Suppose that the true (full) regression model in matrix form is:
![](https://test.transtutors.com/qimg/42198c5e-29e8-48d7-8580-b868a9fcc8bc.png)
However, the analyst assumes that the (reduced) model:
![](https://test.transtutors.com/qimg/99ebd905-9458-47bb-bfcb-fdbf98bd2493.png)
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:
![](https://test.transtutors.com/qimg/6af452df-0502-4150-b261-e97d29bfafbd.png)
![](https://test.transtutors.com/qimg/009f3c17-01a4-4b22-a9c7-b0c7c9e9d0a8.png)
![](https://test.transtutors.com/qimg/520608ee-8bdf-4674-b754-e807aaffca17.png)