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as a measure of model validity is that it can always be increased by adding more variables into the model, except in the unlikely event that the additional variables are exactly uncorrelated with the dependent variable in the data sample being used.
This problem can be avoided by doing an F-test of the statistical significance of the increase in the R, or by instead using the adjusted R2.
If, for example, the out-of-sample mean squared error, also known as the mean squared prediction error, is substantially higher than the in-sample mean square error, this is a sign of deficiency in the model.I made an entry in the Stack Overflow Documentation explaining how to do this: Any validation needs a context to give some information about what is being validated.This can include various information such as the object to be validated, some properties, the name to display in the error message, etc.Different types of plots of the residuals from a fitted model provide information on the adequacy of different aspects of the model.Numerical methods also play an important role in model validation.
If the model fit to the data were correct, the residuals would approximate the random errors that make the relationship between the explanatory variables and the response variable a statistical relationship.