User`s guide

E-48
Logarithmic Regression
Command Calculation Formula
Regression Formula
Constant Term a
a =
n
Σy
i
– b
.
Σlnx
i
Regression Coeffi cient b
b =
n
.
Σ
(
ln
x
i
)
2
–
(
Σlnx
i
)
2
n
.
Σ
(
ln
x
i
)y
i
– Σlnx
i
.
Σ
y
i
Correlation Coeffi cient r
r =
{n
.
Σ
(
ln
x
i
)
2
–
(
Σlnx
i
)
2
}{n
.
Σ
y
i
2
–
(
Σy
i
)
2
}
n
.
Σ
(
ln
x
i
)y
i
– Σlnx
i
.
Σ
y
i
Estimated Value
m
m = e
y –a
b
Estimated Value
n
n = a + bln
x
e
Exponential Regression
Command Calculation Formula
Regression Formula
Constant Term a
a = exp
()
n
Σlny
i
– b
.
Σ
x
i
Regression Coeffi cient b
b =
n
.
Σx
i
2
–
(
Σx
i
)
2
n
.
Σx
i
ln
y
i
– Σx
i
.
Σ
lny
i
Correlation Coeffi cient r
r =
{n
.
Σx
i
2
–
(
Σx
i
)
2
}{n
.
Σ
(
ln
y
i
)
2
–
(
Σlny
i
)
2
}
n
.
Σx
i
ln
y
i
– Σx
i
.
Σ
lny
i
Estimated Value
m
m
=
b
lny – lna
Estimated Value
n
n = ae
bx
ab
Exponential Regression
Command Calculation Formula
Regression Formula
Constant Term a
a = exp
( )
n
Σ
lny
i
– lnb
.
Σx
i
Regression Coeffi cient b
b = exp
()
n
.
Σx
i
2
–
(
Σx
i
)
2
n
.
Σx
i
ln
y
i
– Σx
i
.
Σ
lny
i
Correlation Coeffi cient r
r =
{n
.
Σx
i
2
–
(
Σx
i
)
2
}{n
.
Σ
(
ln
y
i
)
2
–
(
Σlny
i
)
2
}
n
.
Σx
i
ln
y
i
– Σx
i
.
Σ
lny
i