如何用两个变量的所有组合之间的相互作用在R中创建回归模型？
创建具有交互作用的回归模型的最简单方法是输入带有*的乘法符号的变量，但这将创建许多其他高阶组合。如果我们要创建两个变量组合的相互作用，则可以使用幂运算符，如以下示例所示。
例1
x1<−rnorm(10) x2<−rnorm(10,1,0.2) x3<−rnorm(10,1,0.04) y<−rnorm(10,5,1) M1<−lm(y~(x1+x2+x3)^2) summary(M1) Call: lm(formula = y ~ (x1 + x2 + x3)^2) Residuals: 1 2 3 4 5 6 7 8 0.47052 −0.39362 0.37762 −0.80668 0.41637 −0.04845 0.00832 0.27097 9 10 0.14218 −0.43722 Coefficients: Estimate Std. Error t value Pr(>|t|)
输出结果
(Intercept) 0.2893 172.6567 0.002 0.999 x1 28.5300 25.1856 1.133 0.340 x2 7.9753 191.0616 0.042 0.969 x3 3.3123 168.1906 0.020 0.986 x1:x2 1.2607 16.6937 0.076 0.945 x1:x3 −28.3810 19.4585 −1.459 0.241 x2:x3 −6.2240 186.3458 −0.033 0.975
残差标准误差：3个自由度上的0.7372多个R平方：0.7996，调整后的R平方：0.3989F统计：6和3DF上的1.995，p值：0.3048
例2
a1<−rpois(500,5) a2<−rpois(500,8) a3<−rpois(500,10) a4<−rpois(500,2) a5<−rpois(500,12) a6<−rpois(500,15) a7<−rpois(500,9) y<−rpois(500,1) M2<−lm(y~(a1+a2+a3+a4+a5+a6+a7)^2) summary(M2) Call: lm(formula = y ~ (a1 + a2 + a3 + a4 + a5 + a6 + a7)^2) Residuals: Min 1Q Median 3Q Max −1.4849 −0.8804 −0.0342 0.6623 4.2336 Coefficients: Estimate Std. Error t value Pr(>|t|)
输出结果
(Intercept) −0.1225469 1.8336636 −0.067 0.94674 a1 0.4629300 0.1548978 2.989 0.00295 ** a2 −0.0330453 0.1246535 −0.265 0.79105 a3 0.0442927 0.1191984 0.372 0.71037 a4 −0.0661164 0.2644226 −0.250 0.80266 a5 0.0657267 0.1035211 0.635 0.52579 a6 −0.0434769 0.0832513 −0.522 0.60175 a7 −0.0132370 0.1187218 −0.111 0.91127 a1:a2 −0.0055441 0.0072067 −0.769 0.44210 a1:a3 −0.0095850 0.0062517 −1.533 0.12590 a1:a4 −0.0197856 0.0156935 −1.261 0.20802 a1:a5 −0.0063698 0.0055879 −1.140 0.25489 a1:a6 −0.0119008 0.0057317 −2.076 0.03841 * a1:a7 −0.0009957 0.0069639 −0.143 0.88637 a2:a3 −0.0005469 0.0048617 −0.112 0.91049 a2:a4 −0.0096056 0.0119358 −0.805 0.42136 a2:a5 −0.0040884 0.0048707 −0.839 0.40167 a2:a6 0.0059163 0.0045048 1.313 0.18971 a2:a7 0.0023896 0.0052308 0.457 0.64800 a3:a4 −0.0003036 0.0096746 −0.031 0.97498 a3:a5 −0.0070901 0.0045312 −1.565 0.11832 a3:a6 0.0049534 0.0039970 1.239 0.21586 a3:a7 0.0013881 0.0050959 0.272 0.78543 a4:a5 0.0138932 0.0095724 1.451 0.14734 a4:a6 0.0053824 0.0088454 0.608 0.54315 a4:a7 0.0020738 0.0107736 0.192 0.84745 a5:a6 0.0019474 0.0036433 0.535 0.59324 a5:a7 0.0019719 0.0048370 0.408 0.68370 a6:a7 −0.0031881 0.0041510 −0.768 0.44285 −−− Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
残留标准误差：在471自由度上为1.017多个R平方：0.04549，调整后的R平方：-0.01126F-统计量：在28和471DF上为0.8016，p值：0.7563
例子3
z1<−runif(100,1,2) z2<−runif(100,1,4) z3<−runif(100,1,5) z4<−runif(100,2,5) z5<−runif(100,2,10) y<−runif(100,1,10) M3<−lm(y~(z1+z2+z3+z4+z5)^2) summary(M3) Call: lm(formula = y ~ (z1 + z2 + z3 + z4 + z5)^2) Residuals: Min 1Q Median 3Q Max −5.4732 −2.0570 0.0582 2.1667 5.3376
输出结果
Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) −2.03476 14.52311 −0.140 0.8889 z1 3.14344 6.80702 0.462 0.6454 z2 3.85518 3.05398 1.262 0.2103 z3 −1.88782 2.16124 −0.873 0.3849 z4 2.75794 3.11048 0.887 0.3778 z5 −0.70359 1.05400 −0.668 0.5063 z1:z2 −2.09623 1.24757 −1.680 0.0966 . z1:z3 0.17328 0.97128 0.178 0.8588 z1:z4 0.53514 1.26533 0.423 0.6734 z1:z5 0.02687 0.43087 0.062 0.9504 z2:z3 0.15894 0.34335 0.463 0.6446 z2:z4 −0.72427 0.43987 −1.647 0.1034 z2:z5 0.22560 0.16570 1.362 0.1770 z3:z4 −0.16602 0.33847 −0.491 0.6251 z3:z5 0.30484 0.12536 2.432 0.0171 * z4:z5 −0.19887 0.17768 −1.119 0.2662 −−− Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
残留标准误：84个自由度上的2.792
多个R平方：0.1587，调整后的R平方：0.008411
F统计量：15和84DF上的1.056，p值：0.4091