I am trying to construct a quadratic regression model for a data as
$Y=\alpha_0+\alpha_1X_1+\alpha_2X_2+\alpha_3X_1X_2+\alpha_4X_1^2+\alpha_5X_2^2$.
I am getting coefficient of $X_1^2 (\rightarrow\alpha_4)=0.00000006\approx0.$ How can we interpret this model for $X_1^2$ term? What is the impact of $\alpha_4=0$ for the model? Adjusted $R^2=0.9988$.
It implies that there is no quadratic relationship between $X_1$ and $Y$ given $(X_1, X_2, X_1X_2, X_2^2)$, thus the best approximation of the true process with the variables $(X_1, X_2, X_1X_2, X_1^2, X_2^2)$ is $$ Y = \alpha_0 + \alpha_1X_1 + \alpha_2 X_2 + \alpha_3 X_1 X_2 + \alpha_5 X_2^2 $$