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

You wish to fit the line y(x)=ax+b to the data points Write down the normal equations (check formula sheet if you do not remember) for the least squares approximation of the parameter vector 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.
The least squares ``best solution``to is given by the ``normal equations``. 
Make sure you understand the problem fully: What is the question asking you to do? Are there specific conditions or constraints that you should take note of? How will you know if your answer is correct from your work only? Can you rephrase the question in your own words in a way that makes sense to you? 
If you are stuck, check the hint below. Consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it! 
Hint 

Recall that where and our B matrix is
and
To see whats going on, if you expand out these matrices, you get

Checking a solution serves two purposes: helping you if, after having used the hint, you still are stuck on the problem; or if you have solved the problem and would like to check your work.

Solution 

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Please rate my easiness! It's quick and helps everyone guide their studies. or, in other words, So the augmented matrix is The vector is projected to the colum space of the matrix B (ColB) which is the plane spanned by the column vectors of B, namely 