coefficient magnitude "An interpretation based on coefficient magnitude also suggests that an increase of
x (independent variable) by one standard deviation is associated with the
increase of y (dependent variable by 2.63% of its standard deviation."
Could somebody explain to me the formula for calculating 2.63%?
The coefficient of the x is 0.05 and I have other information like mean, std, and standard error
Thanks

You have some variable $x$ in the regression. Calculate the standard deviation of $x$, which we will call $s_x$.
You have the coefficient on $x$ in the regression, which we will call $\hat\beta_x$.
To determine how much changes in $y$ is associated with a change in $x$ of $s_x$, multiply $s_x\times\hat\beta_x$.
Now we know by how much $y$ changes when $x$ changes by one standard deviation. To determine how many standard deviations of $y$ that is, divide by the standard deviation of $y$. If you then want this in terms of percent, multiply by $100\%$.
Overall, this corresponds to $\dfrac{s_x\hat\beta_x}{s_y}\times 100\%$.
Note that all of this assumes a linear model. If you have a nonlinear model or a linear model that acts on nonlinear functions of the original variables (e.g., $x$ and $x^2$ are in the model), then this does not work, as one characteristic of nonlinearity is that the rate of change (related to $\hat\beta_x$) is not constant.
