Linear Algebra : Least Squares

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Example Questions

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Example Question #1 : Least Squares

Let , and , find the least squares solution for a linear line.

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The equation for least squares solution for a linear fit looks as follows.

 

 

Recall the formula for method of least squares.

 

Remember when setting up the A matrix, that we have to fill one column full of ones.

 

 

To make things simpler, lets make , and 

Now we need to solve for the inverse, we can do this simply by doing the following. We flip the sign on the off diagonal, and change the spots on the main diagonal, then we multiply by .

 

 

 

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