Assuming doing a 10-fold cross validation for linear regression (Y = AX + B). It is possible that 10 different As and Bs would be generated, one for each model learned.

Question

Assuming doing a 10-fold cross validation for linear regression (Y = AX + B).  It is possible that 10 different As and Bs would be generated, one for each model learned.

BlackTom AI · Accepted Answer

Here is how to think about the question and each option in turn.
Option 1: True. In 10-fold cross-validation for linear regression, the training data for each fold typically differs from the others because the data is partitioned into 10 distinct training sets (each leaving out a different 1/10th subset for validation). Since the least squares solution (the coefficients A and intercept B) depends on the particular training data, it is entirely possible for each fold to yield a different pair of coefficients. Even though the underlying model form is the same, the estimated parameters can change because the input data used to fit the model changes across folds.
Option 2: False. This would claim that it is impossible to obtain different A and B across folds. However, unless every training set is identical (which would defeat the purpose of cross-validation), the training data across folds are not the same, so the resulting parameter estimates can differ. Therefore, this statement contradicts the fundamental behavior of cross-validated model fitting and is incorrect.
Additional nuance: while it is possible that some folds produce identical coefficients (for example, if the added variation in the training set does not affect the least-squares solution due to collinearity or identical design matrices in certain folds), the general expectation in 10-fold CV is that you will obtain a variety of parameter estimates across folds because the training sub-datasets are different. This supports the notion that multiple different (A, B) pairs can be learned across folds.
In summary, given the standard cross-validation procedure with varying training data across folds, the statement that 10 different A and B could be generated is consistent with how the estimates are derived and is therefore true.

Assuming doing a 10-fold cross validation for linear regression (Y = AX + B). It is possible that 10 different As and Bs would be generated, one for each model learned.

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