Adjusted R-squared measures how well a regression model explains the variation in the data, corrected for the number of predictors used. Plain R-squared rises with every extra variable, even one that adds nothing; the adjusted version penalises unnecessary variables. This allows a fairer comparison of models of different sizes, for instance a sales forecast using three rather than ten factors.
Linear regression is a statistical method that describes the relationship between a target variable and one or more predictors using a straight line or plane. The coefficients are usually chosen to minimise the sum of squared deviations. The method is easy to understand and interpret: for example, it can estimate how much revenue rises when the advertising budget increases by €1,000. It reaches its limits with non-linear relationships.
Overfitting occurs when a model memorises the training data, including random quirks and noise, instead of capturing generally valid patterns. It then appears very accurate on familiar data but performs poorly on new data. A large gap between training and test error is a typical sign. Countermeasures include more or more varied data, simpler models, regularisation, dropout and cross-validation.
Mean absolute error (MAE) shows how far a model’s predictions deviate from the actual values on average, regardless of direction. It is expressed in the unit of the target variable, which makes it easy to understand. Example: an MAE of 12 for a daily sales forecast means the model is off by 12 units on average. It gives less weight to outliers than squared error measures do.
Regularisation covers techniques that stop a model from fitting its training data too closely during training (overfitting). Examples include penalising large weights (L1 or L2 regularisation), randomly switching off neurons (dropout) or stopping training at the right moment (early stopping). The aim is a simpler model that performs more reliably on new, unseen data, even if it scores slightly lower on the training data.
