# Science:Math Exam Resources/Courses/MATH152/April 2012/Question 05 (a)

MATH152 April 2012
Other MATH152 Exams

### Question 05 (a)

You wish to fit the line y(x)=ax+b to the data points

$(x_{1},y_{1})=(2,2),\quad (x_{2},y_{2})=(3,4),\quad (x_{3},y_{3})=(5,6).$ Write down the normal equations (check formula sheet if you do not remember) for the least squares approximation of the parameter vector $\mathbf {x} ={\begin{bmatrix}a\\b\end{bmatrix}}$ to the data. Then, write down the augmented matrix that corresponds to these equations one would use to compute the least squares approximation of a,b (but you don't need to compute a,b). Describe the least squares projection as a projection in three space onto a plane; specifically which vector is being projected onto which plane.

Formula sheet

The least squares best solutionto $B{\vec {x}}={\vec {c}}$ is given by the normal equations$B^{T}B{\vec {x}}=B^{T}{\vec {c}}$ .

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