State with reason whether the following statements are true or false.†

a. An observation can be influential but not an outlier.

b. An observation can be an outlier but not influential.

c. An observation can be both influential and an outlier.

d. If in the model Y_i = β₁ + β₂X_i + β₃X²_i+ u_iβ₃ turns out to be statistically significant, we should retain the linear term X_i even if β₂ is statistically insignificant.

e. If you estimate the model Y_i = β₁ + β₂X_2i + β₃X_3i + u_i or Y_i = α₁ + β₂x_2i+ β₃x_3i + u_i by OLS, the estimated regression line is the same, where x_2i = (X_2i − X̅ ₂) and x_3i = (X_3i – X̅₃).