OLS

In the case of predicting personality from smartphone behavior, according to a priori estimation by the formula, the expected out-of-sample R² of OLS is insufficient to exceed the sample mean baseline (i.e., it is less than or equal to 0), whereas the expected performance of ridge regression can surpass that baseline.

When covariates are imbalanced or skewed, some observations become high-leverage points that exert a disproportionate influence on the regression coefficients, so that even with the same N and p, out-of-sample predictive performance can differ greatly.

In OLS, leverage values are given by the diagonal elements h_ii of the hat matrix H = X(XᵀX)⁻¹Xᵀ, satisfying 0 ≤ h_ii ≤ 1 and Σh_ii = p+1 (when an intercept is included).

The paper's analytical framework is based on leave-one-out cross-validation (LOOCV), and derives the expected out-of-sample performance for OLS and ridge regression separately.

In OLS, the LOOCV residual can be written as e_i/(1-h_ii), where h_ii is exactly the leverage value, which explains why D* naturally enters the formula for expected out-of-sample performance.

Delegated authentication ensures that the agent's access scope for semantic models and reports, as well as RLS and OLS restrictions, is consistent with the logged-in user and cannot bypass security policies.

OLS controls whether users can see specific tables or columns, and columns hidden by OLS do not expose even their field names.

After violating the homoscedasticity assumption, OLS parameter estimates remain unbiased but no longer have minimum variance, and standard error estimates become incorrect.

The Gauss-Markov theorem states that when the error terms satisfy the three conditions of zero mean, homoscedasticity, and no autocorrelation, the OLS estimator is the Best Linear Unbiased Estimator (BLUE).