This example was taken from Mathematical Statistics : A Unified Introduction (ISBN 9780387227696), page 58, under the section 'The Principle of Least Squares'. I think my problem has more to do with algebra but since this is a statistics book, I thought I should post here...
Anyway, I need to estimate k base on this equation:
The goal is to reach here:
I managed to follow the example until I got stuck here:
The explanation to reach to the goal from above is described as follows:
I know how to get k but I totally don't understand how the 'middle term' was eliminated. Please help. I will provide more details if needed.