What is the “slope” of the parabola y = x 2 on [ 0 , 1 ] ? Find the best least squares me that fits the parabola at n evenly spaced points in the interval for (a) n = 10 and (b) n = 20 . Plot the parabola and the lines. What do you expect the result to be as n → ∞ ? (c) Find the minimum of the function F ( c 1 , c 2 ) = ∫ 0 1 ( x 2 − c 1 − c 2 x ) 2 d x , and explain its relation to the problem.
What is the “slope” of the parabola y = x 2 on [ 0 , 1 ] ? Find the best least squares me that fits the parabola at n evenly spaced points in the interval for (a) n = 10 and (b) n = 20 . Plot the parabola and the lines. What do you expect the result to be as n → ∞ ? (c) Find the minimum of the function F ( c 1 , c 2 ) = ∫ 0 1 ( x 2 − c 1 − c 2 x ) 2 d x , and explain its relation to the problem.
Solution Summary: The author calculates the best least squares line that fits the parabola y=x2 by using the command ‘x=1:0.1:1’ in MATLAB.
What is the “slope” of the parabola
y
=
x
2
on
[
0
,
1
]
? Find the best least squares me that fits the parabola at n evenly spaced points in the interval for (a)
n
=
10
and (b)
n
=
20
. Plot the parabola and the lines. What do you expect the result to be as
n
→
∞
? (c) Find the minimum of the function
F
(
c
1
,
c
2
)
=
∫
0
1
(
x
2
−
c
1
−
c
2
x
)
2
d
x
, and explain its relation to the problem.
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