Interpreting continuous interaction terms in multiple linear regression I've looked at this post for reference. And suppose my model is 
$\hat{score} = 12 + 0.4*Age_i + 0.5*Height_i + 0.8*Age_i*Height_i$, then is the following interpretation of my coefficients correct?
For a one unit increase in age, the average score changes by $0.4 + 0.8*Height_i$, holding height constant. 
For a one unit increase in height, the average score changes by $0.5 + 0.8*Age_i$, holding age constant.
 A: Pretty much. But:

For a one unit increase in age, the average score changes by $0.4+0.8∗Height_i$, holding height constant. 

Holding $height$ constant as long as $height\not=0$. If it equals $0$ than the interaction term is also $0$. Also, if $height>0$ and held constant, than for every increased unit of $age$ , the average predicted score will increase by $(0.4+0.8)$, not by $0.4+0.8*height$.
$\beta_1$ (0.4) will be used alone only when $height=0$, or else the interaction will be also coming into play. 
The same principle goes, naturally, also for both covariates.
A: Your interpretation is correct. However, the accepted answer contains incorrect information.
First, your interpretation is correct even when $height = 0$, as then the average score changes by $0.4$.
Second, the assertion in the accepted answer that the average predicted score will increase by $(0.4 + 0.8)$, not by $0.4 + 0.8*height$, is incorrect. To see this, set $age = 10$ and $height = 10$, and observe that the average predicted score is $101$. If $age = 11$ and $height = 10$, the average predicted score is $109.4$, an increase of $0.4 + 0.8*10$.
