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I'm a little confused about how to interpret coefficients when the dependent variable is a proportion/fraction and the independent variables are absolute numbers. For example, let's say I have a regression of the following form:

share of villages with roads = a +b*(money invested by government) +e , where investment is in USD. In this case, how will I interpret b coefficient? If investment increases by 1 USD, does the share of villages increase by b percent? b percentage points? b/100 percent?

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In general, b tells you how many units y changes when x changes by 1 unit. Therefore, in your setting, if Gov investment increases by +1 USD, then the share of villages with roads increases by b.

You have to be careful about what measures/transformations you are using, and think about which one gives you a (more) meaningful interpretation. Also, beware of heteroskedasticity!

As a side note, the interpretation of b changes when logs are used. In particular:

  • if y is in levels and x is in logs, then b/100 is the units change in y when x changes by 1%.
  • if y is in logs and x is in levels, then b is the % change in y when x changes by 1 unit.
  • if y is in logs and x is in logs, then b is the % change in y when x changes by 1%.
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