Robust Estimates of Graduation Rates Model - N=51 U.S. States

OLS: ordinary least squares, full data set
OLS(-3): ordinary least squares, excluding NM, AK, DC
NLLS: non-linear iterated least squares (note: same as OLS)
ABS: minimize sum of abolute values of residuals
HUBER: minimize sum of MAD standardized residuals weighted by Huber(1.7)
HAMPEL: minimize sum of MAD standardized residuals weighted by Hampel (1.7,3.4,8.5)
BISQ: minimize sum of MAD standardized residuals weighted by Bisquare (7)
TRIM(5): 5% residuals with largest absolute values trimmed (49 cases left)
T: weight based on the Student t distribution

Model: grad = b0 + b1*inc + b2*pbla + b3*phis + b4*edexp + b5*urb

(t-ratios in parentheses)
 
Parameter OLS OLS(-3) NLLS ABS HUBER HAMPEL BISQ TRIM(5) T
B0 69.042 62.613 69.042 65.079 67.522 67.522 68.367 70.573 66.017
(12.851) (10.082) (12.851) -- (12.382) (12.382) (12.709) (12.676) (11.988)
B1 .002 .002 .002 .003 .002 .002 .002 .002 .002
(2.225) (2.944) (2.225) -- (2.519) (2.519) (2.353) (1.929) (2.769)
B2 -.414 -.452 -.414 -.373 -.416 -.416 -.412 -.408 -.411
(-6.622) (-5.494) (-6.622) -- (-6.705) (-6.705) (-6.666) (-6.256) (-6.730)
B3 -.407 -.759 -.407 -.428 -.486 -.486 -.427 -.367 -.514
(-3.483) (-4.718) (-3.483) -- (-3.604) (-3.604) (-3.462) (-3.022) (-3.539)
B4 -.001 -.001 -.001 -.003 -.002 -.002 -.001 -.001 -.002
(-.944) (-.674) (-.944) -- (-1.066) (-1.066) (-.985) (-.798) (-1.198)
B5 -.108 -.110 -.108 -.190 -.118 -.118 -.114 -.117 -.128
(-2.353) (-2.324) (-2.353) -- (-2.520) (-2.520) (-2.454) (-2.444) (-2.634)
R2 - Raw -- -- .996 .995 .996 .996 .996 .996 .996
R2 - MC  .624 .684 .624 .587 .618 .618 .623 .619 .611
R2 - OP -- -- .624 .597 .620 .620 .624 .621 .615

Notes:
R2 - Raw: Regression SS/Total SS (means not removed)
R2 - MC: Corrected for means
R2 - OP: Squared correlation of observed and predicted values of Y
MAD: Median absolute deviation from the median of the residuals


Last modified 7 April 1999