  A novel regression method is introduced and studied. The procedure weights
squared residuals based on their magnitude. Unlike the classic least squares
which treats every squared residual equally important, the new procedure
exponentially down-weights squared-residuals that lie far away from the cloud
of all residuals and assigns a constant weight (one) to squared-residuals that
lie close to the center of the squared-residual cloud.
  The new procedure can keep a good balance between robustness and efficiency,
it possesses the highest breakdown point robustness for any regression
equivariant procedure, much more robust than the classic least squares, yet
much more efficient than the benchmark of robust method, the least trimmed
squares (LTS) of Rousseeuw (1984).
  With a smooth weight function, the new procedure could be computed very fast
by the first-order (first-derivative) method and the second-order
(second-derivative) method.
  Assertions and other theoretical findings are verified in simulated and real
data examples.
