Introduction to Probability and Statistics for Engineers and Scientists

400 Chapter 9: Regression

Multiple Linear Regression

Compute coeffs.

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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