Let's say we have a model as given below:
$Y_1 = \beta_0 + \beta_1 X_1 + \beta_2 X_2+ \beta_3 \frac{X_2}{X_1} + \beta_4\frac{X_2^2}{X_1}$, $R^2= 0.98$
Here, $X_1$ & $X_2$ are positive integers.
The value of $\beta_3$ and $\beta_4$ are high compared to $\beta_1$ and $\beta_2$.
If we fit multiple regression model for $Y_1$ with only the linear terms, the R-squared is very high.
$Y_1 = \gamma_0 + \gamma_1 X_1 + \gamma_2 X_2$, $R^2= 0.9$
So, can we say the interaction terms or ratio terms here are not significant? Also how can we find the significance/ contribution of each term to the model prediction?
Following are my observations when fitting only the interaction terms
$Y_1 = \alpha_0 + \alpha_1 \frac{X_2}{X_1}$, $R^2= 0.4$
$Y_1 = \rho_0 + \rho_1 \frac{X_2^2}{X_1}$, $R^2= 0.7$