# Multiplying coefficients of logistic regression to get per 10 unit increase?

I'm working on a project in R where I'm looking at California's census tract-level demographic data in an explanatory logistic regression model. I have 6 demographic variables of interest and am controlling for population density. My binary predictor is 1=exposed to pollutant/0=unexposed to pollutant for each census tract. Here is the summary of my log regression in R:

                    Estimate Std. Error z value Pr(>|z|)
(Intercept)         0.767410   0.782963   0.980 0.327019
percent_unemployed -0.089417   0.036507  -2.449 0.014312 *
percent_minority   -0.008516   0.011571  -0.736 0.461755
percent_no_diploma  0.053393   0.021160   2.523 0.011627 *
percent_uninsured   0.064070   0.039517   1.621 0.104945
percent_under150   -0.016423   0.017528  -0.937 0.348798
percent_disabled   -0.023421   0.033759  -0.694 0.487828
pop_density        -0.352425   0.098325  -3.584 0.000338 ***


I know that exponentiating the coefficients will give me the ORs per 1% increase in the variable. However, I want to know the odds of exposure per 10% increase in the variable (i.e., for each 10% increase in the percent of the population living with a disability, the odds of being exposed increases/decreases by a factor of x). When I code cali_logit$coefficients <- cali_logit$coefficients * 10 and re-run the summary, all of my coefficients suddenly become significant (when many weren't before), as shown below.

                   Estimate Std. Error z value Pr(>|z|)
(Intercept)         7.67410    0.78296   9.801  < 2e-16 ***
percent_unemployed -0.89417    0.03651 -24.493  < 2e-16 ***
percent_minority   -0.08516    0.01157  -7.360 1.84e-13 ***
percent_no_diploma  0.53393    0.02116  25.233  < 2e-16 ***
percent_uninsured   0.64070    0.03952  16.213  < 2e-16 ***
percent_under150   -0.16423    0.01753  -9.369  < 2e-16 ***
percent_disabled   -0.23421    0.03376  -6.938 3.99e-12 ***
pop_density        -3.52425    0.09833 -35.843  < 2e-16 ***


This doesn't seem right...am I missing something? How do I get odds ratios per 10% increase rather than per 1% increase?

• You might want to review our highest-voted answers about odds ratios. BTW, I wonder what you mean by "exposed to pollutant," because it's a fact that everybody everywhere is exposed to every substance that exists (apart from exotic short-lived radionuclides and unstable chemical intermediates).
– whuber
Commented Mar 17, 2023 at 21:13
• @whuber I'm simplifying in my description to keep it succinct - my exposure of interest is animal farms that contain greater than 5,000 animal units. So it's not a specific pollutant, it is if the census tract contains a large farm and is therefore exposed to known water and air pollutants. I looked at the threads you linked but I'm not seeing anything on increasing the units. Commented Mar 18, 2023 at 0:51