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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
Σy
i
– b
.
Σx
i
Regression Coeffi cient b
b =
n
.
Σx
i
2
–
(
Σx
i
)
2
n
.
Σx
i
y
i
– Σx
i
.
Σy
i
Correlation Coeffi cient r
r =
{n
.
Σx
i
2
–
(
Σx
i
)
2
}{n
.
Σy
i
2
–
(
Σy
i
)
2
}
n
.
Σx
i
y
i
– Σx
i
.
Σy
i
Estimated Value
m
m
y – a
b
=
Estimated Value
ţ
n = a + bx
Quadratic Regression
Command Calculation Formula
Regression Formula
Constant Term a
a = – b
()
– c
()
n
Σy
i
n
Σx
i
n
Σx
i
2
Regression Coeffi cient b
b =
Sxx
.
Sx
2
x
2
– (Sxx
2
)
2
Sxy
.
Sx
2
x
2
– Sx
2
y
.
Sxx
2
Regression Coeffi cient c
c =
Sxx
.
Sx
2
x
2
– (Sxx
2
)
2
Sx
2
y
.
Sxx – Sxy
.
Sxx
2
However,
Command Calculation Formula
Estimated Value
m
1
m
1 =
2c
– b +
b
2
– 4c
(
a – y
)
Estimated Value
m
2
m
2 =
2c
– b –
b
2
– 4c
(
a – y
)
Estimated Value
n
n
= a + bx + cx
2
(Σx
i
)
2
Sxx = Σx
i
2
–
n
Sxy = Σx
i
y
i
–
n
(Σx
i
.
Σy
i
)
Sxx
2
= Σx
i
3
–
n
(Σx
i
.
Σx
i
2
)
Sx
2
x
2
= Σx
i
4
–
n
(Σx
i
2
)
2
Sx
2
y = Σx
i
2
y
i
–
n
(Σx
i
2
.
Σy
i
)
(Σx
i
)
2
Sxx = Σx
i
2
–
n
Sxy = Σx
i
y
i
–
n
(Σx
i
.
Σy
i
)
Sxx
2
= Σx
i
3
–
n
(Σx
i
.
Σx
i
2
)
Sx
2
x
2
= Σx
i
4
–
n
(Σx
i
2
)
2
Sx
2
y = Σx
i
2
y
i
–
n
(Σx
i
2
.
Σy
i
)