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Deriving the Normal Equations
• The least squares method was introduced in Chapter 4
and used in Chapter 15. The objective was to
determine the sample regression line

y b bx
0
1
That would minimize the sum of squared deviations
between the points and the line. That is, the method
determines values for b0 and b1 such that

n
SSE   ( y  y )
i
i 1
i

y b bx
is minimized. Since

n
2
0
n
(y  y )  (y  b  b x )
i 1
2
i
i
i 1
i
0
1
i
2
1
, we have