(( Matlab )): linear regressions using the least squares
Nawaf8555
proj.pdf
m P Pk(xk, yk) yk �k
yk
a b
y = ax+b
a b
�
2 = mX
k=1
(yk � (axk + b))2
�
2 k
= mX
k=1
✓ yk � (axk + b)
�k
◆2
Pk
�
2 ����
����M ⇤ �
� B ����
���� 2
2
m a
b M B
x y � a b
\ M B
x y
1 �2k
�
2 = Pm
k=1(yk � (axk + b)) 2
y = ax
�
2
s
xk
x = 0
�
2
yk
0 �k �
2
�
2
�
2 /(m � 2) 1
yk � (axk + b) yk
r =
Pm k=1(xk � x̄)(yk � ȳ)pPm
k=1(xk � x̄)2 pPm
k=1(yk � ȳ)2
x̄ ȳ xk yk r 2 [�1; 1]
�k
Pk(xk, yk)
�
2 �
2
�
2 /(m � 2) r
r
(x, y1), (x, y2) (x, y3) y1 y2 y1 y3 y1
