Page 105 - Applied Statistics with R
P. 105
7.3. DECOMPOSITION OF VARIATION 105
Sum of Squares Total
SST = ∑( − ̄) 2
=1
The quantity “Sum of Squares Total,” or SST, represents the total variation
of the observed values. This should be a familiar looking expression. Note
that,
1 1
2
2
= ∑( − ̄) = SST.
− 1 − 1
=1
Sum of Squares Regression
SSReg = ∑( ̂ − ̄ ) 2
=1
The quantity “Sum of Squares Regression,” SSReg, represents the explained
variation of the observed values.
Sum of Squares Error
SSE = RSS = ∑( − ̂ ) 2
=1
The quantity “Sum of Squares Error,” SSE, represents the unexplained vari-
ation of the observed values. You will often see SSE written as RSS, or
“Residual Sum of Squares.”
SST = sum((y - mean(y)) ^ 2)
SSReg = sum((y_hat - mean(y)) ^ 2)
SSE = sum((y - y_hat) ^ 2)
c(SST = SST, SSReg = SSReg, SSE = SSE)
## SST SSReg SSE
## 32538.98 21185.46 11353.52
Note that,
SSE
2
= .
− 2
