The interpretation of the economic significance in level-log and log-level models

I have the following two models. The first is a level-log model, and the second is a log-level model. These models are two separate regressions and are estimated independently. Assume that α=0.036 and β=0.549. Based on these values, I want to calculate the economic significance of the effects of my independent variables as follows:

Change in the dependent variables in response to one standard deviation increase in the independent variables.

Suppose that after multiplying α and β with the respective standard deviations, the final values are equal to 0.020 and 0.120.

Will you please tell me how should I interpret these two number? in %? How much change is observed in my dependent variable in levels if the independent variable in log increases by 0.020?

I know how to interpret coefficients in level-log model and log-level models but got a bit confused here.

Interpretation of $$\alpha$$ : one percent change in $$X_{it}$$ is associated with $$\alpha * \ln\left(\frac{101}{100}\right)$$ change in $$Y_{it}$$.
Interpretation of $$\beta$$ : an increase of one-unit in the Height would result in $$\left(e^\beta - 1\right)*100\%$$ change in $$Y_{it}$$.
• I suppose 0.02 is $\frac{\alpha}{sd_\alpha}$. If it's this then, the coefficient $\alpha$ will be significant if 0.02 is greater than $t_{(3),\alpha}$ a student statistic. – Abdoul Haki May 27 at 19:27