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## Chapter 8.pdf

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VIII. ANALYZE
M

BOK
vr.A.2

EASURING RELATIONSHI PS/REGRESSION

The Method of Least Squares (Continued)
The best
employed:

fit criterion of goodness known as the principte of least squares

is

Ghoose, as the b_est fitting line, the line that minimizes the sum of squares of
the deviations of the observed values of y from those predicted

Expressed mathematically, minimize the sum of squared errors given by:

ssE=I(r,-i,),
substituting for f, on&quot; obtains the following expression:
sum of squared errors

=

The least square estimator of

ssE =
Fo

E[r,

- (0, * 0,,*,)]'

and p, are calculated as follows:

&quot;

[r*]'/
s,=Ix3-\i=t
x- ?, '
n
s&quot;=r*'''

(aP

0,=* and 0o=i-0,i
6r.&quot;.ng \$l h&quot;r&quot; been computed, substitute their values into the equation of a
9n&quot;:
line to obtain the least

squares prediction equation, or;gglgsspn line.

As noted earlier, the prediction equation for

f

is:

i=6.+6,x
Where: \$o anO \$, ,&quot;pr&quot;&quot;ent estimates of the true and
B,
Br.

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2014

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QUALITY COUNCIL OF INDIANA