8
•Solving
the Linear System : Y = Xb + e
→the basic goal of 3dDeconvolve
→Least Square Estimate (LSE): making sum of squares of residual (unknown/unexplained) error e’e minimal à Normal equation: (X’X)
b = X’Y
→When X is of full rank (all columns are independent), b^ = (X’X)-1X’Y
•Geometric
Interpretation:
→project vector Y onto a space spanned by the regressors (the column
vectors of design matrix X)
→find shortest distance from Y to X-space
Y
e
X-Space
r1
r2
Xb
0