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Table 2 Actual, refitted, and recovered covariance matrices of non-weighted regression coefficients in equations

From: Model errors in tree biomass estimates computed with an approximation to a missing covariance matrix

Eq # Actual Refitted Recovered Recovered
(robust)
P 1
×100
P 2×100 P 3
×100
1 \(\left( {\begin{array}{*{20}c} {2.62 \times 10^{ - 3} } & { - 0.132} \\ { - 0.132} & {8.67} \\ \end{array} } \right)\) \(\left( {\begin{array}{*{20}c} {3.30 \times 10^{ - 3} } & { - 0.179} \\ { - 0.179} & {11.4} \\ \end{array} } \right)\) \(\left( {\begin{array}{*{20}c} {2.75 \times 10^{ - 3} } & { - 0.154} \\ { - 0.154} & {10.2} \\ \end{array} } \right)\) \(\left( {\begin{array}{*{20}c} {3.01 \times 10^{ - 3} } & { - 0.167} \\ { - 0.167} & {10.9} \\ \end{array} } \right)\) 0.5 64 68
2 \(\left( {\begin{array}{*{20}c} {0.267} & { - 0.746} \\ { - 0.746} & {2.25} \\ \end{array} } \right)\) \(\left( {\begin{array}{*{20}c} {0.316} & { - 0.871} \\ { - 0.871} & {2.53} \\ \end{array} } \right)\) \(\left( {\begin{array}{*{20}c} {0.240} & { - 0.677} \\ { - 0.677} & {2.33} \\ \end{array} } \right)\) \(\left( {\begin{array}{*{20}c} {0.264} & { - 0.740} \\ { - 0.740} & {2.19} \\ \end{array} } \right)\) 99 95 98
5 \(\left( {\begin{array}{*{20}c} {1.14 \times 10^{ - 3} } & { - 0.605 \times 10^{ - 1} } \\ { - 0.605 \times 10^{ - 1} } & {3.56} \\ \end{array} } \right)\) \(\left( {\begin{array}{*{20}c} {1.39 \times 10^{ - 3} } & { - 0.598 \times 10^{ - 1} } \\ { - 0.598 \times 10^{ - 1} } & {3.00} \\ \end{array} } \right)\) \(\left( {\begin{array}{*{20}c} {1.02 \times 10^{ - 3} } & { - 0.436 \times 10^{ - 1} } \\ { - 0.436 \times 10^{ - 1} } & {2.21} \\ \end{array} } \right)\) \(\left( {\begin{array}{*{20}c} {1.08 \times 10^{ - 3} } & {0.465 \times 10^{ - 1} } \\ {0.465 \times 10^{ - 1} } & {2.35} \\ \end{array} } \right)\) 4 6 7
6 \(\left( {\begin{array}{*{20}c} {1.47 \times 10^{ - 1} } & { - 0.383} \\ { - 0.383} & {1.04} \\ \end{array} } \right)\) \(\left( {\begin{array}{*{20}c} {2.00 \times 10^{ - 1} } & { - 0.469} \\ { - 0.469} & {1.15} \\ \end{array} } \right)\) \(\left( {\begin{array}{*{20}c} {1.38 \times 10^{ - 1} } & { - 0.319} \\ { - 0.319} & {0.785} \\ \end{array} } \right)\) \(\left( {\begin{array}{*{20}c} {1.46 \times 10^{ - 1} } & { - 0.338} \\ { - 0.338} & {0.831} \\ \end{array} } \right)\) 5 36 36
9 \(\left( {\begin{array}{*{20}c} {5.53 \times 10^{ - 4} } & { - 0.322 \times 10^{ - 1} } \\ { - 0.322 \times 10^{ - 1} } & {2.19} \\ \end{array} } \right)\) \(\left( {\begin{array}{*{20}c} {1.33 \times 10^{ - 3} } & { - 0.636 \times 10^{ - 1} } \\ { - 0.636 \times 10^{ - 1} } & {3.44} \\ \end{array} } \right)\) \(\left( {\begin{array}{*{20}c} {5.61 \times 10^{ - 4} } & { - 0.273 \times 10^{ - 1} } \\ { - 0.273 \times 10^{ - 1} } & {1.50} \\ \end{array} } \right)\) \(\left( {\begin{array}{*{20}c} {6.05 \times 10^{ - 4} } & { - 0.293 \times 10^{ - 1} } \\ { - 0.293 \times 10^{ - 1} } & {1.61} \\ \end{array} } \right)\) 4 3 5
10 \(\left( {\begin{array}{*{20}c} {7.84 \times 10^{ - 2} } & { - 0.227} \\ { - 0.227} & {0.697} \\ \end{array} } \right)\) \(\left( {\begin{array}{*{20}c} {1.27 \times 10^{ - 1} } & { - 0.499} \\ { - 0.499} & {0.86} \\ \end{array} } \right)\) \(\left( {\begin{array}{*{20}c} {8.20 \times 10^{ - 2} } & { - 0.210} \\ { - 0.210} & {0.561} \\ \end{array} } \right)\) \(\left( {\begin{array}{*{20}c} {8.82 \times 10^{ - 2} } & { - 0.225} \\ { - 0.225} & {0.599} \\ \end{array} } \right)\) 12 15 19
  1. Actual covariance matrices are based on a sample size of 50. P i (i = 1, 2, 3) is the probability under H 0 of: (1) actual = refitted; (2) actual = recovered; (3) actual = robust. See Table 1 for reference to equation numbering.