Research Article

A New Look at Worst Case Complexity: A Statistical Approach

Box 5

Regression analysis result for versus and (Box-Cox transformation) on random data sequences (5 * 105 ≤ 50 * 105).
General Regression Analysis:   versus ,
Box-Cox transformation of the response with specified lambda = 0.5
Regression Equation
0.5=2.39481   4.2737e    006 n + 2.34136e    009  
Coefficients
TermCoefSE CoefTP
Constant2.394810.8332612.874020.024
n0.000000.0000013.955140.005
0.000000.0000005.306210.001
Summary of Model
S = 0.606531R-Sq = 95.26%R-Sq(adj) = 93.90%
PRESS = 9.71668R-Sq(pred) = 82.10%
Analysis of Variance
SourceDFSeq SSAdj SSAdj MSFP
Regression251.707251.707225.853670.27740.0000233
n141.34935.75485.754815.64320.0054957
110.357910.357910.357928.15580.0011158
Error72.57522.57520.3679
Total954.2824
Fits and Diagnostics for Unusual Observations for Transformed Response
Obs0.5FitSE FitResidualSt Resid
   108.058417.203520.4627070.8548952.18002R
Fits for Unusual Observations for Original Response
ObsyFit
   1064.93851.8907R
R denotes an observation with a large standardized residual.