Page 87 - Basic Statistics

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ˆ
2
β = ( Xj - X )( Y j - Y ) /  (Xj - X )
1
= [  X i Y i – (  X i )(  Y i) / n ] / [  X i - (  X i ) / n ] ( R4 )
2
2
ˆ
ˆ
β = Y - β X
0
1

Further allegations regression equation, namely

ˆ
ˆ
ˆ
Y = β + β Xj ( R5 )
j
0
1
Note: Often the experimenter may become confused about the interpretation of  0
or its estimate from experimental data. As we indicated earlier in this section, the
linear model is the simplest empirical device for explaining how the data were
produced. Often the characteristics of the model that are computed by the data are
very much dependent on range of X in which the data were taken. In other word,
there is a presumption that the model given by Eq.(R2) holds only in a confined
region of X. If this region covers X=0, then the estimate of  0 can certainly be
interpreted as the mean Y at X=0. But if the data coverage is far away from the
origin, then  0 is merely a regression term that supplies little in the way of

interpretation. Often, in fact, the estimate of  0 turns out to be a value that seems
quite unreasonable, or even impossible in the context of problem. The analyst
must bear in mind that interpretation of  0 is tantamount to extrapolating the
model outside the range in which it was intended to be used.

5.1.2 ANALYSIS OF VARIANCE IN THE LINEAR REGRESSION

Analysis of variance on linear regression present the review of each

partition of the sum of the squares on the term of equation which states:

ˆ
deviation of the estimated value of the actual observations, ie e = Y − Y or
j
j
j
ˆ
written as Y j = Y +e .
j
j

ˆ
2
2
 Yj = (Y +e )
j
j
ˆ
=  Y + e “( The cross-product term Y e = 0 )”
ˆ 2
2
j
j
j
j
ˆ
=  Y +  ( Yj-Y )
2
ˆ 2
j
j
~~* CHAPTER 5 LINEAR REGRESSION MODEL *~~