已知某城市有关 A 商品需求的统计资料如下:[img=1415x191]178bfa68ffae66b.png[/img]假设销售量 [tex=0.857x1.286]h9C4nePGcGllh55hxKIsUw==[/tex] 与该城市的居民人均收入 [tex=1.214x1.214]AKRJ+piA0nf7C/6/dimpFw==[/tex] 以及商品的单价服从线性关系，根据上面数据(1) 建立 [tex=0.857x1.286]h9C4nePGcGllh55hxKIsUw==[/tex] 对 [tex=2.643x1.214]g1eeTNblG8qvUFsjwsMATg==[/tex] 的二元线性回归方程;(2) 对回归方程的显著性进行检验 ([tex=3.786x1.0]j0DyOD2xW8hNkLP53FtTIA==[/tex]) ;(3) 对回归方程的系数进行显著性检验 ([tex=3.786x1.0]j0DyOD2xW8hNkLP53FtTIA==[/tex]) .

2022-06-10

已知某城市有关 A 商品需求的统计资料如下:[img=1415x191]178bfa68ffae66b.png[/img]假设销售量 [tex=0.857x1.286]h9C4nePGcGllh55hxKIsUw==[/tex] 与该城市的居民人均收入 [tex=1.214x1.214]AKRJ+piA0nf7C/6/dimpFw==[/tex] 以及商品的单价服从线性关系，根据上面数据(1) 建立 [tex=0.857x1.286]h9C4nePGcGllh55hxKIsUw==[/tex] 对 [tex=2.643x1.214]g1eeTNblG8qvUFsjwsMATg==[/tex] 的二元线性回归方程;(2) 对回归方程的显著性进行检验 ([tex=3.786x1.0]j0DyOD2xW8hNkLP53FtTIA==[/tex]) ;(3) 对回归方程的系数进行显著性检验 ([tex=3.786x1.0]j0DyOD2xW8hNkLP53FtTIA==[/tex]) .

答案：

解（1） 这是一个二元线性回归分析问题,回归模型为[tex=9.286x1.214]X2G6kD77tTypnkS/9Rnaxy0cLFlRGmr9wGHFofC17cv+viO7S94nC4PbmbI5j4zBZzUkbBmh3qqiggtHnFkM0Q==[/tex].[tex=22.214x4.643]WJjqTt+wsb5RrYXOGySYf+1hJAAfrE0IYy+Ny+81gqw7oklmlWAJjDthIESRhL98Hl1wySw80z50JCnOpOpMDZFBcwGc6Agh64N9idXQ0jav/Oux/cxXBpWXyefUoYyBSomPMrptnjbtTVhKEtL5Gg4qP1X0uV30/50fvVGJDqQmznyM/U0IopenFHpm4etHQl0bPOnn1HZHtYAkqLZNPhtDPd3574YI8p6m5Ih+FUzTJR3kha9N/OmMI2yyIFNlh3+AH3nUJvOsRQ4bAeQjo0am4fL7OEVHs6yYzvZ0F6nAr8bU/0aWAWSgBdGAp/c8a4jCxwOMXxQEbXLsOFKy2Ovej2oD7fN0EPpuNOPkZ2fGkRDqWFiCwvt3wmDlSblj[/tex],[br][/br][tex=20.857x3.5]XyzRmbzgoNDuTkIa0+tf/YOfJjR8vNPnC5ilSrclKFAQEDiAZfucU/GsAvL7iqbFNP828f5zMHxEVVGaH9H9ZphyvxOcA+2CjUOMktghWri+9ySC6HFRnJlDlmsUcxrAVHJ2XyHnJlO8H7PviUMATDsvmjYBEt+gmQBmHNN6qkcT8rFu3mKAifNiyospOKKzCDvYHs/u1ICWq04J8u18oJNMDlvRSVU8U1gf06R2eKZ0ok3136SS/I6/aPoD4BFr[/tex],[br][/br][tex=22.857x3.929]cDjW/IK4RgRaRuO86g4KR3dUAmn18xJoUClN5v7MWqXb1NqUBBsc/Rwc0o9J0OUyRKtNxso4DTDpIKqG21MziEJC1VuvgYvcz8HR5rZag+K96ewuL/LziUdsRWx2hzqqrFTW98iLjgMKfQ5tx0hvjkkZfqgSq1eHAoZI2sRjTk48Eef0L7j83TrMAJ79q8KWsnj4ZmTZ0cMzeV7piuwHPbGgcmW4/HtZds6uqlOg8DU=[/tex],[tex=27.786x9.143]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[/tex],[br][/br]得回归方程[p=align:center][tex=21.214x1.571]2HKmodrSCm3JeN2YR3l9ug3/zXtpdhNLhv3LCPwRfp9n8IM83LgTzJTo4LyJ315A7gOlEsLoaepr9+/Tkq6X0wF8eZ2BS55TvT7gpyvMV6x6FdcTQiMLYaN18uV3Kjggq9+Bs9PrRk1XQSZsPrP7Eg==[/tex] ;（2）回归方程的显著性检验,即检验假设[p=align:center][tex=21.0x1.286]+C6l5R8e/8qdVkS2w+LMfNFaFpeDr8NSB8cEPubpgdm5bYWlLQReTcojranfhq6Oykrkhi2pSp86QlRI2Q7EcuwQwOF1UKi+xqp9J49cluZAlNRExjOVarpOcKiAF7Wf0dcHLqrPDozmOg+7ZHflV0M+Jx00mE/dZx3oVNweX7k=[/tex] ,利用方差分析,有[tex=28.357x2.714]xVHev241iBeGlMB8h7ETnMmX4xSRV6TfLihPM9M3l9o6HJCAseci6UCltCTIq0bnoPQDXXqPf3kvli0VpjDCsgmbz6frnj7K7Bhbku7WmlArzc3mP83B56oZGwschlJW06cOnE4f+XjxjjKPigVczIR3Si7mEUZomKGGV/9qmiE=[/tex],[tex=25.214x5.786]hru8TJ2x1kla7th1V1rijRXTCd+eUYOEsH3hFyqdbErdJF9mbCLMUfeQfHr+D9X4YoC6GW5wyBNRfgAj2uuB3aUbfG+0nfZWhj/E0RuzJf4GdPZbJEkeD96aau8E/JV+SjgB1Vs/mXzLFaiNs+tEERNmavilcbCP9Leh+bSv//9MS38+cDOvUycdOzCqLEYEkZNuB8Qw0cZMd+1EneezCKxdAjMQ73qprJrUFXa8kwgSEBtsCTGcU/l3PfLC1pU/GCmXIaA/54TG/laXtIqTN4W0vrm558GsX5ZNSMGh71c=[/tex][tex=12.643x1.286]LeIig5JXhsq2xFbhUhhG7Eej5F6pCI9Aq/60rUqigCM=[/tex] .方差分析表为[img=1426x230]178bfa80b8ab292.png[/img]由于  [tex=11.714x1.357]0Tc976fBspBlkIGf4LHhpnBC4d51CLunhKp4hKv2ZhM=[/tex] , 故拒绝  [tex=1.214x1.214]CjLrZFKGkKWOR21hfDDU9Q==[/tex] , 即认为回归方程是显著的;（3）需要分别检验假设[tex=12.714x1.286]b6/OGpLsB7V1kbnFEjb3iN+nNuiYNg+kcRzW/vL+iOkMbE7MKQ0xP/fwBZaLPwvgFjRzxzKKtg3Y8VC8HDaeEK5zw6izSv3UBp1IZSIdOJY=[/tex] ; [tex=12.714x1.286]Yxgz7CMCfMGulDRt2FzL0g7DpmYMxlHAx7JpgxnVPYQvL4w+IcogqMFMGEbyr+RAyPau3bI82Krd8jJ6lT9Gf65WUqfoezp0Cj1YaF96c54=[/tex] ,[tex=26.714x2.714]Ia+2PM88BNYwdvPJiXHTidG7ib9Z3S4FdV7eHYqZ0GHFF27hZNhkRtdnhidc5vobBJK3qa4pDWgSHtZ4yDPRNEQlutaymqgOqmpjDZSJtA2Lehc997kayDvdohyyY0P8hDUBN9YyKU3bnMcHW1R+F7lR0A4R60gLvDaWKTXFryAXl1RWJu/abFaRqvob9kEA[/tex],[tex=19.357x5.714]OtkWnJD3mXM6jcHeP48tnmocoux8yAOJJItvbgvWj7w6WyTC1rdy3LlpMHqNcbhrQ176yOhE/Gp7sjUxmREo+Amy6bxADs49lnKUr3D0wfBHIAnUFdgwiT0TtXQJFqyfVgHN8g1erkCKm62H117Sgm2N2viU/Aw9HF5pSRwxZ6xh1sXtz+T6L9324QwHqOzhs2pL4Q0T2BQt8s7NBQejDKJF04Pv6i0XTTdSKgbEm0g/AiW1pfUhRyLUclQYMUIN[/tex] ,[tex=26.286x2.714]+4ZzbiqqxPZiH3GaympKJtvOqksPDIUy93VZO4EK5JZ9O3acp4TeKV0/Bix1C1+ca4mJub2yCUkoDFsbug/n62DRgez6BsAgIeOm+y65rfZL7ABoar4esDMLDtVdEIlg8HCZummXlu+0C9rt5zFJNhbijNu324QeIIoCQfpUA4aqRS7hNnu1xdsIupqmBhkl[/tex],[tex=11.429x2.786]HDzLq5tuz8K7svHqIuuaaDAxXQD82tJ4YGri7kZ/A9j7eany4lTYYloWewGxDTZOYgfAps2KPCLeB5kFM9yG4r11o0pJFtf578q7PFxbZJhVihrAK51eAJxOCGuCBaQj[/tex], [tex=26.0x2.786]Tsod4E9XvonkZ0lu7LCfjxOkOQT0rBLgUDJYRua6YUD3BtIsni38NUBDl2NPE0lb4aLmvzypMS16b+3rgOW0mXW53Xw4U+jAuTtONbyNgJLbXrlnKp5e1DputpbhSv2FyX49gTQOWMmLGAiCv1+SoRnha72856BjpXz30OCbLb1XXhGvnORTKatAxBcGqLB/d8rDhuP7BCrTuMNEPHL1ig/+6A6Wn8oC4JkoZKpPirzIMZJ7CGCS8Q+Tt5EVkuB5[/tex],[tex=22.786x3.071]Gjmjwoq1qoMpFaMTLzFy7BhG/Gg6d5V7pD+Zpi+XhT8yFho5Jp4HQc2BRR2PNBhk7z2za9WX4ORgnsxWX/o4EGEesTt5rvMM8SJMdBbH/2U1+rNEYcHsvoYR6dpje1B/EgK236AGq3lLZYObu4/Ryh/dwJqnwmmdW1q2hmG/vFCntxapIsZmuFPgoZkG3gvI[/tex] ,[tex=24.214x3.071]iHNK4kG7loP8Hf7kfXXthA6onb4Nl1RBTBGdYU6wuD8ASLwFhf8l1AhaVssh7+rzE9qSjlMqlbu1FWrZc50ZDX2ZHqLRWda5C3idb4iqWQphnVK2ZlN2UcPkhnpAeU29NF6qI79wLACD01nGmh4ZREZemY2MsGC69mV8g1Jlo1I=[/tex],由于  [tex=25.571x1.357]o6wWkeGmuJQrsB/K6oB7odrtp5B5xzgg/AcrroX64LPEpUlr2w/VigmCxyafLIOCeBIZ8PFVtpdyYMCal9NKM5JtL0ADK/Lg17xVD8XBOvIlgR++XDls/qjdckovRBEa[/tex] , 故拒绝  [tex=3.571x1.214]/XmCbNrxsfAvklxM8+jPDw==[/tex], 即认为居民收入以及商品的单价均对商品的销售量有显著影响.

举一反三

内容

0
在某个地区随机抽取 9 个家庭,调查得到每个家庭每月人均收入与食品消费支出的数据如下表所示(单位:元):[img=1425x173]178bfc82cd37a01.png[/img]根据上面数据,试求:(1) 人均收入与食品消费支出的相关系数;(2) 建立食品支出 [tex=0.857x1.286]h9C4nePGcGllh55hxKIsUw==[/tex] 对人均收入 [tex=0.571x0.786]c5VsltFnl9nO0qB/vNKOWA==[/tex] 的一元线性回归模型. 并对回归模型进行显著性检验.
1
设[tex=3.643x1.5]CinLUzRWWE6wPkbL8iqt3LoTXotKCKQQAoUOnK9efwuPG4oZQ/RVUn0SwZDsIrgE[/tex]是由变量[tex=2.429x1.357]KpZxGfUsW9d3kaL7HnjeRQ==[/tex]的一组样本观测值 [tex=2.643x1.357]X5TPzVLq6Sjb68b/DlOgURAmIsKkzAhTH3FbMC91Sp4=[/tex][tex=6.429x1.357]AuButhAmDWb+DHc8lMZbICjdTmq85yh+m7vfObPXtGk=[/tex]所求得的经验回归方程，则[br][/br][br][/br] 未知类型：{'options': ['[tex=0.857x1.286]h9C4nePGcGllh55hxKIsUw==[/tex]是[tex=0.571x0.786]ZKO2xs0EgSemzoH7MSmYTA==[/tex]的线性函数;[br][/br][br][/br]', '[tex=0.857x1.286]h9C4nePGcGllh55hxKIsUw==[/tex]与[tex=0.571x0.786]ZKO2xs0EgSemzoH7MSmYTA==[/tex]之间具有近似的线性关系;[br][/br][br][/br]', '若该方程通过关于回归系数的显著性检验，则可断定[tex=0.857x1.286]h9C4nePGcGllh55hxKIsUw==[/tex]是[tex=0.571x0.786]ZKO2xs0EgSemzoH7MSmYTA==[/tex]的线代函数;[br][/br][br][/br]', '若该方程通过关于回归系数的显著性检验，则可认为[tex=0.857x1.286]h9C4nePGcGllh55hxKIsUw==[/tex]与[tex=0.571x0.786]ZKO2xs0EgSemzoH7MSmYTA==[/tex]具有线性相关关系'], 'type': 102}
2
某厂销售收入 [tex=0.929x1.286]uswT/CEcOIwMpCvTz/zeaA==[/tex] 与利润 [tex=0.857x1.286]h9C4nePGcGllh55hxKIsUw==[/tex] 的统计资料如下表7-22所示：[br][/br][img=865x276]17f98038ddab18b.png[/img]（1）问 [tex=0.929x1.286]uswT/CEcOIwMpCvTz/zeaA==[/tex] 与 [tex=0.857x1.286]h9C4nePGcGllh55hxKIsUw==[/tex] 是否有明显的线性关系？简单说明理由。[br][/br]（2）若 [tex=0.929x1.286]uswT/CEcOIwMpCvTz/zeaA==[/tex] 与 [tex=0.857x1.286]h9C4nePGcGllh55hxKIsUw==[/tex] 有线性关系，试求出 [tex=0.857x1.286]h9C4nePGcGllh55hxKIsUw==[/tex] 关于 [tex=0.929x1.286]uswT/CEcOIwMpCvTz/zeaA==[/tex] 的线性回归方程。[br][/br]（3）若销售收入为480万元，利润总额平均值的预测值为多少？
3
下表给出了某班12名同学两次考试的成绩。要求：(1)计算两次考试成绩(X,Y)的相关(2)求Y对X的线性回归方程;（3）对所求方程进行方差分析，以检验其显著性提示: [tex=32.643x1.286]I/NcS0LDveLL2lm9KWY5LD58OUbW3mOKab/gXVs2biQhukfjqQyMsYbqdVyHNSWU+KBYz10rIPPQhNoxSo15XjYyflE4OL/kQH8ndOyWBWBybmZzuzE9E+2AwiLjTgev[/tex][img=1004x134]17cc057c9c476c6.png[/img]
4
表4-4是某种商品的需求量Y,价格[tex=1.214x1.214]AKRJ+piA0nf7C/6/dimpFw==[/tex]以及消费者收入[tex=1.214x1.214]mzDCcy67Z8VvjJDKwZ/vAA==[/tex]的统计资料。[img=622x135]17b115b986d1a78.png[/img] 检验[tex=1.214x1.214]AKRJ+piA0nf7C/6/dimpFw==[/tex]和[tex=1.214x1.214]mzDCcy67Z8VvjJDKwZ/vAA==[/tex]是否存在严重的多重共线性?