![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97ea8f47d8d8d9e1832d52b1c7425450.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4de122ae929b1acaff321dec137622ed.png)
投入额![]() | 2 | 3 | 4 | 5 | 6 | 8 | 9 | 11 |
年收入的附加额![]() | 3.6 | 4.1 | 4.8 | 5.4 | 6.2 | 7.5 | 7.9 | 9.1 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5b4c2f6499be84fd0cfed2bc9307caa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0c4e4e53572984b7d82ad69170bd996.png)
(2)求年收入的附加额
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
参考数据:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57e9cfe60d293737d8f7e5f3b3fa8d9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/807914fddf185f78bfd44340d2e36e36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de001aa106d2c4fa78e0cc82f6b9a2f9.png)
参考公式:在经验回归方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8c732930763d04dd85c1ebe4e708a4d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81ec30e9316c79d956b7c9a483a91632.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d41a9428546796a85f4a4ca69103e08.png)
日期t | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
销售量 | 1.9 | 1.98 | 2.2 | 2.36 | 2.43 | 2.59 | 2.68 | 2.76 | 2.7 | 0.4 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c92127c5138513f69b02d2ba9e1e265.png)
(1)因为优惠券购买火爆,App平台在第10天时系统出现异常,导致当天顾客购买优惠券数量大幅减少,已知销售量y和日期t呈线性关系,现剔除第10天数据,求y关于t的经验回归方程
![](https://img.xkw.com/dksih/QBM/2024/5/26/3505219411517440/3505377059332096/STEM/e3455f6a3a9e4066996d54e0c0a52927.png?resizew=10)
![](https://img.xkw.com/dksih/QBM/2024/5/26/3505219411517440/3505377059332096/STEM/a9629839a0654872852cd4760f3249ee.png?resizew=10)
(2)若购买优惠券的顾客选择A套餐的概率为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56d266a04f3dc7483eddbc26c5e487db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b2a698891d42c70b597f0da4f215f09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf83e20035c3afd6d26ebfd53d768a70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf83e20035c3afd6d26ebfd53d768a70.png)
(3)记(2)中所得概率
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf83e20035c3afd6d26ebfd53d768a70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59a42dac471af0c4f53da171597135ff.png)
①求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf83e20035c3afd6d26ebfd53d768a70.png)
②数列收敛的定义:已知数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/711c92626a97e6b778b3aa86e663ee97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4ccd4537f4dee2050ade38b972eb9b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/985dc26a89252b2e8dea815c529a2ffb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/512e8bacfff15253901cd216a1e42013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c5a325806df1a1c3e7ce609fe99085f.png)
参考公式:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86b12fb0fba9df3f7a1796082ce50ae7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9efa9fbcfb9595e2f031aa691db4564b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9efa9fbcfb9595e2f031aa691db4564b.png)
父亲身高 | 160 | 170 | 175 | 185 | 190 |
儿子身高 | 170 | 174 | 175 | 180 | 186 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b83987177ba2aa2f77049e0063bb9d4d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c4ebf938c63e73d9129dfe70b4d7324.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c7aabfb8f9e872a90aa5d6af686c534.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c8e3fd912e1508bbd2b678865113676.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2dbdbf02e0dd324daba7488c3e3bf31.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a58291bd91befe1061530246da983727.png)
(1)根据表中数据,求出y关于x的线性回归方程,并利用回归直线方程分别确定儿子比父亲高和儿子比父亲矮的条件,由此可得到怎样的遗传规律?
(2)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3451307680d95f67c08f68888077b44e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85719767bc8b764fcde16731c1ea45c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4de122ae929b1acaff321dec137622ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8bc4b176d13f7b6a30b55d726159f1b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b960966c18a5671cc3da5a72c43c682b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef046c85a536174bec951a53d9f60b33.png)
步频![]() ![]() | 0.28 | 0.29 | 0.30 | 0.31 | 0.32 |
步长![]() ![]() | 90 | 95 | 99 | 103 | 117 |
(1)根据表中数据,得到步频和步长近似为线性相关关系,求出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f748a2fff2648c65b80355004b13bbc.png)
(2)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29864b1dacf2cb0869956015ba411cb4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4de122ae929b1acaff321dec137622ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6bc610e71797c5c04da4ee7abf0049a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b960966c18a5671cc3da5a72c43c682b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be10fc01b8643cb07cbf6eca54b90a17.png)
参考数据:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8042b2d43a2cc3b370301b4f095abf19.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee109fb3c1f6e7f440bdfb05677da2eb.png)
参考公式:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07c226c805bf76bc0ad35c45806feb73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a58291bd91befe1061530246da983727.png)
年份序号x | 1 | 2 | 3 | 4 | 5 |
招生人数y/千人 | 0.8 | 1 | 1.3 | 1.7 | 2.2 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
参考数据:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/037b4302e206bd9c0e02d17b389fff0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b225743c8913295d0a4bca108fa1692.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a2d9ee7f57bc0f603c066ca9dd0b88c.png)
参考公式:相关系数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3ae9421919944d997c304d7711b4b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bcecfbd0e0b460f4e4ff6f654bd4608.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2dbdbf02e0dd324daba7488c3e3bf31.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a58291bd91befe1061530246da983727.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
天数![]() | 1 | 2 | 3 | 4 | 5 | 6 |
繁殖个数![]() | 6 | 12 | 25 | 49 | 95 | 190 |
![](https://img.xkw.com/dksih/QBM/editorImg/2023/9/7/4bacce99-5592-4ee8-bcc4-a60b71687351.png?resizew=149)
(1)在图中作出繁殖个数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce3a7d89965c094792f87594bd68afd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bda9896c593ee0a75ac2db7ddd6ee7d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31091823724baad3b893de6214ed243d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0de04adc20200028d604f7bf08582aa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb2de2538d41d5fbc30744fc8c0e4fe3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(2)对于非线性回归方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31091823724baad3b893de6214ed243d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0de04adc20200028d604f7bf08582aa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb2de2538d41d5fbc30744fc8c0e4fe3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54d28162b2a8309f0f7f193e733be414.png)
![]() | ![]() | ![]() | ![]() | ![]() | ![]() |
3.50 | 62.83 | 3.53 | 17.50 | 596.57 | 12.09 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31091823724baad3b893de6214ed243d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54d28162b2a8309f0f7f193e733be414.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b73c7432ba7e04d20bda1363ffa48bc.png)
(ⅱ)根据(ⅰ)的判断结果及表中数据,建立
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
附:对于一组数据
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69f22ea836f2025901725da985790579.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f95523e41adf5e135049d4097a07f189.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c5a0bfe22905260f047609a4180c21e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2fa6156631df6d7b5decf1132b8bdae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea67e676cfb928a4a995347b7d636058.png)
学生编号i | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
数学成绩![]() | 100 | 99 | 96 | 93 | 90 | 88 | 85 | 83 | 80 | 77 |
知识竞赛成绩![]() | 290 | 160 | 220 | 200 | 65 | 70 | 90 | 100 | 60 | 270 |
学生编号i | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 |
数学成绩![]() | 75 | 74 | 72 | 70 | 68 | 66 | 60 | 50 | 39 | 35 |
知识竞赛成绩![]() | 45 | 35 | 40 | 50 | 25 | 30 | 20 | 15 | 10 | 5 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72b5ffe569b3e2420e3bf0296ad15bf0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5785a4a50d8f52dae2b1a48fd03b302.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74cb73d6051e212bf553e65bea5a5684.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/871f222f2a3d1c96fcddf2a1b6e4e3e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/803493ad38a5211a5ccecb6c391ee70a.png)
(1)求这组学生的数学成绩和知识竞赛成绩的样本相关系数(精确到0.01);
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0d39c74f1102624ea5c6a20f7af104d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4bf6e9fcc182f569dc271a9a3deaba0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0384c377c13f28bf4b64d21512d7dacb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/953bedb069a949be816d89860b5199ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97ea8f47d8d8d9e1832d52b1c7425450.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00b375f8853b2aeb89cfaabdd5967c40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a20318c91376fd142453b3a7542c11c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4de122ae929b1acaff321dec137622ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6cf0b27ec1aea779850dbd3e675b273.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e9bb415ebf91617fe843b83d0a140ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2bfc4f64445bf91ead50f0c16daf755e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/171102a883b22fe6ca578efc8926f5b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
(i)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91a78fb7eea08cece87f5212d6e98ee4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2bfc4f64445bf91ead50f0c16daf755e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d513d82f90a06a99a98f476c244627d9.png)
(ii)用(i)的公式求得这组学生的数学成绩和知识竞赛成绩的“斯皮尔曼相关系数”约为0.91,简述“斯皮尔曼相关系数”在分析线性相关性时的优势.
注:参考公式与参考数据.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5019f565326c6fec3a2494e5955a5bec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb6bf90bda94d1344bb8d843a38f716a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/584b6e1f20a8dc940900170b4dbcba48.png)
航空公司编号 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
航班正点率 | 82 | 77 | 77 | 76 | 74 | 73 | 71 | 70 | 91 | 69 |
顾客投诉次数 | 21 | 58 | 79 | 68 | 74 | 93 | 72 | 122 | 18 | 125 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4964d514cdc05bd3b9612252b18b078.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b320260d534078159e2ad0e6ec4c721.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f868b1388c63f1f92de9c2cacb29bcb0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0b30c8131422333ed6ca962ad120a6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/548d415a6ba466c151502d990f2314e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/260568dde210f508dfb43e918242dc42.png)
(1)(i)证明:样本相关系数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06d077f92c1d085e5eedb917a8495ae1.png)
(ii)根据以上数据计算样本相关系数(结果保留2位小数),并由此推断顾客投诉次数与航班正点率之间的线性相关程度(若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f92462aa789e1632c8adcb9b54b7eebb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/864dee00905770e81b79ce42940d45d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e286f46523526bb1f3615b94ba5b746.png)
(2)用一元线性回归模型对上表中的样本数据进行拟合,得到顾客投诉次数关于航班正点率的经验回归方程为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64ac003c529f7a5b502112db662d3d04.png)
参考公式:样本相关系数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3453187f4932911673923e983d5fb10d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc3d84932df1b851b147b5fb3c4fea9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15a9926a68459af801f8ac7c080f80f2.png)
学生编号 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
数学成绩 | 100 | 99 | 96 | 93 | 90 | 88 | 85 | 83 | 80 | 77 |
知识竞赛成绩 | 290 | 160 | 220 | 200 | 65 | 70 | 90 | 100 | 60 | 270 |
学生编号 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 |
数学成绩 | 75 | 74 | 72 | 70 | 68 | 66 | 60 | 50 | 39 | 35 |
知识竞赛成绩 | 45 | 35 | 40 | 50 | 25 | 30 | 20 | 15 | 10 | 5 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f75c485cb2e79a663ab6ae3c733e3eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fdb0cf43da8f127ee78ba8354d1aa406.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bebaf6f0f22ffeda6432bfff3fe05a24.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8baa19bac5cebbab3ef252df9e519f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54738cf1ba98c740b3c7a07742a1f1f7.png)
(1)求这组学生的数学成绩和知识竞赛成绩的样本相关系数(精确到
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e2c4d12b3a705daab723ab243b6cc88.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0d39c74f1102624ea5c6a20f7af104d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19e3a9fffe86189933d0a9546208e8a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e40520d7c3e251f7471f890288c1b2bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a24c21d2f1b48a3252bde2653a0a95b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97ea8f47d8d8d9e1832d52b1c7425450.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcc4d8ff5faa2cee8c2e2dd576b7cb14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a20318c91376fd142453b3a7542c11c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4de122ae929b1acaff321dec137622ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca3db80b84166d02161b3dc5348f7e9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e9bb415ebf91617fe843b83d0a140ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/228668272e982853c944c99d45d121c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/171102a883b22fe6ca578efc8926f5b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
(i)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91a78fb7eea08cece87f5212d6e98ee4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/228668272e982853c944c99d45d121c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d513d82f90a06a99a98f476c244627d9.png)
(ii)用(i)的公式求这组学生的数学成绩和知识竞赛成绩的“斯皮尔曼相关系数”(精确到
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e2c4d12b3a705daab723ab243b6cc88.png)
(3)比较(1)和(2)(ii)的计算结果,简述“斯皮尔曼相关系数”在分析线性相关性时的优势.
注:参考公式与参考数据.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3ae9421919944d997c304d7711b4b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35466cb215d0eb17691675f616836b05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/584b6e1f20a8dc940900170b4dbcba48.png)
10 . 为了研究某种细菌随天数x变化的繁殖个数y,收集数据如下:
天数x | 1 | 2 | 3 | 4 | 5 | 6 |
繁殖个数y | 6 | 12 | 25 | 49 | 95 | 190 |
(1)在图中作出繁殖个数y关于天数x变化的散点图,并由散点图判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33b447ac3d1a965572c31b6e4c18d4b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b96969c5c96977de135616a637ddc52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7936359df4c926b72b48c6fdae55f12d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b76f79be89b8c6227b68eded6b675546.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ec26e45ae36c71ee9761a05e734dde1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b707f7a60da910e1dae29c79dff3300.png)
(2)对于非线性回归方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b96969c5c96977de135616a637ddc52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7936359df4c926b72b48c6fdae55f12d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b76f79be89b8c6227b68eded6b675546.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ec26e45ae36c71ee9761a05e734dde1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b707f7a60da910e1dae29c79dff3300.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54d28162b2a8309f0f7f193e733be414.png)
3.50 | 62.83 | 3.53 | 17.50 | 596.57 | 12.09 |
①证明:“对于,令
,可以得到繁殖个数的对数z关于天数x具有
,β,α为常数)”;
②根据(1)的判断结果及表中数据,建立y关于x的回归方程(系数保留2位小数).
附:对于一组数据,
,…,
,其回归直线方程
的斜率和截距的最小二乘估计分别为
,
.