R语言在散点图中添加lm线性回归公式的问题 R语言在散点图中添加lm线性回

1. 简单的线性回归
2. 使用ggplot2展示

1. 简单的线性回归函数自带的例子（R 中键入?lm），lm(y ~ x)回归y=kx + b， lm( y ~ x -1 )省略b，不对截距进行估计：

require(graphics)## Annette Dobson (1990) "An Introduction to Generalized Linear Models".## Page 9: Plant Weight Data.ctl <- c(4.17,5.58,5.18,6.11,4.50,4.61,5.17,4.53,5.33,5.14)trt <- c(4.81,4.17,4.41,3.59,5.87,3.83,6.03,4.89,4.32,4.69)group <- gl(2, 10, 20, labels = c("Ctl","Trt"))weight <- c(ctl, trt)lm.D9 <- lm(weight ~ group)lm.D90 <- lm(weight ~ group - 1) # omitting interceptanova(lm.D9)summary(lm.D90)opar <- par(mfrow = c(2,2), oma = c(0, 0, 1.1, 0))plot(lm.D9, las = 1)# Residuals, Fitted, ...par(opar)

使用R中自带的mtcars数据，可以得到截距和斜率，也可以得到解释率R-square：

require(ggplot2)library(dplyr) #加载dplyr包library(ggpmisc) #加载ggpmisc包library(ggpubr)require(gridExtra)model=lm(mtcars$wt ~ mtcars$mpg)model## 输出：Call:lm(formula = mtcars$wt ~ mtcars$mpg)Coefficients:(Intercept)mtcars$mpg6.047-0.141``````handlebarssummary(model)## 输出：Call:lm(formula = mtcars$wt ~ mtcars$mpg)Residuals:Min1Q Median3QMax -0.652 -0.349 -0.1380.3191.368 Coefficients:Estimate Std. Error t value Pr(>|t|)(Intercept)6.04730.308719.59< 2e-16 ***mtcars$mpg-0.14090.0147-9.561.3e-10 ***---Signif. codes:0 ‘***' 0.001 ‘**' 0.01 ‘*' 0.05 ‘.' 0.1 ‘ ' 1Residual standard error: 0.494 on 30 degrees of freedomMultiple R-squared:0.753, Adjusted R-squared:0.745 F-statistic: 91.4 on 1 and 30 DF,p-value: 1.29e-10

提取回归R-square值：

通过summary提取：## 上面的例子## mtcars例子model=lm(mtcars$wt ~ mtcars$mpg)res=summary(model)str(res) ## 提取各个值：res$r.squaredres$coefficientsres$adj.r.squared## df 矫正后的结果res$coefficients[1,1]res$coefficients[2,1]

使用默认的plot绘制回归散点：

plot(mtcars$mpg, mtcars$wt, pch=20,cex=2)abline(model,col="red",lwd=2)

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计算Confidence interval（95%）：

test=mtcars[c("mpg","wt")]head(test)colnames(test)=c("x","y")model = lm(y ~ x, test)test$predicted = predict(object = model,newdata = https://www.it610.com/article/test)test$CI = predict(object = model,newdata = test,se.fit = TRUE)$se.fit * qt(1 - (1-0.95)/2, nrow(test))test$predicted = predict(object = model,newdata = test)test$CI_u=test$predicted+test$CItest$CI_l=test$predicted-test$CIplot(mtcars$mpg, mtcars$wt, pch=20,cex=1) ##have replicated x valuesabline(model,col="red",lwd=2)lines(x=test$x,y=test$CI_u,col="blue")lines(x=test$x,y=test$CI_l,col="blue")

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上面的图蓝线有点奇怪，简单绘制最初的plot：

plot(mtcars$mpg, mtcars$wt, pch=20,cex=1,type="b") ##have replicated x values

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实际上面的计算方法没问题，但是数据不合适，因为数据x含有重复值，所以要考虑这个。

2. 使用ggplot2展示 ggplot2例子：

p <- ggplot(df, aes(x=yreal, y=ypred)) +geom_point(color = "grey20",size = 1, alpha = 0.8)#回归线#添加回归曲线p2 <- p + geom_smooth(formula = y ~ x, color = "red",fill = "blue", method = "lm",se = T, level=0.95) +theme_bw() +stat_poly_eq(aes(label = paste(..eq.label.., ..adj.rr.label.., sep = '~~~')),formula = y ~ x,parse = TRUE,color="blue",size = 5, #公式字体大小label.x = 0.05,#位置，0-1之间的比例label.y = 0.95) + labs(title="test",x="Real Value (Huang Huaihai 1777)" , y="Predicted Value (Correlation: 0.5029)")p2

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ggplot版本的手动计算：

require(ggplot2)library(dplyr) #加载dplyr包library(ggpmisc) #加载ggpmisc包library(ggpubr)require(gridExtra)ggplot(data=https://www.it610.com/article/df, aes(x=yreal, y=ypred)) +geom_smooth(formula = y ~ x, color ="blue",fill = "grey10", method = "lm")+geom_point() +stat_regline_equation(label.x=0.1, label.y=-1.5) +stat_cor(aes(label=..rr.label..), label.x=0.1, label.y=-2)test=dfhead(test)colnames(test)=c("x","y")model = lm(y ~ x, test)test$predicted = predict(object = model,newdata = https://www.it610.com/article/test)test$CI = predict(object = model,newdata = test,se.fit = TRUE)$se.fit * qt(1 - (1-0.95)/2, nrow(test))ggplot(test) +aes(x = x, y = y) +geom_point(size = 1,colour="grey40") +geom_smooth(formula =y ~ x,method = "lm",fullrange = TRUE, color = "black") +geom_line(aes(y = predicted + CI), color = "blue") + # uppergeom_line(aes(y = predicted - CI), color = "red") + # lowertheme_classic()

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参考：
https://stackoverflow.com/questions/23519224/extract-r-square-value-with-r-in-linear-models （提取R2）
https://blog.csdn.net/LeaningR/article/details/118971000 （提取R2等）
https://stackoverflow.com/questions/45742987/how-is-level-used-to-generate-the-confidence-interval-in-geom-smooth （添加lm线）
https://zhuanlan.zhihu.com/p/131604431 （知乎）
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