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