methodology of least squares

Paper instructions:

The methodology of least squares is used to fit lines to a set of data points, and is widely used in business, science and engineering (and many other areas too, but these are the most common). By trying to understand what lines best fit the data, especially experimental data, scientists and engineers can (within limits) try to predict how the data will behave in the future. In statistics the technique is called “fitting a regression line” and the topic area is called “regression analysis”.

So let’s talk about how the technique of least squares is used in the real world – whether it is in business, science, engineering, and/or the military. Most commonly it will be used as part of regression analysis, but you may find it used on its own as well. What are some typical real world situations where you find it being used? Pick one such situation and describe it in some detail. What was the most interesting – or surprising – thing you learned about how the technique is put to use?

Sometimes students will create an original math homework-type example as it applies to a particular situation, and even work out the numbers, but not do any internet research.

You can also search online to find least squares and regression applications and examples. Some good websites to start out with are listed below (but there are many, many others online, so please don’t limit yourself to these):

http://en.wikipedia.org/wiki/Least_squares

http://illuminations.nctm.org/LessonDetail.aspx?ID=U117

http://www.math.sjsu.edu/~bremer/Teaching/Math261A/LectureNotes/Lecture02.pdf

https://www.khanacademy.org/math/probability/regression/regression-correlation/v/squared-error-of-regression-line

http://mathworld.wolfram.com/LeastSquaresFitting.html

Be sure to include the source(s) you use in your post.