Least Squares Criterion

The least squares criterion is a method of finding the best fit line for a set of data points. It is based on the idea of minimizing the sum of the squared residuals, which are the vertical distances between the data points and the line.

The least squares criterion is a very common method of fitting lines to data, and it is used in a wide variety of applications, such as regression analysis, curve fitting, and signal processing.

The least squares criterion can be expressed mathematically as follows:

```
min?(yi-ˆyi)2
```

where yi is the observed value of the dependent variable for the ith data point, and ˆyi is the predicted value of the dependent variable for the ith data point.

The least squares criterion can be solved using a variety of methods, such as the normal equations, the Gauss-Newton method, and the Levenberg-Marquardt algorithm.

The least squares criterion is a very efficient method of fitting lines to data, and it is often the method of choice when the goal is to find the line that best minimizes the sum of the squared residuals.

However, the least squares criterion can sometimes be biased, especially when the data is noisy or when there are outliers. In these cases, it may be better to use a different method of fitting lines to data, such as the robust regression method.