Method of Least Squares (Statistics)/Examples

Examples of Use of Method of Least Squares in context of Statistics

Linear Response

Let the expected value of an observation be of the form:

$\expect y = \alpha + \beta x$

Let a set of $n$ paired observations $\tuple {x_i, y_i}$ be given.

The least squares estimators of the unknowns $\alpha$ and $\beta$ are the values $a$ and $b$ which minimise:

$\ds \sum_i \paren {y_i - a - b x_i}^2$