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1、 例3-7在某项实验中，测得变量y与因素x数据如表1所示。试建立适当的y与因素x的回归方程（ ）。表3-14 例3-7实测数据x23457810111415161819y106.42108.2109.58109.5110109.93110.49110.59110.6110.9110.76111111.2解：绘制散点图，如图1所示：图1从图1中可看出，以下三种曲线方程的曲线图都与散点图接近，因此都可以作为曲线回归的选择对象。（1）.（2）.（3）.现对方案1和方案2方案3进行求解分析，通过对S2残作比较，S2残小这则回归方程交优1.方案1选取曲线回归（1）进行求解。令，应用EXCEL进行相应解决
2、算得数据，列入表1。表1 方案1数据解决计算xx=xyx-xyi-y(x-x)(yi-y)21.106.42-1.-3.5.31.108.2-1.-1.2.42109.58-1.-0.0.52.109.5-0.-0.0.72.110-0.0.-0.82.109.93-0.-0.0.103.16227766110.490.0.0.113.31662479110.590.0.0.143.110.60.699227110.0.153.110.90.0.0.164110.760.0.0.184.1111.202310411.1.194.111.21.1.1.39.55159361429.1713.93
3、894078平均3.109.9362平方和132157138.711.6670341421.2105076944.12800113由表2得： 由此得： 故所求的回归方程为： 进行变量还原得回归方程： 检查假设H01：. 对给定的，查F(1,11)表（附表5）得临界值。由于F，检查效果显著，所以拒绝H01，即回归方程故意义。2.方案2表2 方案2数据解决计算xx=lgxYx-xyi-y(x-x)(yi-y)20.301030106.420230-0.616595-3.5162002.16807130.477121108.202300-0.440504-1.7362000.76480340.602
4、060109.580000-0.315565-0.3562000.11240450.698970109.500000-0.218655-0.4362000.09537770.845098110.000000-0.0725270.063800-0.00462780.903090109.930000-0.014535-0.0062000.000090101.000000110.4900000.0823750.5538000.045619111.041393110.5900000.1237680.6538000.080919141.146128110.6000000.2285030.6638000.
5、151680151.176091110.9000000.2584660.9638000.249110161.204120110.7600000.2864950.8238000.236015181.255273111.0000000.3376481.0638000.359189191.278754111.2023000.3611291.2638000.456394总和11.9291271429.170000平均0.917625109.936154平方和1.19471721.21.5104.715045由此得：故所求回归方程：进行变量还原得回归方程：检查假设： 对给定的=0.01，查F(1，11)
6、表得到临界值=9.65.由于F,检查效果显著，所以拒绝,即回归方程故意义。3.方案3选取曲线回归（3）求解。令，应用EXCEL可算的数据，列入表3。表3 方案3数据解决计算xx=xyx-xyi-y(x-x)(yi-y)20.5106.420.-3.-1.30.108.20.-1.-0.40.25109.580.-0.-0.50.2109.50.-0.-0.70.110-0.0.-0.000951580.125109.93-0.-0.0.100.1110.49-0.0.-0.110.110.59-0.0.-0.140.110.6-0.0.-0.150.110.9-0.0.-0.160.06251
7、10.76-0.0.-0.180.111-0.1.-0.190.111.2-0.105128571.-0.2.050881941429.170.21.21050769-2.平均0.109.93615平方和0.157138.66由表3得由此得：故所求的回归方程为：进行变量还原得回归方程：检查假设H01：.对给定的，查F(1,11)表（附表5）得临界值。由于F，检查效果显著，所以拒绝H01，即回归方程故意义。表4方案回归方程F14.557740.191522.602278.660530.5525411.2905由表4，方案3的残差平方和是最小的，因而其回归方程是最优的，拟合效果是最佳的，方案2次之
8、，方案1最差。第三章课后题5、研究平炉炼钢的效率y与出钢量（）和FeO（）的关系，测得数据如下：x1115.396.556.9101.0102.987.9101.4109.8103.4x214.214.614.914.918.213.213.520.013.0y83.578.073.091.483.482.084.080.088.0x1110.680.393.088.088.0108.989.5104.4101.9x215.312.914.718.118.115.418.313.812.2y86.581.088.685.785.781.979.189.980.6（1）建立y关于，的线性回归方程
9、（2）检查所建方程是否故意义（=0.10）（3）检查，是否对y有显著影响（=0.10）（4）假如有对y影响不显著的变量，将其去掉再建立一元回归方程 表 1数据预解决计算1115.314.283.513294.09201.641637.269627.551185.76972.25296.514.6789312.25213.161408.975271138.86084356.914.9733237.61222.01847.814153.71087.75329410114.991.410201222.011504.99231.41361.868353.965102.918.283.410588.41
10、331.241872.788581.861517.886955.56687.913.2827726.41174.241160.287207.81082.467247101.413.58410281.96182.251368.98517.6113470568109.8208012056.0440021968784160064009103.4138810691.561691344.29099.21144774410110.615.386.512232.36234.091692.189566.91323.457482.251180.312.9816448.09166.411035.876504.31
11、044.96561129314.788.68649216.091367.18239.81302.427849.96138816.481.57744268.961443.271721336.66642.25148818.185.77744327.611592.87541.61551.177344.4915108.915.481.911859.21237.161677.068918.911261.266707.611689.518.379.18010.25334.891637.857079.451447.536256.8117104.413.889.910899.36190.441440.729385.561240.628082.0118101.912.280.610383.61148.841243.188213.14983.326496.36和1739.7273.61498.1171359.214240.0426470.99145351.7722743.61125041.51平均96.6515.283.23(1)设由表1得
