81ea\u53d8\u91cf\u4e4b\u95f4\u7684\u56de\u5f52\u5173\u7cfb\u51fd\u6570\u8868\u8fbe\u5f0f(\u79f0\u56de\u5f52\u65b9\u7a0b\u5f0f)\u3002\u56de\u5f52\u5206\u6790\u4e2d\uff0c\u5f53\u7814\u7a76\u7684\u56e0\u679c\u5173\u7cfb\u53ea\u6d89\u53ca\u56e0\u53d8\u91cf\u548c\u4e00\u4e2a\u81ea\u53d8\u91cf\u65f6\uff0c\u53eb\u505a\u4e00\u5143\u56de\u5f52\u5206\u6790;\u5f53\u7814\u7a76\u7684\u56e0\u679c\u5173\u7cfb\u6d89\u53ca\u56e0\u53d8\u91cf\u548c\u4e24\u4e2a\u6216\u4e24\u4e2a\u4ee5\u4e0a\u81ea\u53d8\u91cf\u65f6\uff0c\u53eb\u505a\u591a\u5143\u56de\u5f52\u5206\u6790\u3002\u6b64\u5916\uff0c\u56de\u5f52\u5206\u6790\u4e2d\uff0c\u53c8\u4f9d\u636e\u63cf\u8ff0\u81ea\u53d8\u91cf\u4e0e\u56e0\u53d8\u91cf\u4e4b\u95f4\u56e0\u679c\u5173\u7cfb\u7684\u51fd\u6570\u8868\u8fbe\u5f0f\u662f\u7ebf\u6027\u7684\u8fd8\u662f\u975e\u7ebf\u6027\u7684\uff0c\u5206\u4e3a\u7ebf\u6027\u56de\u5f52\u5206\u6790\u548c\u975e\u7ebf\u6027\u56de\u5f52\u5206\u6790\u3002\u901a\u5e38\u7ebf\u6027\u56de\u5f52\u5206\u6790\u6cd5\u662f\u6700\u57fa\u672c\u7684\u5206\u6790\u65b9\u6cd5\uff0c\u9047\u5230\u975e\u7ebf\u6027\u56de\u5f52\u95ee\u9898\u53ef\u4ee5\u501f\u52a9\u6570\u5b66\u624b\u6bb5\u5316\u4e3a\u7ebf\u6027\u56de\u5f52\u95ee\u9898\u5904\u7406\u3002
\u5206\u5c42\u56de\u5f52\u5176\u5b9e\u662f\u5bf9\u4e24\u4e2a\u6216\u591a\u4e2a\u56de\u5f52\u6a21\u578b\u8fdb\u884c\u6bd4\u8f83\u3002\u6211\u4eec\u53ef\u4ee5\u6839\u636e\u4e24\u4e2a\u6a21\u578b\u6240\u89e3\u91ca\u7684\u53d8\u5f02\u91cf\u7684\u5dee\u5f02\u6765\u6bd4\u8f83\u6240\u5efa\u7acb\u7684\u4e24\u4e2a\u6a21\u578b\u3002\u4e00\u4e2a\u6a21\u578b\u89e3\u91ca\u4e86\u8d8a\u591a\u7684\u53d8\u5f02\uff0c\u5219\u5b83\u5bf9\u6570\u636e\u7684\u62df\u5408\u5c31\u8d8a\u597d\u3002\u5047\u5982\u5728\u5176\u4ed6\u6761\u4ef6\u76f8\u7b49\u7684\u60c5\u51b5\u4e0b\uff0c\u4e00\u4e2a\u6a21\u578b\u6bd4\u53e6\u4e00\u4e2a\u6a21\u578b\u89e3\u91ca\u4e86\u66f4\u591a\u7684\u53d8\u5f02\uff0c\u5219\u8fd9\u4e2a\u6a21\u578b\u662f\u4e00\u4e2a\u66f4\u597d\u7684\u6a21\u578b\u3002\u4e24\u4e2a\u6a21\u578b\u6240\u89e3\u91ca\u7684\u53d8\u5f02\u91cf\u4e4b\u95f4\u7684\u5dee\u5f02\u53ef\u4ee5\u7528\u7edf\u8ba1\u663e\u8457\u6027\u6765\u4f30\u8ba1\u548c\u68c0\u9a8c\u3002
\u6a21\u578b\u6bd4\u8f83\u53ef\u4ee5\u7528\u6765\u8bc4\u4f30\u4e2a\u4f53\u9884\u6d4b\u53d8\u91cf\u3002\u68c0\u9a8c\u4e00\u4e2a\u9884\u6d4b\u53d8\u91cf\u662f\u5426\u663e\u8457\u7684\u65b9\u6cd5\u662f\u6bd4\u8f83\u4e24\u4e2a\u6a21\u578b\uff0c\u5176\u4e2d\u7b2c\u4e00\u4e2a\u6a21\u578b\u4e0d\u5305\u62ec\u8fd9\u4e2a\u9884\u6d4b\u53d8\u91cf\uff0c\u800c\u7b2c\u4e8c\u4e2a\u6a21\u578b\u5305\u62ec\u8be5\u53d8\u91cf\u3002\u5047\u5982\u8be5\u9884\u6d4b\u53d8\u91cf\u89e3\u91ca\u4e86\u663e\u8457\u7684\u989d\u5916\u53d8\u5f02\uff0c\u90a3\u7b2c\u4e8c\u4e2a\u6a21\u578b\u5c31\u663e\u8457\u5730\u89e3\u91ca\u4e86\u6bd4\u7b2c\u4e00\u4e2a\u6a21\u578b\u66f4\u591a\u7684\u53d8\u5f02\u3002\u8fd9\u79cd\u89c2\u70b9\u7b80\u5355\u800c\u6709\u529b\u3002\u4f46\u662f\uff0c\u8981\u7406\u89e3\u8fd9\u79cd\u5206\u6790\uff0c\u4f60\u5fc5\u987b\u7406\u89e3\u8be5\u9884\u6d4b\u53d8\u91cf\u6240\u89e3\u91ca\u7684\u72ec\u7279\u53d8\u5f02\u548c\u603b\u4f53\u53d8\u5f02\u4e4b\u95f4\u7684\u5dee\u5f02\u3002
\u4e00\u4e2a\u9884\u6d4b\u53d8\u91cf\u6240\u89e3\u91ca\u7684\u603b\u4f53\u53d8\u5f02\u662f\u8be5\u9884\u6d4b\u53d8\u91cf\u548c\u7ed3\u679c\u53d8\u91cf\u4e4b\u95f4\u76f8\u5173\u7684\u5e73\u65b9\u3002\u5b83\u5305\u62ec\u8be5\u9884\u6d4b\u53d8\u91cf\u548c\u7ed3\u679c\u53d8\u91cf\u4e4b\u95f4\u7684\u6240\u6709\u5173\u7cfb\u3002
\u9884\u6d4b\u53d8\u91cf\u7684\u72ec\u7279\u53d8\u5f02\u662f\u6307\u5728\u63a7\u5236\u4e86\u5176\u4ed6\u53d8\u91cf\u4ee5\u540e\uff0c\u9884\u6d4b\u53d8\u91cf\u5bf9\u7ed3\u679c\u53d8\u91cf\u7684\u5f71\u54cd\u3002\u8fd9\u6837\uff0c\u9884\u6d4b\u53d8\u91cf\u7684\u72ec\u7279\u53d8\u5f02\u4f9d\u8d56\u4e8e\u5176\u4ed6\u9884\u6d4b\u53d8\u91cf\u3002\u5728\u6807\u51c6\u591a\u91cd\u56de\u5f52\u5206\u6790\u4e2d\uff0c\u53ef\u4ee5\u5bf9\u72ec\u7279\u53d8\u5f02\u8fdb\u884c\u68c0\u9a8c\uff0c\u6bcf\u4e2a\u9884\u6d4b\u53d8\u91cf\u7684\u56de\u5f52\u7cfb\u6570\u5927\u5c0f\u4f9d\u8d56\u4e8e\u6a21\u578b\u4e2d\u7684\u5176\u4ed6\u9884\u6d4b\u53d8\u91cf\u3002
\u5728\u6807\u51c6\u591a\u91cd\u56de\u5f52\u5206\u6790\u4e2d\uff0c\u56de\u5f52\u7cfb\u6570\u7528\u6765\u68c0\u9a8c\u6bcf\u4e2a\u9884\u6d4b\u53d8\u91cf\u6240\u89e3\u91ca\u7684\u72ec\u7279\u53d8\u5f02\u3002\u8fd9\u4e2a\u72ec\u7279\u53d8\u5f02\u5c31\u662f\u504f\u76f8\u5173\u7684\u5e73\u65b9\uff08Squared semi-partial correlation\uff09-sr2\uff08\u504f\u786e\u5b9a\u7cfb\u6570\uff09\u3002\u5b83\u8868\u793a\u4e86\u7ed3\u679c\u53d8\u91cf\u4e2d\u7531\u7279\u5b9a\u9884\u6d4b\u53d8\u91cf\u6240\u5355\u72ec\u89e3\u91ca\u7684\u53d8\u5f02\u3002\u6b63\u5982\u6211\u4eec\u770b\u5230\u7684\uff0c\u5b83\u4f9d\u8d56\u4e8e\u6a21\u578b\u4e2d\u7684\u5176\u4ed6\u53d8\u91cf\u3002\u5047\u5982\u9884\u6d4b\u53d8\u91cf\u4e4b\u95f4\u5b58\u5728\u91cd\u53e0\uff0c\u90a3\u4e48\u5b83\u4eec\u5171\u6709\u7684\u53d8\u5f02\u5c31\u4f1a\u524a\u5f31\u72ec\u7279\u53d8\u5f02\u3002\u9884\u6d4b\u53d8\u91cf\u7684\u72ec\u7279\u6548\u5e94\u6307\u7684\u662f\u53bb\u9664\u91cd\u53e0\u6548\u5e94\u540e\u8be5\u9884\u6d4b\u53d8\u91cf\u4e0e\u7ed3\u679c\u53d8\u91cf\u7684\u76f8\u5173\u3002\u8fd9\u6837\uff0c\u67d0\u4e2a\u9884\u6d4b\u53d8\u91cf\u7684\u7279\u5b9a\u6548\u5e94\u5c31\u4f9d\u8d56\u4e8e\u6a21\u578b\u4e2d\u7684\u5176\u4ed6\u9884\u6d4b\u53d8\u91cf\u3002
\u6807\u51c6\u591a\u91cd\u56de\u5f52\u7684\u5c40\u9650\u6027\u5728\u4e8e\u4e0d\u80fd\u5c06\u91cd\u53e0\uff08\u5171\u540c\uff09\u53d8\u5f02\u5f52\u56e0\u4e8e\u6a21\u578b\u4e2d\u7684\u4efb\u4f55\u4e00\u4e2a\u9884\u6d4b\u53d8\u91cf\u3002\u8fd9\u5c31\u610f\u5473\u7740\u6a21\u578b\u4e2d\u6240\u6709\u9884\u6d4b\u53d8\u91cf\u7684\u504f\u51b3\u5b9a\u7cfb\u6570\u4e4b\u548c\u8981\u5c0f\u4e8e\u6574\u4e2a\u6a21\u578b\u7684\u51b3\u5b9a\u7cfb\u6570\uff08R2\uff09\u3002\u603b\u51b3\u5b9a\u7cfb\u6570\u5305\u62ec\u504f\u51b3\u5b9a\u7cfb\u6570\u4e4b\u548c\u4e0e\u5171\u540c\u53d8\u5f02\u3002\u5206\u5c42\u56de\u5f52\u63d0\u4f9b\u4e86\u4e00\u79cd\u53ef\u4ee5\u5c06\u5171\u540c\u53d8\u5f02\u5206\u914d\u7ed9\u7279\u5b9a\u9884\u6d4b\u53d8\u91cf\u7684\u65b9\u6cd5\u3002
\u5206\u5c42\u56de\u5f52
\u6807\u51c6\u591a\u91cd\u56de\u5f52\u53ef\u4ee5\u6d4b\u91cf\u6a21\u578b\u6240\u89e3\u91ca\u7684\u53d8\u5f02\u91cf\u7684\u5927\u5c0f\uff0c\u5b83\u7531\u590d\u76f8\u5173\u7cfb\u6570\u7684\u5e73\u65b9\uff08R2\uff0c\u5373\u51b3\u5b9a\u7cfb\u6570\uff09\u6765\u8868\u793a\uff0c\u4ee3\u8868\u4e86\u9884\u6d4b\u53d8\u91cf\u6240\u89e3\u91ca\u7684\u56e0\u53d8\u91cf\u7684\u53d8\u5f02\u91cf\u3002\u6a21\u578b\u7684\u663e\u8457\u6027\u68c0\u9a8c\u662f\u5c06\u9884\u6d4b\u53d8\u91cf\u6240\u89e3\u91ca\u7684\u53d8\u5f02\u4e0e\u8bef\u5dee\u53d8\u5f02\u8fdb\u884c\u6bd4\u8f83\uff08\u5373F\u503c\uff09\u3002
\u4f46\u662f\uff0c\u4e5f\u53ef\u4ee5\u91c7\u7528\u76f8\u540c\u7684\u65b9\u5f0f\u6765\u6bd4\u8f83\u4e24\u4e2a\u6a21\u578b\u3002\u53ef\u4ee5\u5c06\u4e24\u4e2a\u6a21\u578b\u6240\u89e3\u91ca\u7684\u53d8\u5f02\u4e4b\u5dee\u4f5c\u4e3aF\u503c\u7684\u5206\u5b50\u3002\u5047\u5982\u4e0e\u8bef\u5dee\u53d8\u5f02\u76f8\u6bd4\uff0c\u4e24\u4e2a\u6a21\u578b\u6240\u89e3\u91ca\u7684\u53d8\u5f02\u5dee\u522b\u8db3\u591f\u5927\uff0c\u90a3\u4e48\u5c31\u53ef\u4ee5\u8bf4\u8fd9\u79cd\u5dee\u522b\u8fbe\u5230\u4e86\u7edf\u8ba1\u7684\u663e\u8457\u6027\u3002\u76f8\u5e94\u7684\u65b9\u7a0b\u5f0f\u5c06\u5728\u4e0b\u9762\u8be6\u7ec6\u9610\u8ff0\u3002
\u5206\u5c42\u56de\u5f52\u5c31\u662f\u91c7\u7528\u7684\u8fd9\u79cd\u65b9\u5f0f\u3002\u5206\u5c42\u56de\u5f52\u5305\u62ec\u5efa\u7acb\u4e00\u7cfb\u5217\u6a21\u578b\uff0c\u5904\u4e8e\u7cfb\u5217\u4e2d\u67d0\u4e2a\u4f4d\u7f6e\u7684\u6a21\u578b\u5c06\u4f1a\u5305\u62ec\u524d\u4e00\u6a21\u578b\u6240\u6ca1\u6709\u7684\u989d\u5916\u9884\u6d4b\u53d8\u91cf\u3002\u5047\u5982\u52a0\u5165\u6a21\u578b\u7684\u989d\u5916\u89e3\u91ca\u53d8\u91cf\u5bf9\u89e3\u91ca\u5206\u6570\u5dee\u5f02\u5177\u6709\u663e\u8457\u7684\u989d\u5916\u8d21\u732e\uff0c\u90a3\u4e48\u5b83\u5c06\u4f1a\u663e\u8457\u5730\u63d0\u9ad8\u51b3\u5b9a\u7cfb\u6570\u3002
\u8fd9\u4e2a\u6a21\u578b\u4e0e\u6807\u51c6\u591a\u91cd\u56de\u5f52\u7684\u5dee\u5f02\u5728\u4e8e\u5b83\u53ef\u4ee5\u5c06\u5171\u540c\u53d8\u5f02\u5206\u914d\u5230\u9884\u6d4b\u53d8\u91cf\u4e2d\u3002\u800c\u5728\u6807\u51c6\u591a\u91cd\u56de\u5f52\u4e2d\uff0c\u5171\u540c\u53d8\u5f02\u4e0d\u80fd\u5206\u914d\u5230\u4efb\u4f55\u9884\u6d4b\u53d8\u91cf\u4e2d\uff0c\u6bcf\u4e2a\u9884\u6d4b\u53d8\u91cf\u53ea\u80fd\u5206\u914d\u5230\u5b83\u6240\u89e3\u91ca\u7684\u72ec\u7279\u53d8\u5f02\uff0c\u5171\u540c\u53d8\u5f02\u5219\u88ab\u629b\u5f03\u4e86\u3002\u5728\u5206\u5c42\u56de\u5f52\u4e2d\uff0c\u5c06\u4f1a\u628a\u91cd\u53e0\uff08\u5171\u540c\uff09\u53d8\u5f02\u5206\u914d\u7ed9\u7b2c\u4e00\u4e2a\u6a21\u578b\u4e2d\u7684\u9884\u6d4b\u53d8\u91cf\u3002\u56e0\u6b64\uff0c\u5171\u540c\u53d8\u5f02\u5c06\u4f1a\u5206\u914d\u7ed9\u4f18\u5148\u8fdb\u5165\u6a21\u578b\u7684\u53d8\u91cf\u3002
\u91cd\u53e0\u7684\u9884\u6d4b\u53d8\u91cf(\u76f8\u5173\u7684\u9884\u6d4b\u53d8\u91cfPredictor variables that overlap)
\u7b80\u5355\u5730\u770b\u6765\uff0c\u7531\u4e00\u7cfb\u5217\u9884\u6d4b\u53d8\u91cf\u6240\u89e3\u91ca\u7684\u53d8\u5f02\u5c31\u50cf\u4e00\u5757\u5757\u86cb\u7cd5\u5806\u79ef\u5728\u4e00\u8d77\u3002\u6bcf\u4e2a\u9884\u6d4b\u53d8\u91cf\u90fd\u6709\u81ea\u5df1\u660e\u786e\u7684\u4e00\u5757\u3002\u5b83\u4eec\u5230\u8fbe\u684c\u5b50\u7684\u65f6\u95f4\u662f\u65e0\u5173\u7d27\u8981\u7684\uff0c\u56e0\u4e3a\u603b\u6709\u540c\u6837\u5927\u5c0f\u7684\u86cb\u7cd5\u5728\u7b49\u7740\u5b83\u4eec\u3002\u4e0d\u540c\u90e8\u5206\u53d8\u5f02\u7684\u7b80\u5355\u76f8\u52a0\u5c31\u6784\u6210\u4e86\u67d0\u4e2a\u6a21\u578b\u6240\u89e3\u91ca\u7684\u603b\u4f53\u53d8\u5f02\u3002
\u4f46\u662f\uff0c\u8fd9\u79cd\u52a0\u6cd5\u7684\u89c2\u70b9\u53ea\u6709\u5728\u6bcf\u4e2a\u9884\u6d4b\u53d8\u91cf\u4e92\u76f8\u72ec\u7acb\u7684\u60c5\u51b5\u4e0b\u624d\u662f\u6b63\u786e\u7684\u3002\u5bf9\u4e8e\u591a\u91cd\u56de\u5f52\u6765\u8bf4\uff0c\u5219\u5f80\u5f80\u4e0d\u6b63\u786e\u3002\u5047\u5982\u9884\u6d4b\u53d8\u91cf\u5f7c\u6b64\u76f8\u5173\uff0c\u5b83\u4eec\u5c31\u4f1a\u5728\u89e3\u91ca\u53d8\u5f02\u65f6\u5f7c\u6b64\u7ade\u4e89\u3002\u5f52\u56e0\u4e8e\u67d0\u4e2a\u9884\u6d4b\u53d8\u91cf\u7684\u53d8\u5f02\u6570\u91cf\u8fd8\u53d6\u51b3\u4e8e\u6a21\u578b\u4e2d\u6240\u5305\u542b\u7684\u5176\u4ed6\u53d8\u91cf\u3002\u8fd9\u5c31\u4f7f\u5f97\u6211\u4eec\u5bf9\u4e24\u4e2a\u6a21\u578b\u7684\u6bd4\u8f83\u8fdb\u884c\u89e3\u91ca\u65f6\uff0c\u60c5\u51b5\u53d8\u5f97\u66f4\u4e3a\u590d\u6742\u3002
\u65b9\u5dee\u5206\u6790\u6a21\u578b\u662f\u5efa\u7acb\u5728\u6a21\u578b\u4e2d\u7684\u56e0\u7d20\u76f8\u4e92\u72ec\u7acb\u7684\u57fa\u7840\u4e0a\u7684\u3002\u5728ANOVA\u4e2d\uff0c\u56e0\u7d20\u5bf9\u5e94\u4e8e\u591a\u91cd\u56de\u5f52\u4e2d\u7684\u9884\u6d4b\u53d8\u91cf\u3002\u8fd9\u4e9b\u56e0\u7d20\u5177\u6709\u52a0\u6cd5\u6548\u5e94\uff0c\u53d8\u5f02\uff08\u65b9\u5dee\uff09\u53ef\u4ee5\u88ab\u6574\u9f50\u5730\u5207\u5f00\u6216\u5206\u5272\u3002\u8fd9\u4e9b\u56e0\u7d20\u4e4b\u95f4\u662f\u6b63\u4ea4\u7684\u3002
\u4f46\u662f\uff0c\u5728\u591a\u91cd\u56de\u5f52\u4e2d\uff0c\u53d8\u91cf\u8fdb\u5165\u6a21\u578b\u7684\u987a\u5e8f\u4f1a\u5f71\u54cd\u8be5\u53d8\u91cf\u6240\u5206\u914d\u7684\u53d8\u5f02\u91cf\u3002\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u9884\u6d4b\u53d8\u91cf\u5c31\u50cf\u4e00\u5757\u5757\u6d78\u5728\u5496\u5561\u676f\u4e2d\u7684\u6d77\u7ef5\u3002\u6bcf\u4e00\u5757\u90fd\u5438\u6536\u4e86\u4e00\u4e9b\u53d8\u5f02\u3002\u5728\u5206\u5c42\u591a\u91cd\u56de\u5f52\u4e2d\uff0c\u7b2c\u4e00\u5757\u6d78\u5165\u5496\u5561\u676f\u7684\u6d77\u7ef5\u9996\u5148\u5438\u6536\u53d8\u5f02\uff0c\u5b83\u8d2a\u5a6a\u5730\u5438\u6536\u5c3d\u53ef\u80fd\u591a\u7684\u53d8\u5f02\u3002\u5047\u5982\u4e24\u4e2a\u9884\u6d4b\u53d8\u91cf\u76f8\u5173\uff0c\u90a3\u5b83\u4eec\u6240\u89e3\u91ca\u7684\u53d8\u5f02\u5c31\u5b58\u5728\u91cd\u53e0\u3002\u5982\u679c\u4e00\u4e2a\u53d8\u91cf\u9996\u5148\u8fdb\u5165\u6a21\u578b\uff0c\u90a3\u5b83\u5c31\u5c06\u91cd\u53e0\uff08\u5171\u540c\uff09\u53d8\u5f02\u5438\u6536\u636e\u4e3a\u5df1\u6709\uff0c\u4e0d\u518d\u4e0e\u53e6\u4e00\u4e2a\u53d8\u91cf\u5206\u4eab\u3002
\u5728\u6807\u51c6\u591a\u91cd\u56de\u5f52\u4e2d\uff0c\u6240\u6709\u9884\u6d4b\u53d8\u91cf\u540c\u65f6\u8fdb\u5165\u6a21\u578b\uff0c\u5c31\u50cf\u5c06\u6240\u6709\u6d77\u7ef5\u540c\u65f6\u6254\u8fdb\u5496\u5561\u676f\u4e00\u6837\uff0c\u5b83\u4eec\u4e92\u76f8\u5206\u4eab\u5171\u540c\u53d8\u5f02\u3002\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u504f\u76f8\u5173\u7684\u5e73\u65b9\uff08sr2\uff09\u4e0e\u56de\u5f52\u7cfb\u6570\u76f8\u7b49\uff0c\u5b83\u4eec\u68c0\u9a8c\u4e86\u76f8\u540c\u7684\u4e1c\u897f\uff1a\u6392\u9664\u4e86\u4efb\u4f55\u5171\u540c\u53d8\u5f02\u540e\u7684\u72ec\u7279\u53d8\u5f02\u3002\u8fd9\u6837\uff0c\u5728\u591a\u91cd\u56de\u5f52\u4e2d\uff0c\u5bf9\u56de\u5f52\u7cfb\u6570\u7684T\u68c0\u9a8c\u5c31\u662fsr2\u7684\u7edf\u8ba1\u663e\u8457\u6027\u68c0\u9a8c\u3002\u4f46\u662f\uff0c\u5728\u5206\u5c42\u56de\u5f52\u6216\u9010\u6b65\u56de\u5f52\u4e2d\uff0csr2\u4e0d\u518d\u4e0e\u56de\u5f52\u7cfb\u6570\u76f8\u7b49\u3002\u4f46T\u68c0\u9a8c\u4ecd\u7136\u662f\u5bf9\u56de\u5f52\u7cfb\u6570\u7684\u68c0\u9a8c\u3002\u8981\u4f30\u8ba1sr2\u662f\u5426\u663e\u8457\uff0c\u5fc5\u987b\u5bf9\u6a21\u578b\u8fdb\u884c\u6bd4\u8f83\u3002
\u6a21\u578b\u6bd4\u8f83\u5c31\u662f\u9996\u5148\u5efa\u7acb\u4e00\u4e2a\u6a21\u578b\uff08\u6a21\u578ba\uff09\uff0c\u4f7f\u5b83\u5305\u62ec\u9664\u4e86\u8981\u68c0\u9a8c\u7684\u53d8\u91cf\u4ee5\u5916\u7684\u6240\u6709\u53d8\u91cf\uff0c\u7136\u540e\u518d\u5c06\u60f3\u8981\u68c0\u9a8c\u7684\u53d8\u91cf\u52a0\u5165\u6a21\u578b(\u6a21\u578bb)\uff0c\u770b\u6240\u89e3\u91ca\u7684\u53d8\u5f02\u662f\u5426\u663e\u8457\u63d0\u9ad8\u3002\u8981\u68c0\u9a8c\u6a21\u578bb\u662f\u5426\u8981\u6bd4\u6a21\u578ba\u663e\u8457\u5730\u89e3\u91ca\u4e86\u66f4\u591a\u7684\u53d8\u5f02\uff0c\u5c31\u8981\u8003\u5bdf\u5404\u4e2a\u6a21\u578b\u6240\u89e3\u91ca\u7684\u53d8\u5f02\u4e4b\u5dee\u662f\u5426\u663e\u8457\u5927\u4e8e\u8bef\u5dee\u53d8\u5f02\u3002\u4e0b\u9762\u5c31\u662f\u68c0\u9a8c\u65b9\u7a0b\u5f0f\uff08Tabachnik and Fidell, 1989\uff09\u3002
(R2b-R2a)\uff0fM
F = \u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014
(1+ R2b) \uff0fdferror
\uff082\u4e3a\u5e73\u65b9\uff0ca,b\u4e3a\u4e0b\u6807\u3002\u4e0d\u77e5\u9053\u5728blog\u91cc\u5982\u4f55\u8bbe\u7f6e\u6587\u5b57\u683c\u5f0f\uff09
\u539f\u6587\uff08DATA ANALYSIS FOR PSYCHOLOGY, George Dunbar\uff09\u5982\u6b64\uff0c\u4f46\u53c2\u8003\u4e86\u5176\u4ed6\u4e66\u540e\uff0c\u89c9\u5f97\u8fd9\u662f\u8bef\u5370\uff0c\u771f\u6b63\u7684\u516c\u5f0f\u5e94\u8be5\u662f\u8fd9\u6837\u7684\uff1a
(R2b-R2a)\uff0fM
F = \u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014
(1- R2b) \uff0fdferror
\u6ce8\uff1a
M\u662f\u6307\u6a21\u578bb\u4e2d\u6dfb\u52a0\u7684\u9884\u6d4b\u53d8\u91cf\u6570\u91cf
R2b\u662f\u6307\u6a21\u578bb\uff08\u5305\u542b\u66f4\u591a\u9884\u6d4b\u53d8\u91cf\u7684\u6a21\u578b\uff09\u7684\u590d\u76f8\u5173\u7cfb\u6570\u7684\u5e73\u65b9\uff08\u51b3\u5b9a\u7cfb\u6570\uff09\u3002
R2a\u662f\u6307\u6a21\u578ba\uff08\u5305\u542b\u8f83\u5c11\u9884\u6d4b\u53d8\u91cf\u7684\u6a21\u578b\uff09\u7684\u590d\u76f8\u5173\u7cfb\u6570\u7684\u5e73\u65b9\uff08\u51b3\u5b9a\u7cfb\u6570\uff09\u3002
dferror\u662f\u6307\u6a21\u578bb\u8bef\u5dee\u53d8\u5f02\u7684\u81ea\u7531\u5ea6\u3002
\u5206\u5c42\u56de\u5f52\u4e0e\u5411\u524d\u56de\u5f52\u3001\u5411\u540e\u56de\u5f52\u548c\u9010\u6b65\u56de\u5f52\u7684\u533a\u522b
\u540e\u4e09\u8005\u90fd\u662f\u9009\u62e9\u53d8\u91cf\u7684\u65b9\u6cd5\u3002
\u5411\u524d\u56de\u5f52\uff1a\u6839\u636e\u81ea\u53d8\u91cf\u5bf9\u56e0\u53d8\u91cf\u7684\u8d21\u732e\u7387\uff0c\u9996\u5148\u9009\u62e9\u4e00\u4e2a\u8d21\u732e\u7387\u6700\u5927\u7684\u81ea\u53d8\u91cf\u8fdb\u5165\uff0c\u4e00\u6b21\u53ea\u52a0\u5165\u4e00\u4e2a\u8fdb\u5165\u6a21\u578b\u3002\u7136\u540e\uff0c\u518d\u9009\u62e9\u53e6\u4e00\u4e2a\u6700\u597d\u7684\u52a0\u5165\u6a21\u578b\uff0c\u76f4\u81f3\u9009\u62e9\u6240\u6709\u7b26\u5408\u6807\u51c6\u8005\u5168\u90e8\u8fdb\u5165\u56de\u5f52\u3002
\u5411\u540e\u56de\u5f52\uff1a\u5c06\u81ea\u53d8\u91cf\u4e00\u6b21\u7eb3\u5165\u56de\u5f52\uff0c\u7136\u540e\u6839\u636e\u6807\u51c6\u5220\u9664\u4e00\u4e2a\u6700\u4e0d\u663e\u8457\u8005\uff0c\u518d\u505a\u4e00\u6b21\u56de\u5f52\u5224\u65ad\u5176\u4f59\u53d8\u91cf\u7684\u53d6\u820d\uff0c\u76f4\u81f3\u4fdd\u7559\u8005\u90fd\u8fbe\u5230\u8981\u6c42\u3002
\u9010\u6b65\u56de\u5f52\u662f\u5411\u524d\u56de\u5f52\u6cd5\u548c\u5411\u540e\u56de\u5f52\u6cd5\u7684\u7ed3\u5408\u3002\u9996\u5148\u6309\u81ea\u53d8\u91cf\u5bf9\u56e0\u53d8\u91cf\u7684\u8d21\u732e\u7387\u8fdb\u884c\u6392\u5e8f\uff0c\u6309\u7167\u4ece\u5927\u5230\u5c0f\u7684\u987a\u5e8f\u9009\u62e9\u8fdb\u5165\u6a21\u578b\u7684\u53d8\u91cf\u3002\u6bcf\u5c06\u4e00\u4e2a\u53d8\u91cf\u52a0\u5165\u6a21\u578b\uff0c\u5c31\u8981\u5bf9\u6a21\u578b\u4e2d\u7684\u6bcf\u4e2a\u53d8\u91cf\u8fdb\u884c\u68c0\u9a8c\uff0c\u5254\u9664\u4e0d\u663e\u8457\u7684\u53d8\u91cf\uff0c\u7136\u540e\u518d\u5bf9\u7559\u5728\u6a21\u578b\u4e2d\u7684\u53d8\u91cf\u8fdb\u884c\u68c0\u9a8c\u3002\u76f4\u5230\u6ca1\u6709\u53d8\u91cf\u53ef\u4ee5\u7eb3\u5165\uff0c\u4e5f\u6ca1\u6709\u53d8\u91cf\u53ef\u4ee5\u5254\u9664\u4e3a\u6b62\u3002
\u5411\u524d\u56de\u5f52\u3001\u5411\u540e\u56de\u5f52\u548c\u9010\u6b65\u56de\u5f52\u90fd\u8981\u6309\u7167\u4e00\u5b9a\u5224\u65ad\u6807\u51c6\u6267\u884c\u3002\u5373\u5728\u5c06\u81ea\u53d8\u91cf\u52a0\u5165\u6216\u5220\u9664\u6a21\u578b\u65f6\uff0c\u8981\u8fdb\u884c\u504fF\u68c0\u9a8c\uff0c\u8ba1\u7b97\u516c\u5f0f\u4e3a\uff1a
(R2b-R2a)\uff0fM
F = \u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014
(1- R2b) \uff0fdferror
SPSS\u56de\u5f52\u6240\u8bbe\u5b9a\u7684\u9ed8\u8ba4\u6807\u51c6\u662f\u9009\u62e9\u8fdb\u5165\u8005\u65f6\u504fF\u68c0\u9a8c\u503c\u4e3a3.84\uff0c\u9009\u62e9\u5220\u9664\u8005\u65f6\u7684F\u68c0\u9a8c\u503c\u4e3a2.71\u3002
\u4ece\u4e0a\u9762\u53ef\u4ee5\u770b\u51fa\uff0c\u5206\u5c42\u56de\u5f52\u548c\u5404\u79cd\u9009\u62e9\u81ea\u53d8\u91cf\u7684\u65b9\u6cd5\uff0c\u5176\u5b9e\u90fd\u6d89\u53ca\u6a21\u578b\u4e4b\u95f4\u7684\u6bd4\u8f83\u95ee\u9898\uff0c\u800c\u4e14F\u68c0\u9a8c\u7684\u516c\u5f0f\u4e5f\u76f8\u7b49\uff0c\u8bf4\u660e\u5b83\u4eec\u62e5\u6709\u76f8\u540c\u7684\u7edf\u8ba1\u5b66\u57fa\u7840\u3002\u4f46\u662f\uff0c\u5b83\u4eec\u53c8\u662f\u4e0d\u540c\u8303\u7574\u7684\u6982\u5ff5\u3002\u5206\u5c42\u56de\u5f52\u662f\u5bf9\u4e8e\u6a21\u578b\u6bd4\u8f83\u800c\u8a00\u7684\uff0c\u800c\u4e0a\u9762\u4e09\u79cd\u65b9\u6cd5\u5219\u662f\u9488\u5bf9\u81ea\u53d8\u91cf\u800c\u8a00\u7684\u3002\u4e0a\u9762\u4e09\u79cd\u9009\u62e9\u81ea\u53d8\u91cf\u7684\u65b9\u6cd5\uff0c\u90fd\u662f\u7531\u8f6f\u4ef6\u6839\u636e\u8bbe\u5b9a\u6807\u51c6\u6765\u81ea\u52a8\u9009\u62e9\u8fdb\u5165\u6a21\u578b\u7684\u53d8\u91cf\u3002\u800c\u5206\u5c42\u56de\u5f52\u5219\u662f\u7531\u7814\u7a76\u8005\u6839\u636e\u7ecf\u9a8c\u548c\u7406\u8bba\u601d\u8003\u6765\u5c06\u81ea\u53d8\u91cf\u5206\u6210\u4e0d\u540c\u7684\u7ec4\uff08block\uff09\uff0c\u7136\u540e\u518d\u5b89\u6392\u6bcf\u4e00\u7ec4\u53d8\u91cf\u8fdb\u5165\u6a21\u578b\u7684\u987a\u5e8f\uff0c\u8fdb\u5165\u7684\u987a\u5e8f\u4e0d\u662f\u6839\u636e\u8d21\u732e\u7387\uff0c\u800c\u662f\u6839\u636e\u76f8\u5e94\u7684\u7406\u8bba\u5047\u8bbe\u3002\u800c\u4e14\uff0c\u7814\u7a76\u8005\u8fd8\u53ef\u4ee5\u4e3a\u4e0d\u540c\u7ec4\u7684\u81ea\u53d8\u91cf\u9009\u7528\u4e0d\u540c\u7684\u7eb3\u5165\u53d8\u91cf\u7684\u65b9\u6cd5\u3002
\u5206\u5c42\u56de\u5f52\u5728SPSS\u4e0a\u7684\u5b9e\u73b0
\u5728\u7ebf\u6027\u56de\u5f52\u4e3b\u5bf9\u8bdd\u6846\u4e2d\uff0c\u5728\u5b9a\u4e49\u5b8c\u4e00\u7ec4\u81ea\u53d8\u91cf\u540e\uff0c\u5728\u56e0\u53d8\u91cf\u4e0d\u53d8\u7684\u60c5\u51b5\u4e0b\uff0c\u5229\u7528block\u524d\u540e\u7684previous\u548cnext\u6309\u94ae\uff0c\u7ee7\u7eed\u5c06\u5176\u4ed6\u53d8\u91cf\u7ec4\u52a0\u5165\u6a21\u578b\u3002
分层回归其实是对两个或多个回归模型进行比较。我们可以根据两个模型所解释的变异量的差异来比较所建立的两个模型。一个模型解释了越多的变异，则它对数据的拟合就越好。假如在其他条件相等的情况下，一个模型比另一个模型解释了更多的变异，则这个模型是一个更好的模型。两个模型所解释的变异量之间的差异可以用统计显著性来估计和检验。
绛旓細鍒嗗眰鍥炲綊閫氬父鐢ㄤ簬涓粙浣滅敤鎴栬呰皟鑺備綔鐢ㄧ爺绌朵腑銆傚垎鏋愭椂閫氬父绗竴灞傛斁鍏ュ熀鏈釜浜轰俊鎭椤规垨鎺у埗鍙橀噺锛涚浜屽眰鏀惧叆鏍稿績鐮旂┒椤广備娇鐢⊿PSSAU鍦ㄧ嚎spss鍒嗘瀽锛岃緭鍑烘牸寮忓潎涓烘爣鍑嗘牸寮忥紝澶嶅埗绮樿创鍒皐ord鍗冲彲浣跨敤銆傚垎灞傚洖褰掑叾瀹炴槸瀵逛袱涓垨澶氫釜鍥炲綊妯″瀷杩涜姣旇緝銆傛垜浠彲浠ユ牴鎹袱涓ā鍨嬫墍瑙ｉ噴鐨勫彉寮傞噺鐨勫樊寮傛潵姣旇緝鎵寤虹珛鐨勪袱涓ā...
绛旓細鎵璋撳洖褰掑垎鏋愭硶锛屾槸鍦ㄦ帉鎻″ぇ閲忚瀵熸暟鎹殑鍩虹涓婏紝鍒╃敤鏁扮悊缁熻鏂规硶寤虹珛鍥犲彉閲忎笌鑷彉閲忎箣闂寸殑鍥炲綊鍏崇郴鍑芥暟琛ㄨ揪寮(绉板洖褰掓柟绋嬪紡)銆傚洖褰掑垎鏋愪腑锛屽綋鐮旂┒鐨勫洜鏋滃叧绯诲彧娑夊強鍥犲彉閲忓拰涓涓嚜鍙橀噺鏃讹紝鍙仛涓鍏冨洖褰掑垎鏋;褰撶爺绌剁殑鍥犳灉鍏崇郴娑夊強鍥犲彉閲忓拰涓や釜鎴栦袱涓互涓婅嚜鍙橀噺鏃讹紝鍙仛澶氬厓鍥炲綊鍒嗘瀽銆傛澶栵紝鍥炲綊鍒嗘瀽涓紝鍙堜緷鎹弿...
绛旓細1. 鍒嗗眰鍥炲綊鍒嗘瀽鏄竴绉嶆ā鍨嬫瘮杈冪殑鏂规硶锛屽畠閫氳繃姣旇緝涓嶅悓妯″瀷涓娴嬪彉閲忔墍瑙ｉ噴鐨勫彉寮傞噺鏉ヨ瘎浼板彉閲忕殑閲嶈鎬銆傚湪鍒嗗眰鍥炲綊涓紝鑷彉閲忔寜鐓ф煇绉嶉『搴忓垎鎵硅繘鍏ユā鍨嬶紝姣忎竴鎵硅嚜鍙橀噺閮藉皾璇曡В閲婂洜鍙橀噺鐨勫彉寮傦紝鑰屽悗缁壒娆＄殑鑷彉閲忎細灏濊瘯鍦ㄥ凡鏈夋ā鍨嬪熀纭涓婂鍔犻澶栫殑瑙ｉ噴鍔涖2. 涓庡垎灞傚洖褰掍笉鍚岋紝閫愭鍥炲綊鏄竴绉嶈嚜鍔ㄥ寲鐨勫彉閲...
绛旓細1銆佺洰鐨勶細鍒嗗眰鍥炲綊鐨勪富瑕佺洰鐨勬槸鎺㈢┒澶氫釜棰勬祴鍙橀噺瀵瑰洜鍙橀噺鐨勫奖鍝锛屼笖鎸夌収鐞嗚鎴栧疄闄呮儏鍐靛皢棰勬祴鍙橀噺鍒嗕负澶氫釜灞傛杩涜鍒嗘瀽銆傞愭鍥炲綊鐨勭洰鐨勬槸浠庝竴缁勭殑棰勬祴鍙橀噺涓夋嫨鍑烘渶浣崇殑瀛愰泦锛屼互寤虹珛涓涓緝绠娲佷笖鍏锋湁棰勬祴鑳藉姏鐨勬ā鍨嬨2銆佸彉閲忛夋嫨锛氬垎灞傚洖褰掑湪鍒嗘瀽杩囩▼涓紝棰勫厛灏嗛娴嬪彉閲忔寜鐓ф煇绉嶉昏緫鎴栫悊璁哄垎涓哄涓眰娆★紝鍚...
绛旓細閫愭鍥炲綊鏄竴绉嶇嚎鎬у洖褰掓ā鍨嬭嚜鍙橀噺閫夋嫨鏂规硶锛屽叾鍩烘湰鎬濇兂鏄皢鍙橀噺涓涓竴涓紩鍏ワ紝寮曞叆鐨勬潯浠舵槸鍏跺亸鍥炲綊骞虫柟鍜岀粡楠屾槸鏄捐憲鐨勩傚悓鏃讹紝姣忓紩鍏ヤ竴涓柊鍙橀噺鍚庯紝瀵瑰凡鍏ラ夊洖褰掓ā鍨嬬殑鑰佸彉閲忛愪釜杩涜妫楠岋紝灏嗙粡妫楠岃涓轰笉鏄捐憲鐨勫彉閲忓垹闄わ紝浠ヤ繚璇佹墍寰楄嚜鍙橀噺瀛愰泦涓瘡涓涓彉閲忛兘鏄樉钁楃殑銆傛杩囩▼缁忚繃鑻ュ共姝ョ洿鍒颁笉鑳藉啀寮曞叆鏂...
绛旓細鍒嗗眰鍥炲綊閫傚悎浜庡鐞嗕笉鍚岀兢浣撲箣闂寸殑宸紓锛屽彲灏嗘暟鎹垎鎴愬瓙闆嗗悗鏋勫缓涓嶅悓鐨勫洖褰掓ā鍨嬶紱鑰澶氬厓鍥炲綊鍒欓傜敤浜庝及璁″涓嚜鍙橀噺瀵瑰洜鍙橀噺鐨勫奖鍝嶃2銆佸弬鏁颁及璁℃柟寮忎笉鍚岋細鍒嗗眰鍥炲綊鍙傛暟浼拌鏂瑰紡鏄牴鎹笉鍚岀粍鍒殑鏁版嵁瀛愰泦寤虹珛鍗曠嫭鐨勫洖褰掓ā鍨嬶紝鍦ㄥ鍏冨洖褰掍腑锛屽弬鏁颁及璁℃柟寮忔槸姹傝В涓涓仈鍚堢殑鏂圭▼锛岃绠楁墍鏈夎嚜鍙橀噺鐨勫洖褰掔郴鏁般
绛旓細鍦⊿PSS涓繘琛澶氬厓闃跺眰鍥炲綊鍒嗘瀽鐨勬楠ゅ涓嬶細1. 棣栧厛锛岄夋嫨SPSS涓殑鍒嗗眰鍥炲綊鍔熻兘锛岄氬父鍙互閫氳繃鑿滃崟涓殑鈥滃垎鏋愨濋夐」鎵惧埌銆2. 灏嗛渶瑕佸垎鏋愮殑鍙橀噺鏀惧叆鍒嗘瀽椤逛腑锛孲PSS浼氳嚜鍔ㄥ鐞嗗叾浠栫浉鍏虫寚鏍囷紝鏃犻渶鎵嬪姩璁剧疆銆3. 瀹屾垚璁剧疆鍚庯紝SPSS浼氱敓鎴愬寘鍚爣鍑嗗寲鐨勭郴鏁般乼鍊笺丳鍊肩瓑淇℃伅鐨勭粺璁¤〃锛屼互鍙婃櫤鑳藉寲鐨勬枃瀛楀垎鏋愮粨鏋滐紝...
绛旓細1. 鍒嗗眰鍥炲綊鍒嗘瀽甯稿簲鐢ㄤ簬涓粙鏁堝簲鎴栬皟鑺傛晥搴旂殑鐮旂┒涓2. 鍦ㄨ繘琛屽垎鏋愭椂锛岄鍏堝皢鍩烘湰鐨勪釜浜轰俊鎭垨鎺у埗鍙橀噺鏀惧叆绗竴灞傘3. 鎺ョ潃锛屽皢鏍稿績鐨勭爺绌跺彉閲忔斁鍏ョ浜屽眰銆4. 浣跨敤SPSSAU鍦ㄧ嚎SPSS鍒嗘瀽宸ュ叿鏃讹紝杈撳嚭鐨勬牸寮忔槸鏍囧噯鍖栫殑锛屽彲浠ョ洿鎺ュ鍒跺苟绮樿创鍒癢ord涓娇鐢ㄣ
绛旓細1銆佽皟鑺備綔鐢ㄧ殑妫楠屽氨鏄垎灞傚鍏冨洖褰锛屽氨鏄仛鍑犳鍥炲綊鐨勬剰鎬濄傚叿浣撴楠わ細瀵硅嚜鍙橀噺鍜岃皟鑺傚彉閲忔爣鍑嗗寲锛屾瀯閫犱箻绉」锛屾妸鏍囧噯鍖栧悗鐨勮嚜鍙橀噺鍜岃皟鑺傚彉閲忕浉涔樸2銆佺涓娆″洖褰掞紝濡傛灉鏈夋帶鍒跺彉閲忥紝灏辨槸鍥犲彉閲忓鎺у埗鍙橀噺鍥炲綊涓涓嬶紝鏂圭▼鏄捐憲鍗冲彲锛屼笉闇瑕佺湅姣忎釜鎺у埗鍙橀噺鏄笉鏄樉钁楋紝涓昏鏄负浜嗗悗闈綋鐜版帶鍒朵綔鐢紝濡傛灉娌℃湁...
绛旓細鍙娇鐢╯pssau鐨鍒嗗眰鍥炲綊锛屾搷浣滅畝鍗曚袱姝ュ嚭缁撴灉銆傛搷浣滄楠わ細1銆侀夋嫨spssau鐨勫垎灞傚洖褰掋2銆佹斁鍏鍒嗘瀽椤癸紝鍏朵粬鎸囨爣椤瑰潎鑷姩鐢熸垚涓嶇敤璁剧疆銆傚悓鏃剁敓鎴愭爣鍑嗚〃鏍肩粨鏋滃強鏅鸿兘鏂囧瓧鍒嗘瀽锛屼笉浼氱粺璁″涔熷彲浠ョ湅鎳傘
