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E-47
A Regression Coeffi cient and Estimated Value Calculation
Formula Table
The following table shows the calculation formulas used by the regression coeffi cient and
estimated value commands for each regression calculation type.
Linear Regression
Command Calculation Formula
Regression Formula
Constant Term a a=n
Σyib.Σxi
Regression Coeffi cient b b=n.Σxi2(Σxi)2
n.ΣxiyiΣxi.Σyi
Correlation Coeffi cient r r=
{n.Σxi2(Σxi)2}{n.Σyi2(Σyi)2}
n.ΣxiyiΣxi.Σyi
Estimated Value mmy – a
b
=
Estimated Value ţn = a + bx
Quadratic Regression
Command Calculation Formula
Regression Formula
Constant Term a a= – b
()
c
()
n
Σyin
Σxin
Σxi2
Regression Coeffi cient b b=Sxx.Sx2x2– (Sxx2)2
Sxy.Sx2x2Sx2y.Sxx2
Regression Coeffi cient c c=Sxx.Sx2x2– (Sxx2)2
Sx2y.Sxx Sxy.Sxx2
However,
Command Calculation Formula
Estimated Value m1
m
1=2c
b+b24c(a y)
Estimated Value m2
m
2=2c
bb24c(a y)
Estimated Value n
n
= a + bx + cx2
(Σxi)2
Sxx =Σxi2n
Sxy =Σxiyin
(Σxi.Σyi)
Sxx2=Σxi3n
(Σxi.Σxi2)
Sx2x2=Σxi4n
(Σxi2)2
Sx2y=Σxi2yin
(Σxi2.Σyi)
(Σxi)2
Sxx =Σxi2n
Sxy =Σxiyin
(Σxi.Σyi)
Sxx2=Σxi3n
(Σxi.Σxi2)
Sx2x2=Σxi4n
(Σxi2)2
Sx2y=Σxi2yin
(Σxi2.Σyi)
48


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