| X1 X2 |
| X1 | Left-skewed covariate |
| X2 | Right- skewed covariate |
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| D1 binary |
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| (skewness, kurtosis) | Mean | SD | (S, K) Coefficient | SE | Power | Mean | SD | (S, K) Coefficient | SE | Power | Coefficient SE | SE | Power |
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| 70 | 8 | β1 = 0.05 |
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| 160 | 25 | β2 = 0.02 |
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| β2 = 0.83 |
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| Correlation of (X1, X2) = 0.0 |
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| (0.0 0.0, 0.0 0.0) | 70.0 | 8.0 | (0.0, 0.0) 0.051 | 0.015 | 0.943 | 160.1 | 25.0 | (0.0, 0.0) 0.020 | 0.005 | 0.997 | 0.846 | 0.233 | 0.947 |
| (−0.5 0.5, 0.0 0.0) | 70.0 | 8.0 | (−0.5, 0.5) 0.051 | 0.015 | 0.930 | 160.1 | 25.0 | (0.0, 0.0) 0.020 | 0.005 | 0.995 | 0.846 | 0.233 | 0.945 |
| (−1.0 1.0, 0.0 0.0) | 70.0 | 8.0 | (−1.0, 1.0) 0.051 | 0.016 | 0.919 | 160.1 | 25.0 | (0.0, 0.0) 0.020 | 0.005 | 0.996 | 0.843 | 0.233 | 0.942 |
| (0.0 0.0, 0.4 0.3) | 70.0 | 8.0 | (0.0, 0.0) 0.051 | 0.015 | 0.945 | 160.0 | 25.0 | (0.4, 0.3) 0.020 | 0.005 | 0.996 | 0.846 | 0.234 | 0.947 |
| (0.0 0.0, 0.8 0.6) | 70.0 | 8.0 | (0.0, 0.0) 0.051 | 0.015 | 0.938 | 160.0 | 25.0 | (0.8, 0.6) 0.020 | 0.005 | 0.997 | 0.843 | 0.234 | 0.950 |
| (−0.5 0.5, 0.4 0.3) | 70.0 | 8.0 | (−0.5, 0.5) 0.051 | 0.015 | 0.929 | 160.0 | 25.0 | (0.4, 0.3) 0.020 | 0.005 | 0.996 | 0.845 | 0.234 | 0.949 |
| (−1.0 1.0, 0.8 0.6) | 70.0 | 8.0 | (−1.0, 1.0) 0.051 | 0.016 | 0.922 | 160.0 | 25.0 | (0.8, 0.6) 0.020 | 0.004 | 0.999 | 0.841 | 0.234 | 0.945 |
| Correlation of (X1, X2) = 0.3 |
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| (0.0, 0.0) (0.0, 0.0) | 70.0 | 8.0 | (0.0, 0.0) 0.051 | 0.015 | 0.919 | 160.0 | 25.0 | (0.0, 0.0) 0.020 | 0.005 | 0.984 | 0.852 | 0.234 | 0.957 |
| (−0.5, 0.5) (0.0, 0.0) | 70.0 | 8.0 | (−0.5, 0.5) 0.051 | 0.016 | 0.903 | 160.0 | 25.0 | (0.0, 0.0) 0.020 | 0.005 | 0.988 | 0.852 | 0.233 | 0.960 |
| (−1.0, 1.0) (0.0, 0.0) | 70.0 | 8.0 | (−1.0, 1.0) 0.052 | 0.017 | 0.880 | 160.0 | 25.0 | (0.0, 0.0) 0.020 | 0.005 | 0.987 | 0.853 | 0.233 | 0.965 |
| (0.0, 0.0) (0.4, 0.3) | 70.0 | 8.0 | (0.0, 0.0) 0.051 | 0.015 | 0.920 | 160.0 | 25.0 | (0.4, 0.3) 0.020 | 0.005 | 0.990 | 0.850 | 0.234 | 0.953 |
| (0.0, 0.0) (0.8, 0.6) | 70.0 | 8.0 | (0.0, 0.0) 0.051 | 0.015 | 0.920 | 160.0 | 25.0 | (0.8, 0.6) 0.020 | 0.005 | 0.991 | 0.849 | 0.235 | 0.952 |
| (−0.5, 0.5) (0.4, 0.3) | 70.0 | 8.0 | (−0.5, 0.5) 0.051 | 0.016 | 0.902 | 160.0 | 25.0 | (0.4, 0.3) 0.020 | 0.005 | 0.992 | 0.852 | 0.234 | 0.954 |
| (−1.0, 1.0) (0.8, 0.6) | 70.0 | 8.0 | (−1.0, 1.0) 0.052 | 0.017 | 0.879 | 160.0 | 25.0 | (0.8, 0.6) 0.020 | 0.005 | 0.991 | 0.850 | 0.234 | 0.957 |
| Correlation of (X1, X2) = 0.6 |
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| (0.0, 0.0) (0.0, 0.0) | 70.0 | 8.0 | (0.0, 0.0) 0.051 | 0.018 | 0.811 | 160.0 | 25.0 | (0.0, 0.0) 0.021 | 0.006 | 0.949 | 0.853 | 0.235 | 0.962 |
| (−0.5, 0.5) (0.0, 0.0) | 70.0 | 8.0 | (−0.5, 0.5) 0.051 | 0.019 | 0.772 | 160.0 | 25.0 | (0.0, 0.0) 0.020 | 0.006 | 0.945 | 0.851 | 0.234 | 0.960 |
| (−1.0, 1.0) (0.0, 0.0) | 70.0 | 8.0 | (−1.0, 1.0) 0.052 | 0.020 | 0.753 | 160.0 | 25.0 | (0.0, 0.0) 0.020 | 0.006 | 0.951 | 0.853 | 0.233 | 0.966 |
| (0.0, 0.0) (0.4, 0.3) | 70.0 | 8.0 | (0.0, 0.0) 0.051 | 0.018 | 0.815 | 160.0 | 25.0 | (0.4, 0.3) 0.020 | 0.006 | 0.959 | 0.852 | 0.235 | 0.946 |
| (0.0, 0.0) (0.8, 0.6) | 70.0 | 8.0 | (0.0, 0.0) 0.051 | 0.018 | 0.819 | 160.0 | 25.0 | (0.8, 0.6) 0.020 | 0.005 | 0.970 | 0.850 | 0.236 | 0.947 |
| (−0.5, 0.5) (0.4, 0.3) | 70.0 | 8.0 | (−0.5, 0.5) 0.051 | 0.019 | 0.785 | 160.0 | 25.0 | (0.4, 0.3) 0.020 | 0.006 | 0.959 | 0.853 | 0.235 | 0.956 |
| (−1.0, 1.0) (0.8, 0.6) | 70.0 | 8.0 | (−1.0, 1.0) 0.052 | 0.020 | 0.757 | 160.0 | 25.0 | (0.8, 0.6) 0.020 | 0.005 | 0.979 | 0.850 | 0.234 | 0.966 |