# Interpretation of regression variables

I hope you are well and that you are keeping safe.

I was hoping you would be able to help me with an interpretation of a coefficient in my dissertation. I'm looking into the effects of air pollution on stock market returns, as it can have adverse health effects which reduce investor sentiment. I have estimated the following equation:

where $$R_t$$: daily percentage returns (in %)

If the coefficient of PM2.5 is -0.00113, which of my following interpretations is correct:

• one unit increase in PM2.5 leads to a -0.00113-percentage point reduction in daily returns

• one unit increase in PM2.5 leads to a -0.113% reduction in daily percentage returns

• if Pm2.5 were logged a 1% increase would lead to a -0.113-percentage point reduction in returns

**using original pm2.5 values

My apologies if this sounds a bit silly, a lot of different papers have been giving me conflicting answers.

• You have three intepretations. Since $R_t$ is in percentage, the second interpretation sound least pausible to me. As for the first and third one, it would depend on how you processed the PM2.5 value, is it the original values? or is it normalized? – doubllle May 4 at 15:45
• Hi, Thank you very much for responding. The pm2.5 data are the original values – Akky May 4 at 15:57
• Hi, Thank you very much for responding. The pm2.5 data are the original values – Akky May 4 at 16:04
• also please note that the percentages are not decimal i.e 0.5 but are daily returns so in that case would be 50% – Akky May 4 at 16:11
• according to the information you provide, the first interpretation seems the correct one, but logically, negative percentage of reduction means increasing. – doubllle May 4 at 18:52