Influence of a data point on the regression result? Let's say I perform multiple regression where y = income, x1 = educaiton, x2 = sex, and x3 = religion from 2003 to 2018, where the data is measured daily.

Is there any way to quantify an impact of a single day data (e.x. 2005-07-01) on the regression result?
It is hard to quantify exactly what a single point is doing, but you would benefit from plotting data to look for suspicious points and then measuring differences in statistics if you remove it.

Don't forget about the value of plotting data! Anscombe's quartet is a great reminder of how important this is. https://en.wikipedia.org/wiki/Anscombe%27s_quartet