Use the data in ECONMATH to answer this question. The population model is score = 0

Use the data in ECONMATH to answer this question. The population model is

score = β₀ + β₁act + u.

(i) For how many students is the ACT score missing? What is the fraction of the sample? Define a new variable, actmiss, which equals one if act is missing, and zero otherwise.

(ii) Create a new variable, say act0, which is the act score when act is reported and zero when act is missing. Find the average of act0 and compare it with the average for act.

(iii) Run the simple regression of score on act using only the complete cases. What do you obtain for the slope coefficient and its heteroskedasticity-robust standard error?

(iv) Run the simple regression of score on act0 using all of the cases. Compare the slope coefficient with that in part (iii) and comment.

(v) Now use all of the cases and run the regression

score_i on act0_i, actmiss_i.

What is the slope estimate on act0_i? How does it compare with the answers in parts (iii) and (iv)?

(vi) Comparing regressions in parts (iii) and (v), does using all cases and adding the missing data estimator improve estimation of β₁?

(vii) If you add the variable colgpa to the regressions in parts (iii) and (v), does this change your answer to part (vi)?