Table 1 Comparisons between parameters obtained using ordinary least squares (OLS) and total least squares method (TLS)

Antarctic snow

(Case 1, n = 178)

Slope ± standard error

7.00 ± 0.08

7.16 ± 0.08

Intercept

− 5.89 ± 0.94

– 4.05 ± 0.95

R²

0.978

0.977

Water vapor

(Case 2, n = 48)

Slope

7.75 ± 0.14

7.87 ± 0.14

Intercept

10.06 ± 2.40

12.01 ± 2.42

R²

0.985

0.984

Precipitation of Jeju island (S^*, n = 156; W^*, n = 147, Case 3)

Slope

8.09 ± 0.14 (S)

7.86 ± 0.11 (W)

8.45 ± 0.15 (S)

8.09 ± 0.13 (W)

Intercept

9.56 ± 1.16 (S)

21.03 ± 0.82 (W)

12.54 ± 1.16 (S)

22.60 ± 0.94 (W)

R²

0.956 (S)

0.972 (W)

0.954 (S)

0.962 (W)

Slope

7.9 ± 0.05 (1)

7.59 ± 0.08 (2)

8.18 ± 0.05 (1)

8.47 ± 0.09 (2)

Random samples (1, 2, n = 1000)

Intercept

9.14 ± 0.37 (1)

7.08 ± 0.65 (2)

11.17 ± 0.37 (1)

13.67 ± 0.68 (2)

R²

0.966 (1)

0.895 (2)

0.964 (1)

0.870 (2)