I'm currently enrolled in a statistics course and we are studying regression models. What does it mean to develop a regression model that contains both a straight line in the regressor, as well as a quadratic model outside of the range for x where the model is continuous and differentiable at every value of x?
I'm not looking for an answer, but more of what is this question even asking? Should I create a value for $x_1$ = 1, for example, and then $x_2$ is both a quadratic that can take on any value besides 1?
This regression model is piecewise defined.
$$y_i=\begin{cases} b_0+b_1x_i+\epsilon_i \ \ \forall \ x_i\leq x^* \\ \\b_2+b_3x_i+b_4x_i^2+\epsilon_i \ \ \forall \ x_i> x^*,\end{cases}$$
where $\epsilon_i$ is the error term.
Next the intersection of the two functions has to be calculated in order to find $x^*$. This can be done with the quadratic formula.