# Calculating income elasticity of demand

My model is as follows: $$Y=\beta_0+\beta_1X_1+\beta_2X_2+\beta_3X_3+\beta_4X_4.$$

My income variable is represented by $X_2$. When it comes to calculating the income elasticity of demand (demand being represented by $Y$) I am aware that the formula is $\beta \frac{\bar{I}}{\bar{Q}}$, where $I$ is income and $Q$ is the demand variable.

My question is, when running a least squares regression, using EViews, would I run a regression with my $Y$ dependent variable and all my other independent variables ($X_1, X_2, X_3, X_4$ and the intercept) or do I just run the regression with $Y$ and $X_2$? (In this case are we assuming that all other variables do not matter? Or that we are holding these other variables constant?).

Moreover, I am aware that one can log the values in a regression and then extract the coefficient value as the elasticity value without needing to conduct more calculations. In this case, would we run the regression with $\log{Y}$ dependent variable and all my other independent variables logged ($X_1, X_2, X_3, X_4$ and the intercept) or do I just run the regression with $\log{Y}$ and $\log{X_2}$, or do I include the other independent variables and only log the $Y$ variable and $X_2$ variable.

I hope my question makes some sense. Essentially, I want to understand how one would calculate the income elasticity of demand in EViews based on the above model.

Any help with be greatly appreciated. Thank you.