I am regressing a growth measure (in fraction form, between 0 and 1) on another fraction that lies between 0 and 1 (let's call the variable ``share"). The regression is performed using OLS. What is the interpretation of my regression coefficient, b?
My best guess: a one unit change in the share changes growth by b units.
But what is a one unit change in the share? Is it the same as a 1% change? Moreover, does the same interpretation of a unit hold for the left-hand-side variable? That is, am I right to interpret the coefficient as: "for a 1% change in share, growth changes by b%"?
On a broader note, what unit measurement do we use for fractions?
EDIT: I'll now be more precise about my lack of understanding, as prompted by @NickCox. I have results from a number of regressions and I am struggling to understand the output. The key right-hand-side variable is a fraction between 0 and 1 (there are other controls in every regression). The left-hand-side varies: in some regressions it is a fraction between 0 and 1, in some it is a change (first-difference) in logs of a variable, and sometimes it is a dummy or indicator variable. I know the standard deviations of each variable, and I'd like to be able to interpret all of my coefficients on the key dependent variable in terms of a one standard deviation change in variable and in terms of a one unit change.
That is, I would like help interpreting the coefficient b -- in unit changes and standard deviations changes -- in the regression of a:
- Fraction on a fraction (and other controls)
- Change in log on a fraction (and other controls)
- Binary variable on a fraction (and other controls).
Note for the final model, I am using a linear-probability model (I'm confident of my choice of this model for other reasons, plus it is consistent with the literature).
Finally, a lot of my problems have come from reading published papers and trying to back out their logic for interpreting coefficients. There seems to be a lack of consistency. For example, I am studying a paper where the regression is a binary dependent variable regressed on a change (first-difference) in logs of a variable (estimated by OLS). The authors have interpreted the coefficient (-0.21) as: "a one standard deviation increase in the change in logs leads to a 6.3% percentage point decrease in the probability of an event"; a result that seems to come from dividing the coefficient by 1 over the standard deviation of the change in logs (1/0.3=3.33). Is this correct?