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Stoica, P., and Ganesan, G., Linear Regression Constrained to a Ball, Digital Signal Processing11 (2001), 80–90. A worst case lower bound (WCLB) result obtained by Nemirovskii suggests that a potentially significant estimation accuracy enhancement may be achieved provided the true parameter vector is known to belong to a ball. In this paper we discuss the many facets and implications of Nemirovskiirs result by using linear regression as a vehicle for illustration. In particular, we address briefly such issues as biased versus unbiased estimation, minimax optimal estimation, tightness of the WCLB, and comparison of WCLB with the performance of the least squares estimator constrained to the ball and that of the linear minimax estimator.