From the multiple measurements, we might have noise and inexactitudes that prevent us from fitting a line (the known relationship between variables). For that, we want to fit a line, but we need to know if it’s a good fit. For that, we define what’s called an objective function. From it, we can find the line that minimizes the objective function.
Finding the distance between that line and each of the values can be done through the distance:
- In the distance: the horizontal displacement between the point and the line — it doesn’t make a lot of sense
- The distance perpendicular to the line that crosses the point, this makes sense for some machine learning models (like Classifiers)
- The distance: the vertical displacement between the point and the line — this is the one that we’ll use most of the time, representing the distance between the predicted value by the line and the actual value from the measurement.