In the recitation video "Least Squares Approximation," the instructor solves At*A for the following:

[ 1 2 -1 ]
[ 1 4 1 ]
*
[ 1 1 ]
[ 2 4 ]
[-1 1 ]

and gets:
[ 6 8 ]
[ 8 10 ]

However, shouldn't entry [2,2] be (1*1 + 4*4 + 1*1) = 18?? How does he get 10 for entry [2,2]?

Question

In the recitation video "Least Squares Approximation," the instructor solves At*A for the following:

[ 1 2 -1 ] 
[ 1 4   1 ]
*
[  1  1 ]  
[  2  4 ]
[-1  1 ]

and gets: 
[ 6  8   ]
[ 8  10 ]

However, shouldn't entry [2,2] be (1*1 + 4*4 + 1*1) = 18??  How does he get 10 for entry [2,2]?

anonymous · Answer

I had the same question. I tried fitting that matrix in Matlab and came up with a different answer - 1.86 and 0.227 for the c and d, respectively. By hand I get 123/66 and 5/22.