Question: The multiple regression model in partitioned matrix notation is y = x1????1 + X2????2 + u (T 1), where x1 is T 1,

The multiple regression model in partitioned matrix notation is y = x1????1 + X2????2 + u (T × 1), where x1 is T × 1, and X2 is T × k − 1, and the multiple least squares estimator of ????1 is

????̂1 =

x′

1M2y x′

1M2x1

(a) Show that for the case k = 3, where themodel contains an intercept, this formula is identical to (2) in Question 2.

(b) Derive a significance test for ????1, assuming fixed regressors and normal and independently distributed disturbances with mean zero and variance ????2.

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