決定係數（coefficient ofdetermination），有的書上翻譯為判定係數，也稱為擬合優度。
決定係數反應了y的波動有多少百分比能被x的波動所描述，即表徵依變數Y的變異中有多少百分比,可由控制的自變數X來解釋.
表達式：R2=SSR/SST=1-SSE/SST
其中：SST=SSR+SSE，SST(total sum of squares)為總平方和，SSR(regression sum of squares)為回歸平方和，SSE(error sum of squares) 為殘差平方和。
回歸平方和：SSR(Sum of Squares forregression) = ESS (explained sum of squares)
殘差平方和：SSE（Sum of Squares for Error） = RSS(residual sum of squares)
總離差平方和：SST(Sum of Squares fortotal) = TSS(total sum of squares)
SSE+SSR=SST RSS+ESS=TSS
意義：擬合優度越大，自變量對因變量的解釋程度越高，自變量引起的變動佔總變動的百分比高。觀察點在回歸直線附近越密集。取值範圍：0-1.
舉例：
假設有10個點，如下圖：
用R來實現如何求線性方程和R2：
# 線性回歸的方程
mylr = function(x,y){
plot(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)
m = (x_mean*y_mean - xy_mean)/(x_mean^2 - xx_mean)
b = y_mean - m*x_mean
f = m*x+b# 線性回歸方程
lines(x,f)
sst = sum((y-y_mean)^2)
sse = sum((y-f)^2)
ssr = sum((f-y_mean)^2)
result = c(m,b,sst,sse,ssr)
names(result) = c('m','b','sst','sse','ssr')
return(result)
}
x = c(60,34,12,34,71,28,96,34,42,37)
y = c(301,169,47,178,365,126,491,157,202,184)
f = mylr(x,y)
f['m']
f['b']
f['sse']+f['ssr']
f['sst']
R2= f['ssr']/f['sst']
最後方程為：f(x)=5.3x-15.5
R2為99.8，說明x對y的解釋程度非常高。