Question: Question 3: Using the data given in Question (1). The following model is used:

\[y={{\beta }_{0}}+{{\beta }_{1}}{{x}_{1}}+{{\beta }_{2}}x_{1}^{2}+u\]

and this is known as the quadratic model.

a. Obtain the best fitted model and interpret the estimated coefficients.

b. Is the sign of \({{\hat{\beta }}_{2}}\) the same as what you expect? Why?

c. What x2 value will maximize (or minimize) predicted y? What is the corresponding predicted y value?