400 Chapter 9: Regression
Multiple Linear Regression
Compute coeffs.
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Enter 8 response values:
8.4
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Response Values
11.6
16.1
9.3
9.1
8.4
7.7
Interval Estimates
Estimates of the
regression coefficients:
B(0) = 3.5073534
B(1) = -0.0002477
B(2) = 0.2609466
The sum of the squares of the residuals is SSR = 34.1212
Display Inverse
Inverse Matrix (X'X)-1
-9.73E-0
-2.55E-0
0.0037
2.78312
0.00002
-9.73E-02
0.00002
2.70E-08
-2.55E-06
FIGURE 9.17
and so
Bi− 1 =
∑n
l= 1
CilYl
Bj− 1 =
∑n
r= 1
CjrYr
Hence
Cov(Bi− 1 ,Bj− 1 )=Cov
( n
∑
l= 1
CilYl,
∑n
r= 1
CjrYr
)
=
∑n
r= 1
∑n
l= 1
CilCjrCov(Yl,Yr)
NowYlandYrare independent whenl=r, and so
Cov(Yl,Yr)=
{
0ifl=r
Var(Yr)ifl=r