INTRODUCTION TO ECONOMETRICS II
ECO 306
NOUN
75 the true unknown parameters. Our earlier stated definition of goodness of fit is the minimization of RSS, which is the sum of squares of the residuals
∑
…[2.50] Where e
i
is again, the residual in observation i, the difference between the actual value
Y
i
in that observation and the value
predicted by the regression equation
̂
…[2.51]
̂
…[2.52] It could be observed that the X variables now have two subscripts. The first identifies the X variable and the second identifies the observation. Applying [2.52] into [2.50];
…[2.53] From first-order conditions fora minimum
[2.52] will give the following equations
∑
(
)
…[2.54]
∑
(
)
…[2.55]
∑
(
)
…[2.56] Resulting in three equations from the three unknowns, b
1
, b
2
, and b
3
The first can easily be rearranged to express b
1
regardingb
2
, b
3
, and the data on Y, X
2
, and X
3
:
̅
̅̅̅
̅̅̅
…[2.57]
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