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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
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                            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
-------------------------------------------------------
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I think there is no need to do log-transform given that your purpose is to see "if wage growth/decline throughout one's career is correlated with the number of children they have." All you need is a variable that measures wage change, a variable that measures number of children, and a correctly specified regression function(or a set of good control variables with correct functional form). Suppose your regression function is correcly specified as follows:

$Y_i=\beta_0+\beta_1X_i+\gamma'\mathbf{Z}_i+\epsilon_i$ 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.

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  • $\begingroup$ Thanks, that makes sense! I have updated my post with some results, thoughts? $\endgroup$ – maa425 May 22 at 22:12
  • $\begingroup$ @maa425 So is the coefficient in front of X exactly zero? $\endgroup$ – JTS365 May 22 at 22:33
  • $\begingroup$ Correct, it is statically significant and the coefficient is exactly = 0.00 $\endgroup$ – maa425 May 22 at 22:45
  • $\begingroup$ @maa425 Hmm, looks like something is wrong here. This is not the significance we want as your standard error is 0 and your t-statistic is infinity. Can you check your data, for example, can you give me summary statistics of all variables? $\endgroup$ – JTS365 May 22 at 23:14
  • $\begingroup$ Thanks, you are correct. I have made an error in measuring wage growth rates, will revise and update results. $\endgroup$ – maa425 May 23 at 0:50

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