# Table 4 Simulation results when Y has an asymmetric distribution

Model A
$$\widehat{Y}=\widehat{\alpha}+\widehat{\beta}\cdotp X$$
Model B
$$\widehat{Y}=\widehat{\alpha}+\widehat{\beta}\cdotp { \log}_b(X)$$
Model C
$$\widehat{{ \log}_a(Y)}=\widehat{\alpha}+\widehat{\beta}\cdotp X$$
Model D
$$\widehat{{ \log}_a(Y)}=\widehat{\alpha}+\widehat{\beta}\cdotp { \log}_b(X)$$
Beta-hat coefficient and standard error from regression model $$\widehat{\beta}$$ = 0.625
se($$\widehat{\beta}$$) = 0.254
$$\widehat{\beta}$$ = 5.834
se($$\widehat{\beta}$$) = 2.441
$$\widehat{\beta}$$ = 0.011
se($$\widehat{\beta}$$) = 0.005
$$\widehat{\beta}$$ = 0.103
se($$\widehat{\beta}$$) = 0.044
Absolute change in Y for an absolute change of c units in X Effect size 0.625 0.557 0.551 0.493
95% CI (0.128–1.122) (0.101–1.013) (0.100–1.006) (0.080–0.909)
Absolute change in Y for a relative change of k times in X Effect size 0.625 0.557 0.551 0.493
95% CI (0.128–1.122) (0.101–1.013) (0.100–1.006) (0.080–0.909)
Relative change in Y for an absolute change of c units in X Effect size 1.0125 1.0111 1.0110 1.0099
95% CI (1.0026–1.0224) (1.0020–1.0203) (1.0020–1.0201) (1.0016–1.0182)
Relative change in Y for a relative change of k times in X Effect size 1.0125 1.0111 1.0110 1.0099
95% CI (1.0026–1.0224) (1.0020–1.0203) (1.0020–1.0201) (1.0016–1.0182)
1. Note: c = 1 and k = 1.1