E-48
Logarithmic Regression
Command
Calculation Formula
Regression Formula
Constant Term a
a
=
n
Σ
y
i
–
b
.
Σ
ln
x
i
Regression Coeffi cient b
b
=
n
.
Σ
(ln
x
i
)
2
–
(
Σ
ln
x
i
)
2
n
.
Σ
(ln
x
i
)
y
i
–
Σ
ln
x
i
.
Σ
y
i
Correlation Coeffi cient r
r
=
{
n
.
Σ
(ln
x
i
)
2
–
(
Σ
ln
x
i
)
2
}{
n
.
Σ
y
i
2
–
(
Σ
y
i
)
2
}
n
.
Σ
(ln
x
i
)
y
i
–
Σ
ln
x
i
.
Σ
y
i
Estimated Value
m
m
=
e
y
– a
b
Estimated Value
n
n
=
a
+
b
ln
x
e
Exponential Regression
Command
Calculation Formula
Regression Formula
Constant Term a
a
=
exp
(
)
n
Σ
ln
y
i
–
b
.
Σ
x
i
Regression Coeffi cient b
b
=
n
.
Σ
x
i
2
–
(
Σ
x
i
)
2
n
.
Σ
x
i
ln
y
i
–
Σ
x
i
.
Σ
ln
y
i
Correlation Coeffi cient r
r
=
{
n
.
Σ
x
i
2
–
(
Σ
x
i
)
2
}{
n
.
Σ
(ln
y
i
)
2
–
(
Σ
ln
y
i
)
2
}
n
.
Σ
x
i
ln
y
i
–
Σ
x
i
.
Σ
ln
y
i
Estimated Value
m
m
=
b
ln
y –
ln
a
Estimated Value
n
n
=
a
e
b
x
ab
Exponential Regression
Command
Calculation Formula
Regression Formula
Constant Term a
a
=
exp
(
)
n
Σ
ln
y
i
–
ln
b
.
Σ
x
i
Regression Coeffi cient b
b
=
exp
(
)
n
.
Σ
x
i
2
–
(
Σ
x
i
)
2
n
.
Σ
x
i
ln
y
i
–
Σ
x
i
.
Σ
ln
y
i
Correlation Coeffi cient r
r
=
{
n
.
Σ
x
i
2
–
(
Σ
x
i
)
2
}{
n
.
Σ
(ln
y
i
)
2
–
(
Σ
ln
y
i
)
2
}
n
.
Σ
x
i
ln
y
i
–
Σ
x
i
.
Σ
ln
y
i