# Interpreting Regression Results with Ratio Independent Variable

I am running a simple regression as part of an exploratory data analysis with my dataset, where my outcome is the number of children that an individual has and my primary X is the average change in their wages throughout their career. The current form of average change in wages is a decimal number (i.e. .10 if average wage is 10%, .03 if 3% etc...)

I essentially would like to see if wage growth/decline throughout one's career is correlated with the number of children they have.

However, I was wondering if I should use log-transformations to standardize my Y and X variables as it does not seem intuitive to interpret the results with my independent variable being a ratio or decimal number, while my is an integer.

A simple regression for a random sample of 1000 individuals out of 80K in the overall sample shows the following, and that's why I was not sure how to interpret the findings clearly:

Standard errors: OLS
-------------------------------------------------------
Est.   S.E.   t val.      p
------------------------- ------ ------ -------- ------
(Intercept)                 5.57   0.26    21.68   0.00
average_growth_rate         0.00   0.00      Inf   0.00
-------------------------------------------------------


$$Y_i=\beta_0+\beta_1X_i+\gamma'\mathbf{Z}_i+\epsilon_i$$ with $$E(\epsilon_i|X_i,\mathbf{Z}_i)=0$$ and $$\mathbf{Z}_i$$ is the vector of control variables. Then $$E(Y|x,\mathbf{z})=\beta_0+\beta_1x+\gamma'\mathbf{z}$$ and $$\beta_1=\frac{\partial E(Y|x,\mathbf{z})}{\partial x}$$. In your problem, $$X$$ is average change in their wages throughout their career measured in percentage and $$Y$$ is the number of children that an individual has, then $$\beta_1$$ is interpreted as if career wage change by 1 percentage, holding other things constant, how many more children on average will people have. I guess this is intuitive enough to understand.