I have 3 datasets of the same system. But for the first one, I have 21 measurements. For the second and the third one I have only 9 measurements. Now I made a model using these 3 datasets (so 3 models, 1 per dataset). When I want to compare the error between these two datasets. Is there a clear advantage by using the MSE in stead of the LSE (least squared error). On the internet I do not find a clear answer for this. What are the main advantages?
Solved – Mean squared error versus Least squared error, which one to compare datasets
least squaressums-of-squares
Best Answer
I think you're confusing how to build a model from data and how to quantify a model accuracy once it's built.
When you want to build a model (linear regression in your case I guess?), you would usually use the least square error method that is minimizing the "total" euclidean distance between a line and the data points. Theoretically the coefficients of this line can be found using calculus but in practice, an algorithm will perform a gradient descent which is faster.
Once you have your model, you want to evaluate its performances. Thus, in the case of regression, it may be good to compute a metric which evaluate "how far" is your model to the actual data points (or test set data if you have one) in average. The MSE is a good estimate that you might want to use !
To sum up, keep in mind that LSE is a method that builds a model and MSE is a metric that evaluate your model's performances.