Determinate Coefficient

决定系数

决定系数（英语：coefficient of determination，记为R2或r2）在统计学中用于度量因变量的变异中可由自变量解释部分所占的比例，以此来判断统计模型的解释力。

对于简单线性回归而言，决定系数为样本相关系数的平方。当加入其他回归自变量后，决定系数相应地变为多重相关系数的平方。

mylr = function(x,y){
  
  x_mean = mean(x)
  y_mean = mean(y)
  xy_mean = mean(x*y)
  xx_mean = mean(x*x)
  yy_mean = mean(y*y)
  
  slope = (x_mean*y_mean - xy_mean)/(x_mean^2 - xx_mean)
  intercept = y_mean - slope*x_mean
  
  #f = slope*x+intercept #linear regression
  f = x # custom linear regression
  plot(x, y)
  lines(x, f)
  
  SStotal = sum((y-y_mean)^2)
  SSres = sum((y-f)^2)
  SSreg = sum((f-y_mean)^2)
  R2 = 1 - (SSres/SStotal)
  cor2 = cor(x, y)^2
  
  result = c(slope, intercept, SSres, R2, cor2)
  names(result) = c('slope', 'intercept', 'SSres', 'R2', 'cor2')
  
  return(result)
}


x <- c(1,2,3,4,5,6,7,8,9,10)
y <- c(1,2,3,4,5,6,7,8,9,10)
z <- c(2,4,6,8,10,12,14,16,18,20)
w <- c(1.1,2.2,3.3,4.4,5.5,6.6,7.7,8.8,9.9,11)


mylr(x,y)
mylr(x,z)
mylr(x,w)

Reference

What Is R Squared And Negative R Squared

决定系数R2能否为负数？