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1、第十一章 多元回归及复相关分析11.1 嗜酸乳杆菌（Lactobacillus acidophilus Lakcid） 是存在于肠道中的一种重要益生菌，为研究肠道中的条件对该菌生存的影响，设计了在体外不同的胆汁盐浓度和不同时间该菌的存活数（活菌数/mL），结果如下表59：时间/h胆汁盐/（g kg-1）123417.201081.041091.761092.041096.401068.401062.621031.7410321.641091.921099.601087.401081.221079.201062.091031.8910331.301091.421093.461086.001082
2、.261062.041061.861031.8210349.801087.801081.021083.821081.301061.261061.321031.22103以该菌的存活数为因变量，胆汁盐浓度和时间为自变量，求二元回归方程并检验偏回归系数的显著性。答：程序和结果如下：options linesize=76 nodate;data mulreg; infile e:dataer11-1e.dat; input num time bile ;run;proc reg; model num=time bile;run; The SAS System The REG Procedure Mo
3、del: MODEL1 Dependent Variable: num Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr F Model 2 9.070013E18 4.535006E18 27.66 |t|Intercept 1 2020493645 237390215 8.51 .0001time 1 -144947822 64019380 -2.26 0.0312bile 1 -453586204 64019380 -7.09 .0001由以上结果得出回归方程：其中：X1为时间，X2为胆汁盐浓度。从偏
4、回归系数的t检验结果可以得知，时间在0.05水平上显著，而胆汁盐浓度的显著性概率P F Model 2 0.00023670 0.00011835 1553.36 |t| Intercept 1 -0.03651 0.00484 -7.54 0.0001 h 1 0.00031062 0.00004217 7.37 0.0002 w 1 0.00072984 0.00004228 17.26 .0001由参数估计列可以得到回归方程：其中X1为身高，X2为体重，身高和体重的偏回归系数都极显著。11.3 社鼠头骨若干特征的度量值与年龄存在相关性，下表列出了40只社鼠的鉴定年龄（a）和头骨8个特征的
5、度量值(mm)78：序号鉴定年龄YX1X2X3X4X5X6X7X81334.6033.6231.2616.105.448.746.126.742334.5033.4431.6815.924.829.005.826.483437.3636.3634.2817.465.489.966.086.724436.9435.8034.1017.145.289.805.466.625538.0037.7235.7417.465.149.925.846.686538.3037.4435.6417.085.1410.265.726.907539.7239.1836.7217.845.6010.505.766.6
6、28127.3426.4223.5013.464.707.594.505.129436.7836.3634.5216.485.369.445.966.7810437.1236.1234.2416.445.149.525.906.3811334.7833.5631.4015.465.148.425.685.8812231.3830.8628.5614.545.087.825.786.0013436.5035.7233.4816.425.068.905.446.4014233.8032.9230.7016.885.088.245.666.0015232.2831.1428.5015.384.887.685.605.3816437.8837.0634.5416.605.669.925.526.8417232.7431.8229.5815.305.148.006.005.0818130.0028.5626.1813.924.987.125.105.1219233.2232.10
