Fitting a quadratic function

Problem

Consider the data in the Excel file Nonlinear.xlsx.

a. Fit the model

\[y_i=β_1+β_2x_{2i}+β_3x_{2i}^2+ε_i\]

by changing the trendline from linear to quadratic (You need to click off and on the “display equation on chart” for it to update). Explain why the exogeneity assumption is more credible in this case.

b. Find   \(\hat{y}\) for \(x=50\)

c. According to your estimates, which value of \(x\) will maximize \(y\) ?