# Fitting least square approximations

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## The Attempt at a Solution

Thanks in advance for the help.

The problem I'm having is not so much as to how to solve the problem, but how to proceed using MATLAB. I'm having trouble figuring out how to enter in the respective components of this question into MATLAB.

The method I will try to solve this is by normal equations. To do this, I have to at least first specify what my A, b and x matrix/vectors are.

From here, I had that A is a matrix given by

A = [1 t1^2 t2^3 t3^4]
[1 t1^2 t2^3 t3^4]
[etc ]

and x is given by

x = [x1]
[x2]
[x3]
[x4]

b is given by

b = [phi(1)]
[phi(2)]
[phi(3)]
[phi(4)]

So my question is, how do I define these into matrix form without having actual numerical data points? We've only been shown how to approximate using normal equations/QR factorization, but with numerical data points, hence we could define the matrices.

t = -1:0.1:1
A = [t.^0 , t.^1, t.^2, t.^3]

then after entering in the matrices, would then proceed to using backslash to solve hence plotting the approximation?

Any help, hint would be much appreciated.

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