Use the data in ECONMATH to answer this question.

(i) Logically, what are the smallest and largest values that can be taken on by the variable score? What are the smallest and largest values in the sample?

(ii) Consider the linear model

score = β₀ + β₁colgpa + β₂actmth + β₃acteng + u.

Why cannot Assumption MLR.6 hold for the error term u? What consequences does this have for using the usual t statistic to test H₀: β₃ = 0?

(iii) Estimate the model from part (ii) and obtain the t statistic and associated p-value for testing H₀: β₃ = 0. How would you defend your findings to someone who makes the following statement: “You cannot trust that p-value because clearly the error term in the equation cannot have a normal distribution?”