Residuen en de kleinste-kwadratenmethode

Consider the weekly data for the number of positive results versus COVID tests during the pandemic. A regression line drawn on the scatter plot shows a linear trend between the variables.

Whether this regression line is the best fit line is determined using residuals- the vertical distances of the original data points from the predicted values on the regression line.

For example, for the data point with coordinates 820 and 48, the predicted value can be found by substituting x with 820 in the regression equation.

The difference between the observed and predicted values gives the residual value. Similarly, residuals for the remaining data points are also calculated.

The square of these residuals can be visualized by drawing square areas using the original point.

The sum of the area of all these squares must be a minimum for the regression line to be the best fit line. This is called the least-squares property.

For any other straight line, the sum of the areas is higher, hence cannot be considered the best fit line.