# Seasonal adjustment question, why do days matter?

I have a simple ols equation where the independent variable is total production in a month. I seasonally adjust the data with an x12 and run the ols and get my estimates. The strange thing is, if I change the independent variable to average production per day by dividing by the number of days in the month, and then seasonally adjusting the series my R-squared goes up by almost 0.1. Does anyone have any idea why that might be?

• If production depends on the amount of time invested in it (which is a reasonable assumption), then the result is as expected. You are reflecting a relevant feature in the second model, but you are not reflecting it in the first one; hence, no wonder that the second model has a higher $R^2$. That should happen regardless of seasonality. However, seasonality may mess things up. – Richard Hardy Jun 16 '15 at 19:37
• I don't follow you. The same information is in both series just presented a difference way. – rinnovo Jun 16 '15 at 19:39
• Well, one of us is too quick: either I did not quite get the setting right, or you did not quite get the idea behind my argument. Some more time spent reflecting should help :) – Richard Hardy Jun 16 '15 at 19:41
• Why do you say the first one doesn't reflect time invested? Shouldnt the seasonal adjustment correct for the number of days in the month? – rinnovo Jun 16 '15 at 19:52
• If it does, then my comment is irrelevant. I do not know exactly what x12 does. – Richard Hardy Jun 16 '15 at 20:03