Least Squares Line Fitting

y = a x + b
0 1
2 1
4 4
Hx y L =
0 1
a
2 1 K O =
b
4 1
1
1
4
K
0 1
1
a
0 2 4
0 2 4
O 2 1 K O = K
O 1
1 1 1
b
1 1 1
4 1
4
K
a
20 6
18
OK O = K
O
6 3
b
6
3
4
1
2
a
K O =
b
y =
1
2
+
3x
4
4
1
0
2
4
y = a x + b
2 4
3 0
4 3
Hx y L =
2 1
a
3 1 K O =
b
4 1
4
0
3
K
2 1
4
a
2 3 4
2 3 4
O 3 1 K O = K
O 0
1 1 1
b
1 1 1
4 1
3
K
a
29 9
20
OK O = K
O
9 3
b
7
1
2
23
6
-
a
K O =
b
y =
23
6
-
x
2
4
3
0
2
3
4
y = a x + b
0 1
1 1
3 4
Hx y L =
0 1
a
1 1 K O =
b
3 1
1
1
4
K
0 1
1
a
0 1 3
0 1 3
O 1 1 K O = K
O 1
1 1 1
b
1 1 1
3 1
4
K
a
10 4
13
OK O = K
O
4 3
b
6
15
14
4
7
a
K O =
b
4
y =
7
+
15 x
14
4
1
0
1
3
y = a x + b
0 2
1 3
2 0
Hx y L =
0 1
a
1 1 K O =
b
2 1
2
3
0
K
0 1
2
a
0 1 2
0 1 2
O 1 1 K O = K
O 3
1 1 1
b
1 1 1
2 1
0
K
a
5 3
3
OK O = K O
3 3
b
5
K
a
O =
b
y =
8
3
-1
8
3
-x
3
2
0
0
1
2
y = a x + b
0 4
2 1
3 0
Hx y L =
0 1
a
2 1 K O =
b
3 1
4
1
0
K
0 1
4
a
0 2 3
0 2 3
O 2 1 K O = K
O 1
1 1 1
b
1 1 1
3 1
0
K
a
13 5
2
OK O = K O
5 3
b
5
19
14
55
14
-
a
K O =
b
55
y =
14
-
19 x
14
4
1
0
0
2
3
y = a x + b
0 2
1 0
3 2
Hx y L =
0 1
a
1 1 K O =
b
3 1
2
0
2
K
0 1
2
a
0 1 3
0 1 3
O 1 1 K O = K
O 0
1 1 1
b
1 1 1
3 1
2
K
a
10 4
6
OK O = K O
4 3
b
4
1
7
8
7
a
K O =
b
8
y =
7
+
x
7
2
0
0
1
3
y = a x + b
1 3
3 0
4 3
Hx y L =
1 1
a
3 1 K O =
b
4 1
3
0
3
K
1 1
3
a
1 3 4
1 3 4
O 3 1 K O = K
O 0
1 1 1
b
1 1 1
4 1
3
K
a
26 8
15
OK O = K
O
8 3
b
6
3
14
18
7
-
a
K O =
b
18
y =
7
-
3x
14
3
0
1
3
4
y = a x + b
0 2
2 0
3 4
Hx y L =
0 1
a
2 1 K O =
b
3 1
2
0
4
K
0 1
2
a
0 2 3
0 2 3
O 2 1 K O = K
O 0
1 1 1
b
1 1 1
3 1
4
K
a
13 5
12
OK O = K
O
5 3
b
6
3
7
9
7
a
K O =
b
9
y =
7
+
3x
7
4
2
0
0
2
3
y = a x + b
0 2
2 1
3 2
Hx y L =
0 1
a
2 1 K O =
b
3 1
2
1
2
K
0 1
2
a
0 2 3
0 2 3
O 2 1 K O = K
O 1
1 1 1
b
1 1 1
3 1
2
K
a
13 5
8
OK O = K O
5 3
b
5
1
14
25
14
-
a
K O =
b
25
y =
14
-
x
14
2
1
0
2
3
y = a x + b
0 1
2 1
3 4
Hx y L =
0 1
a
2 1 K O =
b
3 1
1
1
4
K
0 1
1
a
0 2 3
0 2 3
O 2 1 K O = K
O 1
1 1 1
b
1 1 1
3 1
4
K
a
13 5
14
OK O = K
O
5 3
b
6
6
7
4
7
a
K O =
b
4
y =
7
+
6x
7
4
1
0
2
3
y = a x + b
1 0
3 3
4 3
Hx y L =
1 1
a
3 1 K O =
b
4 1
0
3
3
K
1 1
0
a
1 3 4
1 3 4
O 3 1 K O = K
O 3
1 1 1
b
1 1 1
4 1
3
K
a
26 8
21
OK O = K
O
8 3
b
6
15
14
6
7
a
K O =
b
y = -
6
7
+
15 x
14
3
0
1
3
4
y = a x + b
0 0
1 1
3 0
Hx y L =
0 1
a
1 1 K O =
b
3 1
0
1
0
K
0 1
0
a
0 1 3
0 1 3
O 1 1 K O = K
O 1
1 1 1
b
1 1 1
3 1
0
K
a
10 4
1
OK O = K O
4 3
b
1
-
a
K O =
b
3
y =
7
-
1
14
3
7
x
14
1
0
0
1
3
y = a x + b
1 0
2 2
4 3
Hx y L =
1 1
a
2 1 K O =
b
4 1
0
2
3
K
1 1
0
a
1 2 4
1 2 4
O 2 1 K O = K
O 2
1 1 1
b
1 1 1
4 1
3
K
a
21 7
16
OK O = K
O
7 3
b
5
13
14
1
2
a
K O =
b
y = -
1
2
+
13 x
14
3
2
0
1
2
4
y = a x + b
1 1
3 0
4 3
Hx y L =
1 1
a
3 1 K O =
b
4 1
1
0
3
K
1 1
1
a
1 3 4
1 3 4
O 3 1 K O = K
O 0
1 1 1
b
1 1 1
4 1
3
K
a
26 8
13
OK O = K
O
8 3
b
4
K
a
O =
b
1
2
0
x
y =
2
3
1
0
1
3
4
y = a x + b
1 0
2 3
3 2
Hx y L =
1 1
a
2 1 K O =
b
3 1
0
3
2
K
1 1
0
a
1 2 3
1 2 3
O 2 1 K O = K
O 3
1 1 1
b
1 1 1
3 1
2
K
a
14 6
12
OK O = K
O
6 3
b
5
K
a
O =
b
y = -
1
3
1
-
1
3
+x
3
2
0
1
2
3
y = a x + b
0 2
2 3
3 4
Hx y L =
0 1
a
2 1 K O =
b
3 1
2
3
4
K
0 1
2
a
0 2 3
0 2 3
O 2 1 K O = K
O 3
1 1 1
b
1 1 1
3 1
4
K
a
13 5
18
OK O = K
O
5 3
b
9
9
14
27
14
a
K O =
b
27
y =
14
+
9x
14
4
3
2
0
2
3
y = a x + b
0 0
1 3
2 4
Hx y L =
0 1
a
1 1 K O =
b
2 1
0
3
4
K
0 1
0
a
0 1 2
0 1 2
O 1 1 K O = K
O 3
1 1 1
b
1 1 1
2 1
4
K
a
5 3
11
OK O = K
O
3 3
b
7
K
a
O =
b
y =
1
3
2
1
3
+2x
4
3
0
0
1
2
y = a x + b
0 0
2 3
4 2
Hx y L =
0 1
a
2 1 K O =
b
4 1
0
3
2
K
0 1
0
a
0 2 4
0 2 4
O 2 1 K O = K
O 3
1 1 1
b
1 1 1
4 1
2
K
a
20 6
14
OK O = K
O
6 3
b
5
1
2
2
3
a
K O =
b
y =
2
3
+
x
2
3
2
0
0
2
4
y = a x + b
0 0
1 2
2 3
Hx y L =
0 1
a
1 1 K O =
b
2 1
0
2
3
K
0 1
0
a
0 1 2
0 1 2
O 1 1 K O = K
O 2
1 1 1
b
1 1 1
2 1
3
K
a
5 3
8
OK O = K O
3 3
b
5
3
2
1
6
a
K O =
b
y =
1
6
+
3x
2
3
2
0
0
1
2
y = a x + b
0 2
2 2
3 4
Hx y L =
0 1
a
2 1 K O =
b
3 1
2
2
4
K
0 1
2
a
0 2 3
0 2 3
O 2 1 K O = K
O 2
1 1 1
b
1 1 1
3 1
4
K
a
13 5
16
OK O = K
O
5 3
b
8
4
7
12
7
a
K O =
b
12
y =
7
+
4x
7
4
2
0
2
3
y = a x + b
0 3
1 1
2 2
Hx y L =
0 1
a
1 1 K O =
b
2 1
3
1
2
K
0 1
3
a
0 1 2
0 1 2
O 1 1 K O = K
O 1
1 1 1
b
1 1 1
2 1
2
K
a
5 3
5
OK O = K O
3 3
b
6
1
2
5
2
-
a
K O =
b
y =
5
2
-
x
2
3
2
1
0
1
2
y = a x + b
2 1
3 3
4 0
Hx y L =
2 1
a
3 1 K O =
b
4 1
1
3
0
K
2 1
1
a
2 3 4
2 3 4
O 3 1 K O = K
O 3
1 1 1
b
1 1 1
4 1
0
K
a
29 9
11
OK O = K
O
9 3
b
4
1
2
17
6
-
a
K O =
b
y =
17
6
-
x
2
3
1
0
2
3
4
y = a x + b
1 4
2 4
3 0
Hx y L =
1 1
a
2 1 K O =
b
3 1
4
4
0
K
1 1
4
a
1 2 3
1 2 3
O 2 1 K O = K
O 4
1 1 1
b
1 1 1
3 1
0
K
a
14 6
12
OK O = K
O
6 3
b
8
K
a
O =
b
y =
20
3
-2
20
3
-2x
4
0
1
2
3
y = a x + b
1 1
2 3
4 4
Hx y L =
1 1
a
2 1 K O =
b
4 1
1
3
4
K
1 1
1
a
1 2 4
1 2 4
O 2 1 K O = K
O 3
1 1 1
b
1 1 1
4 1
4
K
a
21 7
23
OK O = K
O
7 3
b
8
13
14
1
2
a
K O =
b
1
y =
2
+
13 x
14
4
3
1
1
2
4
y = a x + b
0 1
3 0
4 3
Hx y L =
0 1
a
3 1 K O =
b
4 1
1
0
3
K
0 1
1
a
0 3 4
0 3 4
O 3 1 K O = K
O 0
1 1 1
b
1 1 1
4 1
3
K
a
25 7
12
OK O = K
O
7 3
b
4
4
13
8
13
a
K O =
b
y =
8
13
+
4x
13
3
1
0
0
3
4
y = a x + b
0 4
2 3
4 2
Hx y L =
0 1
a
2 1 K O =
b
4 1
4
3
2
K
0 1
4
a
0 2 4
0 2 4
O 2 1 K O = K
O 3
1 1 1
b
1 1 1
4 1
2
K
a
20 6
14
OK O = K
O
6 3
b
9
K
a
O =
b
y = 4-
-
1
2
4
x
2
4
3
2
0
2
4
y = a x + b
0 4
1 2
2 2
Hx y L =
0 1
a
1 1 K O =
b
2 1
4
2
2
K
0 1
4
a
0 1 2
0 1 2
O 1 1 K O = K
O 2
1 1 1
b
1 1 1
2 1
2
K
a
5 3
6
OK O = K O
3 3
b
8
K
a
O =
b
y =
11
3
-1
11
3
-x
4
2
0
1
2
y = a x + b
0 1
3 4
4 1
Hx y L =
0 1
a
3 1 K O =
b
4 1
1
4
1
K
0 1
1
a
0 3 4
0 3 4
O 3 1 K O = K
O 4
1 1 1
b
1 1 1
4 1
1
K
a
25 7
16
OK O = K
O
7 3
b
6
3
13
19
13
a
K O =
b
y =
19
13
+
3x
13
4
1
0
3
4
y = a x + b
2 0
3 1
4 4
Hx y L =
2 1
a
3 1 K O =
b
4 1
0
1
4
K
2 1
0
a
2 3 4
2 3 4
O 3 1 K O = K
O 1
1 1 1
b
1 1 1
4 1
4
K
a
29 9
19
OK O = K
O
9 3
b
5
K
a
O =
b
y = -
2
-
13
3
13
3
+2x
4
1
0
2
3
4
y = a x + b
0 3
2 0
3 0
Hx y L =
0 1
a
2 1 K O =
b
3 1
3
0
0
K
0 1
3
a
0 2 3
0 2 3
O 2 1 K O = K
O 0
1 1 1
b
1 1 1
3 1
0
K
a
13 5
0
OK O = K O
5 3
b
3
15
14
39
14
-
a
K O =
b
39
y =
14
-
15 x
14
3
0
0
2
3
y = a x + b
0 2
1 1
4 3
Hx y L =
0 1
a
1 1 K O =
b
4 1
2
1
3
K
0 1
2
a
0 1 4
0 1 4
O 1 1 K O = K
O 1
1 1 1
b
1 1 1
4 1
3
K
a
17 5
13
OK O = K
O
5 3
b
6
9
26
37
26
a
K O =
b
y =
37
26
+
9x
26
3
2
1
0
1
4
y = a x + b
0 1
3 3
4 1
Hx y L =
0 1
a
3 1 K O =
b
4 1
1
3
1
K
0 1
1
a
0 3 4
0 3 4
O 3 1 K O = K
O 3
1 1 1
b
1 1 1
4 1
1
K
a
25 7
13
OK O = K
O
7 3
b
5
2
13
17
13
a
K O =
b
y =
17
13
+
2x
13
3
1
0
3
4
y = a x + b
Hx y L =
0 0
3 0
4 3
0 1
a
3 1 K O =
b
4 1
0
0
3
K
0 1
0
a
0 3 4
0 3 4
O 3 1 K O = K
O 0
1 1 1
b
1 1 1
4 1
3
K
a
25 7
12
OK O = K
O
7 3
b
3
15
26
9
26
a
K O =
b
y = -
9
26
+
15 x
26
3
0
0
3
4
y = a x + b
0 1
1 3
4 2
Hx y L =
0 1
a
1 1 K O =
b
4 1
1
3
2
K
0 1
1
a
0 1 4
0 1 4
O 1 1 K O = K
O 3
1 1 1
b
1 1 1
4 1
2
K
a
17 5
11
OK O = K
O
5 3
b
6
3
26
47
26
a
K O =
b
y =
47
26
+
3x
26
3
2
1
0
1
4
y = a x + b
1 4
2 0
4 2
Hx y L =
1 1
a
2 1 K O =
b
4 1
4
0
2
K
1 1
4
a
1 2 4
1 2 4
O 2 1 K O = K
O 0
1 1 1
b
1 1 1
4 1
2
K
a
21 7
12
OK O = K
O
7 3
b
6
K
a
O =
b
y = 3-
-
3
7
3
3x
7
4
2
0
1
2
4
y = a x + b
2 2
3 0
4 1
Hx y L =
2 1
a
3 1 K O =
b
4 1
2
0
1
K
2 1
2
a
2 3 4
2 3 4
O 3 1 K O = K
O 0
1 1 1
b
1 1 1
4 1
1
K
a
29 9
8
OK O = K O
9 3
b
3
1
2
5
2
-
a
K O =
b
y =
5
2
-
x
2
2
1
0
2
3
4
y = a x + b
0 4
1 3
3 0
Hx y L =
0 1
a
1 1 K O =
b
3 1
4
3
0
K
0 1
4
a
0 1 3
0 1 3
O 1 1 K O = K
O 3
1 1 1
b
1 1 1
3 1
0
K
a
10 4
3
OK O = K O
4 3
b
7
19
14
29
7
-
a
K O =
b
29
y =
7
-
19 x
14
4
3
0
0
1
3
y = a x + b
Hx y L =
2 0
3 1
4 3
2 1
a
3 1 K O =
b
4 1
0
1
3
K
2 1
0
a
2 3 4
2 3 4
O 3 1 K O = K
O 1
1 1 1
b
1 1 1
4 1
3
K
a
29 9
15
OK O = K
O
9 3
b
4
3
2
19
6
a
K O =
b
y = -
19
6
+
3x
2
3
1
0
2
3
4
y = a x + b
0 3
1 3
2 2
Hx y L =
0 1
a
1 1 K O =
b
2 1
3
3
2
K
0 1
3
a
0 1 2
0 1 2
O 1 1 K O = K
O 3
1 1 1
b
1 1 1
2 1
2
K
a
5 3
7
OK O = K O
3 3
b
8
1
2
19
6
-
a
K O =
b
y =
19
6
-
x
2
3
2
0
1
2
y = a x + b
1 3
3 3
4 1
Hx y L =
1 1
a
3 1 K O =
b
4 1
3
3
1
K
1 1
3
a
1 3 4
1 3 4
O 3 1 K O = K
O 3
1 1 1
b
1 1 1
4 1
1
K
a
26 8
16
OK O = K
O
8 3
b
7
4
7
27
7
-
a
K O =
b
27
y =
7
-
4x
7
3
1
1
3
4
y = a x + b
0 1
1 1
3 2
Hx y L =
0 1
a
1 1 K O =
b
3 1
1
1
2
K
0 1
1
a
0 1 3
0 1 3
O 1 1 K O = K
O 1
1 1 1
b
1 1 1
3 1
2
K
a
10 4
7
OK O = K O
4 3
b
4
5
14
6
7
a
K O =
b
6
y =
7
+
5x
14
2
1
0
1
3
y = a x + b
0 3
3 1
4 1
Hx y L =
0 1
a
3 1 K O =
b
4 1
3
1
1
K
0 1
3
a
0 3 4
0 3 4
O 3 1 K O = K
O 1
1 1 1
b
1 1 1
4 1
1
K
a
25 7
7
OK O = K O
7 3
b
5
7
13
38
13
-
a
K O =
b
y =
38
13
-
7x
13
3
1
0
3
4
y = a x + b
0 3
1 0
4 1
Hx y L =
0 1
a
1 1 K O =
b
4 1
3
0
1
K
0 1
3
a
0 1 4
0 1 4
O 1 1 K O = K
O 0
1 1 1
b
1 1 1
4 1
1
K
a
17 5
4
OK O = K O
5 3
b
4
4
13
24
13
-
a
K O =
b
y =
24
13
-
4x
13
3
1
0
0
1
4
y = a x + b
2 1
3 4
4 4
Hx y L =
2 1
a
3 1 K O =
b
4 1
1
4
4
K
2 1
1
a
2 3 4
2 3 4
O 3 1 K O = K
O 4
1 1 1
b
1 1 1
4 1
4
K
a
29 9
30
OK O = K
O
9 3
b
9
3
2
3
2
a
K O =
b
y = -
3
2
+
3x
2
4
1
2
3
4
y = a x + b
2 2
3 1
4 3
Hx y L =
2 1
a
3 1 K O =
b
4 1
2
1
3
K
2 1
2
a
2 3 4
2 3 4
O 3 1 K O = K
O 1
1 1 1
b
1 1 1
4 1
3
K
a
29 9
19
OK O = K
O
9 3
b
6
1
2
1
2
a
K O =
b
y =
1
2
+
x
2
3
2
1
2
3
4
y = a x + b
Hx y L =
1 4
2 1
3 4
1 1
a
2 1 K O =
b
3 1
4
1
4
K
1 1
4
a
1 2 3
1 2 3
O 2 1 K O = K
O 1
1 1 1
b
1 1 1
3 1
4
K
a
14 6
18
OK O = K
O
6 3
b
9
K
a
0
O = K O
b
3
y = 3
4
1
1
2
3
y = a x + b
1 2
2 4
4 3
Hx y L =
1 1
a
2 1 K O =
b
4 1
2
4
3
K
1 1
2
a
1 2 4
1 2 4
O 2 1 K O = K
O 4
1 1 1
b
1 1 1
4 1
3
K
a
21 7
22
OK O = K
O
7 3
b
9
3
14
5
2
a
K O =
b
5
y =
2
+
3x
14
4
3
2
1
2
4
y = a x + b
0 0
1 1
4 1
Hx y L =
0 1
a
1 1 K O =
b
4 1
0
1
1
K
0 1
0
a
0 1 4
0 1 4
O 1 1 K O = K
O 1
1 1 1
b
1 1 1
4 1
1
K
a
17 5
5
OK O = K O
5 3
b
2
5
26
9
26
a
K O =
b
y =
9
26
+
5x
26
1
0
0
1
4
y = a x + b
0 2
1 4
3 4
Hx y L =
0 1
a
1 1 K O =
b
3 1
2
4
4
K
0 1
2
a
0 1 3
0 1 3
O 1 1 K O = K
O 4
1 1 1
b
1 1 1
3 1
4
K
a
10 4
16
OK O = K
O
4 3
b
10
4
7
18
7
a
K O =
b
18
y =
7
+
4x
7
4
2
0
1
3
y = a x + b
0 1
2 0
3 2
Hx y L =
0 1
a
2 1 K O =
b
3 1
1
0
2
K
0 1
1
a
0 2 3
0 2 3
O 2 1 K O = K
O 0
1 1 1
b
1 1 1
3 1
2
K
a
13 5
6
OK O = K O
5 3
b
3
3
14
9
14
a
K O =
b
9
y =
14
+
3x
14
2
1
0
0
2
3