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VIII. ANALYZE

BOK

MEASURI NG RELATIONSHIPS'REGRESSION

vt.A.2

Simple Linear Regression Model (Continued)
The mathematical equation of a straight line is:

Y=Fo+Frx
Where Bo is the y intercept when x = 0 and p, is the slope of the line. PIease note in
Figure 8.2 that the x axis does not go to zero so the y intercept appears too high.
The equation for a straight line in this example is too simplistic. There will actually
be a random error which is the difference between an observed value of y and the
mean value of y for a given value of x. One assumes that for any given value of x,
the observed value of y varies in a random manner and possesses a normal
probability distribution. The concept is illustrated in Figure 8.3:

xl

x2

x3

Figure 8.3 Variation in y as a Function of x
The probabilistic model for any particular observed value of y is:

y=

fMean value of v for\
* (random error)
|( a^ grven
.---'-;--=..^:----,
vatue
or x )I \

y=Fo+8,x+e

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2014

vl[ -4

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QUALITY COUNCIL OF ]NDIANA