I know that AdaBoost can be used for classification, but how about regression?
With classification, it is clear how to assign the "amount of say" (or weight) to the predictions of each model (stump) in the final ensemble of models. Each of the stumps will make different errors. Would it be reasonable to weight each of the model's prediction according to the mean (mean squared) error?
AdaBoost is a meta-algorithm, which means it can be used together with other algorithms for perfomance improvement. Indeed, the concept of boosting is a type of linear regression.
Now, specifically answering your question, AdaBoost is actually intented for classification and regression problems. Scikit-Learn, for example, has an implemetation of an Adaboost regressor:
An AdaBoost regressor is a meta-estimator that begins by fitting a regressor on the original dataset and then fits additional copies of the regressor on the same dataset but where the weights of instances are adjusted according to the error of the current prediction. As such, subsequent regressors focus more on difficult cases.
