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Math 33a/2, Quiz 5bd, November 15, 2007
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1. Find the straight line
y
=
c
0
+
c
1
x
that provides the best ﬁt (in the leastsquares sense)
to the four points (0
,

1)
,
(1
,
2)
,
(2
,
1)
,
(3
,
4).
Solution.
Plugging in the four points into the straightline formula
y
=
c
0
+
c
1
x
, we
have

1 =
c
0
+ 0
·
c
1
,
2 =
c
0
+ 1
·
c
1
,
1 =
c
0
+ 2
·
c
1
,
4 =
c
0
+ 3
·
c
1
, or
1 0
1 1
1 2
1 3
±
c
0
c
1
²
=

1
2
1
4
.
We wish to ﬁnd the vector
±
c
0
c
1
²
which provides the best leastsquares approximation
to a solution. To do this, we multiply both sides by the matrix
±
1 1 1 1
0 1 2 3
²
and solve the
resulting system of equations:
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Unformatted text preview: ± 1 1 1 1 0 1 2 3 ² 1 0 1 1 1 2 1 3 ± c c 1 ² = ± 1 1 1 1 0 1 2 3 ² 1 2 1 4 ± 4 6 6 14 ²± c c 1 ² = ± 6 16 ² . The inverse of the matrix ± 4 6 6 14 ² is 1 4 · 146 · 6 ± 1466 4 ² = 1 20 ± 1466 4 ² . Hence ± c c 1 ² = 1 20 ± 1466 4 ²± 6 16 ² = 1 20 ±12 28 ² = 1 5 ±3 7 ² . Hence the bestﬁt line to the four points is y =3 5 + 7 5 x . 1...
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This note was uploaded on 04/02/2008 for the course MATH 33a taught by Professor Lee during the Fall '08 term at UCLA.
 Fall '08
 lee
 Math

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