Question

What are the limitations to using R-Squared as a measure of the validity of a model?

Answer 1

The R-squared should not be used for model validation. This is a value that you look at when you have validated your model.

Explanation:

A linear model is validated if the data are homogeneous, follow a normal distribution, the explanatory variables are independent and if you know exactly the value of your explanatory variables (narrow error on X)

The R-squared can be used to compare two models that you already validated. The one with the highest value is the one that best fit the data. However, it might exist better indices, like the AIC (Akaike criterion)