Final answer:
The claim that a model with the highest adjusted R-squared has no noise variables is false. Although a higher adjusted R-squared may indicate a better model fit, it does not guarantee the absence of noise variables that do not contribute significantly to the predictive power and can lead to overfitting.
Step-by-step explanation:
The statement that a model with the highest adjusted R-squared (R2) has no noise variables is false. The adjusted R-squared value is used in statistics to give some idea of the goodness of fit of a model and adjusts for the number of explanatory variables in a model relative to the number of data points. While a higher adjusted R-squared indicates a potentially better fit, it does not guarantee that all included variables contribute significantly to the model; noise variables might still be present. Variables that are not genuinely predictive can 'accidentally' correlate with the dependent variable in a specific sample, and as a result, they can inflate both R-squared and adjusted R-squared.
An important concept related to this is overfitting, which occurs when a model learns the detail and noise in the training data to the extent that it negatively impacts the performance of the model on new data. Consideration of other metrics is necessary to ensure a robust model. Hence, while a high adjusted R-squared value is desirable, it is not a definitive indicator of the absence of noise variables.