A New Look at Worst Case Complexity: A Statistical Approach

Box 7

Regression analysis for versus , , and (randomized quicksort) on random data sequences (5 * 10⁵ ≤ ≤ 50 * 10⁵).

The regression equation is

Y = −8.38 + 1.90 n −  0.107  2 + 0.00174  3

PredictorCoefSE CoefTP

Constant−8.3784.456−1.880.109

n1.90250.66792.850.029

2−0.106750.02756−3.870.008

30.00174110.00033055.270.002

S = 2.29581R-Sq = 97.8%R-Sq(adj) = 96.7%

PRESS = 278.092R-Sq(pred) = 80.37%

Analysis of Variance

SourceDFSSMSFP

Regression31385.32 461.7787.610.000

Residual Error631.625.27

Total91416.95

SourceDFSeq SS

n1789.97

21449.04

31146.31

R denotes an observation with a large standardized residual.

Durbin-Watson statistic = 1.75322