Outlier-Resistant 𝐿_𝟏 Orthogonal Regression via the Reformulation-Linearization Technique

Table 4

Summary of regression models for IBI on QHEI, pH, and alkalinity (ALK) using 𝐿₁OR, 𝐿₂OR, ppOR-mad, ppOR-qn, CH, and PCA-𝐿₁.

Method	Variable	Estimate	Standard error∗	T value	𝑃 value
𝐿1OR	QHEI	−0.67248	5.58039	−0.12051	.90433
	pH	0.70695	9.31363	0.07591	.93965
	ALK	−1.26714	5.60148	−0.22622	.82150
𝐿2OR	QHEI	0.17841	5.79662	0.03078	.97551
	pH	−11.25396	86.54848	−0.13003	.89681
	ALK	3.97315	64.00076	0.06208	.95062
ppOR-mad	QHEI	0.07038	5.57955	0.01261	.98996
	pH	4.31182	68.31064	0.06312	.94980
	ALK	−4.36975	41.89404	−0.10430	.91714
ppOR-qn	QHEI	−1.88655	4.41714	−0.42710	.67024
	pH	21.51640	83.28626	0.25834	.79668
	ALK	−13.92729	60.63738	−0.22968	.81881
CH	QHEI	0.33704	3.75244	0.08982	.92861
	pH	21.25614	53.26711	0.39905	.69072
	ALK	−21.16159	67.57228	−0.31317	.75481
PCA-𝐿1	QHEI	−0.97810	9.09927	−0.10749	.91462
	pH	−3.61571	107.89751	−0.03351	.97333
	ALK	3.33549	79.46839	0.04197	.96661

∗Standard errors are bootstrap standard errors based on 100 bootstrap samples.