Step 1: Statistical Significance

The interpretation of statistically significant coefficients remains the same as in a simple linear regression. In this example, we interpret two coefficients: county median income and county college experience.


	% shift to Trump, 2012-2016

County median income ($1,000s)	-0.158^*	-0.013
	(0.006)	(0.007)

County college experience		-0.344^*
		(0.012)

Constant	8.337^*	20.103^*
	(0.351)	(0.512)


Observations	3,111	3,111
Adjusted R²	0.203	0.371

Note:	* p<0.05

County median income

The coefficient for county income, -0.013. is negative and does NOT have stars.
The lack of stars indicates that we are NOT confident that the effect of county income is negative. It could be zero, or it could be positive. We simply do not have enough information to have any confidence in sign of the coefficient.
Note that the simple linear regression in the first column of numbers, which excludes county education, has a statistically significant coefficient for county median income. The multiple regression with education does not have a statistically significant coefficient for income. Statistical significance and coefficient sizes may change when you add new variables to a regression. These changes can be dramatic when a new variable is correlated with any of the original $x$ variables.

County college experience

The coefficient for county education, -0.344, is negative and it DOES have stars.
Because $p < 0.05$, we are at least 95% confident that the effect of county education is not zero.