An Application of Linear Algebra

Kevin McGoldrick - Math 345, Fall 2009

Least Squares Estimation

Practical Applications

Least squares estimation is commonly used in social sciences, e.g. economics and psychology.† As mentioned in the overview, when variables are theorized to have a simple linear relationship, it can be helpful to estimate the unknown slope and intercept.

 

In economics, variables such as an individualís income level may be posited as directly related to his/her education level.† Or, a nationís GDP could be dependent on unemployment conditions.† In psychology, a personís happiness level may be explained by the number of people they consider friends.† Any number of possibilities exist, and using linear algebra, i.e. least squares estimation, we can estimate these effects.

 

After collecting the data points, calculations are fairly simple as we have observed.† Note though, that the matrices could become fairly large, and thus computers may be required to find the least squares solution.††† There are also a number of other considerations to ensure that the least square solutions are unbiased and valid, however linear algebra is all we need to find the actual estimates.