生物统计学第十一章

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 F Model 8 53.17231 6.64654 64.33 |t| Intercept 1 -6.14927 1.68879 -3.64 0.0010 x1 1 -0.22296 0.20853 -

5、1.07 0.2932 x2 1 0.56813 0.25038 2.27 0.0304 x3 1 0.01771 0.19207 0.09 0.9271 x4 1 -0.12007 0.12562 -0.96 0.3466 x5 1 -0.39754 0.31415 -1.27 0.2151 x6 1 0.20935 0.19346 1.08 0.2875 x7 1 -0.34198 0.23671 -1.44 0.1586 x8 1 0.21464 0.20076 1.07 0.2932从参数估计列可以得到回归方程：复相关系数：（2）逐步回归分析：options linesize=76 n

6、odate;data stepreg; infile e:dataer11-3e.dat; input y x1-x8;run;proc reg; model y=x1-x8/selection=stepwise slentry=0.05 slstay=0.05;run; The SAS System The REG Procedure Model: MODEL1 Dependent Variable: y Stepwise Selection: Step 1 Variable x2 Entered: R-Square = 0.9188 and C(p) = 8.2905 Analysis o

7、f Variance Sum of Mean Source DF Squares Square F Value Pr F Model 1 51.79923 51.79923 430.17 F Intercept -10.24579 0.64700 30.19713 250.78 .0001 x2 0.39483 0.01904 51.79923 430.17 F Model 2 52.39734 26.19867 243.70 F Intercept -8.33902 1.01352 7.27767 67.70 .0001 x2 0.41889 0.02068 44.11123 410.32

8、F Model 3 52.81516 17.60505 178.04 F Intercept -8.42672 0.97297 7.41726 75.01 .0001 x2 0.35766 0.03579 9.87513 99.87 F 1 x2 1 0.9188 0.9188 8.2905 430.17 F Model 1 39.96265 39.96265 276.71 F Intercept -14.87681 1.08114 27.34609 189.35 .0001 x1 0.63413 0.03812 39.96265 276.71 F Model 2 40.61122 20.30

9、561 162.40 F Intercept -13.31331 1.21786 14.94162 119.50 .0001 x1 0.44066 0.09205 2.86530 22.92 F Model 3 41.12125 13.70708 125.03 F Intercept -13.50669 1.14392 15.28437 139.41 .0001 x1 0.56648 0.10408 3.24772 29.62 F 1 x1 1 0.9111 0.9111 11.3797 276.71 .0001 2 x6 2 0.0148 0.9259 7.3289 5.19 0.0312

10、3 x8 3 0.0116 0.9375 4.5706 4.65 0.0408在0.05水平上筛选出三个变量，它们分别是：X1，X6和X8。回归方程为：方差分析表：变差来源平方和自由度均方FP回 归41.121 25313.707 08125.03 F Model 2 35.61535 17.80767 15.61 0.0071 Error 5 5.70225 1.14045 Corrected Total 7 41.31760 Root MSE 1.06792 R-Square 0.8620 Dependent Mean 8.05000 Adj R-Sq 0.8068 Coeff Var 13.26607 Parameter Estimates Parameter Standard Variable DF Estimate Error t Value Pr |t| Intercept 1 -19.57060 5.70767 -3.43 0.0187 x1 1 7.29381 1.41032 5.17 0.0035 x2 1 -0.44357 0.08239 -5.38 0.0030回归方程为：一次项和二次项的回归系数都是极显著的。11.6 两种农药“呋喃丹”和“铁灭克”，在不同 pH条件