 # Regression coefficient is zero I am trying to construct a quadratic regression model for a data a Yesenia Obrien 2022-07-03 Answered
Regression coefficient is zero
I am trying to construct a quadratic regression model for a data as
$Y={\alpha }_{0}+{\alpha }_{1}{X}_{1}+{\alpha }_{2}{X}_{2}+{\alpha }_{3}{X}_{1}{X}_{2}+{\alpha }_{4}{X}_{1}^{2}+{\alpha }_{5}{X}_{2}^{2}$
I am getting coefficient of ${X}_{1}^{2}\left(\to {\alpha }_{4}\right)=0.00000006\approx 0.$. How can we interpret this model for ${X}_{1}^{2}$ term? What is the impact of ${\alpha }_{4}=0$ for the model? Adjusted ${R}^{2}=0.9988$
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It implies that there is no quadratic relationship between ${X}_{1}$ and Y given $\left({X}_{1},{X}_{2},{X}_{1}{X}_{2},{X}_{2}^{2}\right)$, thus the best approximation of the true process with the variables $\left({X}_{1},{X}_{2},{X}_{1}{X}_{2},{X}_{1}^{2},{X}_{2}^{2}\right)$ is
$Y={\alpha }_{0}+{\alpha }_{1}{X}_{1}+{\alpha }_{2}{X}_{2}+{\alpha }_{3}{X}_{1}{X}_{2}+{\alpha }_{5}{X}_{2}^{2}$