生物统计学第3版杜荣骞 课后习题答案 第十一章多元回归及复相关分析.docx

1、生物统计学第3版杜荣骞 课后习题答案 第十一章 多元回归及复相关分析第十一章 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）123417.201081.041091.761092.041096.401068.401062.621031.7410321.641091.921099.601087.401081.221079.201062.091031.8

2、910331.301091.421093.461086.001082.261062.041061.861031.8210349.801087.801081.021083.821081.301061.261061.321031.22103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; T

3、he SAS System The REG Procedure Model: 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 .00

4、01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

5、.64 0.0010 x1 1 -0.22296 0.20853 -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

6、系数：（2）逐步回归分析：options linesize=76 nodate;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

7、.9188 and C(p) = 8.2905 Analysis of 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 x

8、2 0.41889 0.02068 44.11123 410.32 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 .0001 2 x7 2 0.0106 0.9294 4.5012 5.56 0.0237 3 x8 3 0.0074 0.9369 2.4570 4.23 0.0471引入方程中的三个变量没有剔除，最终保留在方程中的三个变

9、量，在0.05水平上全都是显著的。方程如下：11.4 下表给出了高山姬鼠头骨8个特征的测量值和鉴定年龄79，用逐步回归方法从8个特征中选出与鉴定年龄关系最密切的变量，并对结果做回归的方差分析。序号鉴定年龄/a头 骨 特 征 /mmX1X2X3X4X5X6X7X81530.6430.0028.3414.324.308.784.525.662328.7828.5626.7814.004.568.064.345.463328.0027.1225.0413.864.487.564.345.024226.6426.1624.5213.144.687.064.464.865226.0825.5023.76

10、13.284.526.944.364.946429.4028.7027.8614.144.868.244.685.487124.8224.0422.0612.444.526.384.344.748226.5625.7423.7813.024.587.164.185.149227.1826.2624.4413.064.747.344.205.2010226.4625.8224.1213.064.587.064.204.5011429.6228.8227.0413.524.448.284.345.4812530.1029.8828.2414.024.668.824.385.4613531.1830.6229.0614.604.868.864.825.9214327.5426.9225.3014.144.587.544