什么是R² ？

在回归模型中，因变量（y）总的方差（信息）可以被称作总平方和（Total sum of squares，TSS），它由两部分组成[1]：

1. 模型可以解释的那部分信息（Model sum of squares, MSS）

2. 模型解释不了的那部分信息，也称为error（Residual sum of squares, RSS）

R² 指的是模型可以解释的那部分信息所占的百分比，即MSS/TSS。

如果R²越大，那该模型能解释的部分也就越多，模型当然就越佳。

上述的概念看上去枯燥，并不是那么有意思。

所以，小编接下来将会用图片呈现6个不同大小的R²，有助于了解不同R²到底“长”什么样，一定让你终身难忘~

首先载入所需R包：

# install.packages("correlation")
# install.packages("ggplot2")
# install.packages("patchwork")library(correlation)   # 用于创建数据
library(ggplot2)
library(patchwork)

马上开始作图。

第一张图：R² = 0%

mydata_0 <- simulate_simpson(n = 500, r = 0, groups = 1)p1 <- ggplot(mydata_0, aes(V1, V2)) + geom_point(shape = 1, fill = "white", color = "firebrick1") + geom_smooth(method = "lm", se = FALSE, color = "firebrick1") + theme_minimal() + annotate("text", x = 3, y = -3, label = "R-squared: 0%") + labs(x = "", y = "")
p1

第二张图： R² = 10%

mydata_0.1 <- simulate_simpson(n = 500, r = sqrt(0.1), groups = 1)p2 <- ggplot(mydata_0.1, aes(V1, V2)) + geom_point(shape = 1, fill = "white", color = "deepskyblue3") + geom_smooth(method = "lm", se = FALSE, color = "deepskyblue3") + theme_minimal() + annotate("text", x = 3, y = -3, label = "R-squared: 10%") + labs(x = "", y = "")
p2

第三张图： R² = 50%

mydata_0.5 <- simulate_simpson(n = 500, r = sqrt(0.5), groups = 1)p3 <- ggplot(mydata_0.5, aes(V1, V2)) + geom_point(shape = 1, fill = "white", color = "goldenrod1") + geom_smooth(method = "lm", se = FALSE, color = "goldenrod1") + theme_minimal() + annotate("text", x = 3, y = -3, label = "R-squared: 50%") + labs(x = "", y = "")
p3

第四张图： R² = 70%

mydata_0.7 <- simulate_simpson(n = 500, r = sqrt(0.7), groups = 1)p4 <- ggplot(mydata_0.7, aes(V1, V2)) + geom_point(shape = 1, fill = "white", color = "mediumpurple1") + geom_smooth(method = "lm", se = FALSE, color = "mediumpurple1") + theme_minimal() + annotate("text", x = 3, y = -3, label = "R-squared: 70%") + labs(x = "", y = "")
p4

第五张图： R² = 90%

mydata_0.9 <- simulate_simpson(n = 500, r = sqrt(0.9), groups = 1)p5 <- ggplot(mydata_0.9, aes(V1, V2)) + geom_point(shape = 1, fill = "white", color = "orange3") + geom_smooth(method = "lm", se = FALSE, color = "orange3") + theme_minimal() + annotate("text", x = 3, y = -3, label = "R-squared: 90%") + labs(x = "", y = "")
p5

第六张图： R² = 100%

mydata_1 <- simulate_simpson(n = 500, r = sqrt(1), groups = 1)p6 <- ggplot(mydata_1, aes(V1, V2)) + geom_point(shape = 1, fill = "white", color = "palegreen4") + geom_smooth(method = "lm", se = FALSE, color = "palegreen4") + theme_minimal() + annotate("text", x = 3, y = -3, label = "R-squared: 100%") + labs(x = "", y = "") p6

最后，将6张图片合并，然后点击收藏：

(p1 + p2 + p3) / (p4 + p5 + p6)

好啦，今天的内容就到这里。

如果有帮助，记得分享给需要的人！

参考文献

[1]. The Elements of Statistical Learning

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