用R语言进行简单线性回归分析.docx

fire.txt ：（数据出自何晓群-应用回归分析）x y3.4 26.21.8 17.84.6 31.32.3 23.13.1 27.55.5 360.7 14.13.0 22.32.6 19.64.3 31.32.1 241.1 17.36.1 43.24.8 36.43.8 26.1#-#数据准备fire - read.table(D:/fire.txt, head = T)#-#回归分析plot(fire$y fire$x)fire.reg - lm(fire$y fire$x, data = fire) #回归拟合summary(fire.reg) #回归分析表anova(fire.reg) #方差分析表abline(fire.reg, col = 2, lty = 2) #拟合直线#-#残差分析fire.res - residuals(fire.reg) #残差fire.sre - rstandard(fire.reg) #学生化残差plot(fire.sre)abline(h = 0)text(11, fire.sre11, label = 11, adj = (-0.3), col = 2) #标注点#-#预测与控制attach(fire) #连接fire.reg - lm(y x) #这种回归拟合简单fire.points - data.frame(x = c(3.5, 4)fire.pred - predict(fire.reg, fire.points, interval = prediction, level = 0.95) #预测：置信区间fire.preddetach(fire) #取消连接-#附自编的过程程序：（R最大的好处是可以自己编想要的程序和函数，尤其没有内置函数的时候）fire - read.table(D:/fire.txt, head = T)attach(fire)-lxy - function(x)sum - 0sum0 - 0 for(i in 1:length(x)sum0 - (xi - mean(x) * (yi-mean(y)sum - sum + sum0sum-#用这个就不需要循环了lxy - function(x)mid - (x - mean(x) * (y-mean(y)sum - sum(mid)sum#对于数据框、列表等数据对象要善用apply()函数。-lxx - function(x)sum - 0sum0 - 0 for(i in 1:length(x)sum0 - (xi - mean(x)2sum - sum + sum0sumLxx - lxx(x)Lyy - lxx(y)Lxy - lxy(x)b1 - Lxy / Lxx; b1 #回归系数斜率b0 - mean(y) - b1 * mean(x); b0 #回归系数截距residu - y - (b0 + b1*x); residu #残差r - Lxy / sqrt(Lxx * Lyy); r #相关系数rsqure - r2; rsqure #决定系数adrsqure - 1 - (length(x)-1)/(length(x)-2)*(1-r2) #调整后的决定系数-esrequre - function(x) #求标准差平方估计值sum - 0sum0 - 0 for(i in 1:length(x)sum0 - residui2sum - sum + sum0residusqure - sum/(length(x)-2)residusqureesterreq - esrequre(x); esterreq #标准差平方估计值(MSE)ester - sqrt(esrequre(x); ester #标准差估计值(回归分析表给出的标准误差)val_t - b1*sqrt(Lxx) / ester; val_t #检验回归系数斜率b1的t值SSe - function(x) #求残差平方和sum - 0sum0 - 0 for(i in 1:length(x)sum0 - residui2sum - sum + sum0sumSSE - SSe(x); SSE #残差平方和MSE - SSE/(length(x)-2); MSE #残差均方和SSr - function(x)sum - 0sum0 - 0 for(i in 1:length(x)sum0 - (b0 + b1*xi) - mean(y)2sum - sum + sum0sumSSR - SSr(x); SSR #回归平方和MSR - SSR/1; MSR #回归均方和val_F - SSR / MSE; val_F #检验回归方程F值hi - 1/length(x) + (x-mean(x)2/Lxx #杠杆值ZRE