# Interpretation of regression coefficients with examples

1. Y=\alpha+2X_1+e
This means that 1 unit change in X brings about 2 units change in Y.

2. Y=\alpha+0.8X_1-0.3X_1^2+e
This is a bit tricky. It is obvious that 1 unit change in X_1 brings about 0.8 units change in Y but what about 0.5?. For this let's carry out maths work.
Y'=0.8-0.6\timesX_1
So, change in Y is dependent on 0.8 as well as with -0.6\timesX_1. The regression equation will exhibit a 'U' shaped curve.

3. lnY=\alpha+2lnX_1+e
This means that 1 percent change in X brings about a 2 percent change in Y.

Source: Chegg.com