Correct and uses it for purposes of estimation for example, Basic Statistics

Correct and uses it for purposes of estimation for example

Suppose that the true (full) regression model in matrix form is:

However, the analyst assumes that the (reduced) model:

is correct and uses it for purposes of estimation. For example, the X matrix for the reduced model (XI) might include only an intercept column and columns for first-order terms, while the true model involves first-order terms (Xd and some two-factor interaction terms (X₂).

a. Show that:

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