Compared with Eq. (3.1.2), Eq. (3.3.6) is easy to use, for it does not require computing ui for each observation although such a computation will be useful in its own right (as we shall see in Chapters 11 and 12). Since
18The term number of degrees of freedom means the total number of observations in the sample (= n) less the number of independent (linear) constraints or restrictions put on them. In other words, it is the number of independent observations out of a total of n observations. For example, before the RSS (3.1.2) can be computed, ¿ 1 and ¿2 must first be obtained. These two estimates therefore put two restrictions on the RSS. Therefore, there are n — 2, not n, independent observations to compute the RSS. Following this logic, in the three-variable regression RSS will have n — 3 df, and for the A:-variable model it will have n — k df. The general rule is this: df = (n — number of parameters estimated).
78 PART ONE: SINGLE-EQUATION REGRESSION MODELS
an alternative expression for computing £ U2 is
In passing, note that the positive square root of â2
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