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A certain experiment produces the data $(1,7.9),(2,5.4),$ and $(3,-9) .$ Describe the model that produces a least-squares fit of these points by a function of the form$y=A \cos x+B \sin x$

$X=\left[\begin{array}{cc}{\cos 1} & {\sin 1} \\ {\cos 2} & {\sin 2} \\ {\cos 3} & {\sin 3}\end{array}\right], y=\left[\begin{array}{c}{7.9} \\ {5.4} \\ {-0.9}\end{array}\right], \beta=\left[\begin{array}{l}{A} \\ {B}\end{array}\right]$ and $\epsilon=\left[\begin{array}{c}{\epsilon_{1}} \\ {\epsilon_{2}} \\ {\epsilon_{3}}\end{array}\right]$

Calculus 3

Chapter 6

Orthogonality and Least Square

Section 6

Applications to Linear Models

Vectors

Johns Hopkins University

Harvey Mudd College

Baylor University

Boston College

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question given is an experiment produces our data is thesis and we need to find a model that best feast or lead square method. Ah, function. Why questo Echo sex b sine x. Okay, so this points must satisfy the this equation. Plus, there will be some matter because there is no true function that can be obtained. Okay, so first point, if you take one and 7.9, so we have 7.9 is equals to eight times cause off one plus B times. Sign off one and there will be some error. One that will be generated or that will be present residue letter. Similarly, for second point, we'll have 5.4 is equals to a cause to plus B sine too. And some error toe and third will be minus nine. Is request toe a cost three plus b sine three plus some error. E three. Okay, so now we can represent this in matrix form as this is a wise. So we'll write it in the vector 7.95 point four, minus nine. Here this values can be representative metrics has cost one sign one cost to sign to cost three and sign three in this will be multiplied with a be victor. And we have error Error. One error to error. Three. Okay, so that is a model off the square method that will give us these functions. Well, thank you.

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