In univariate missing data, where there are missing values for only one variable in a data set, some of the apparently distinct methods for handling missing data produce identical results for certain...

In univariate missing data, where there are missing values for only one variable in a data set, some of the apparently distinct methods for handling missing data produce identical results for certain statistics. Consider Table 20.1 on page 612, for example, where data are missing on the variable X₂
but not on X₁. Note that the complete-case, available-case, and mean-imputation estimates of the slope β₁₂
for the regression of X₁
on X₂
are identical. Prove that this is no accident. Are there are any other apparent agreements between or among methods in the table? If so, can you determine whether they are coincidences?