E-47, Linear regression, Quadratic regression – Casio fx-50F PLUS User Manual
Page 48
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
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
+
b
x
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
=
S
xx.
S
x
2
x
2
– (S
xx
2
)
2
S
xy.
S
x
2
x
2
– S
x
2
y.
S
xx
2
Regression Coeffi cient c
c =
S
xx.
S
x
2
x
2
– (S
xx
2
)
2
S
x
2
y.
S
xx
– S
xy.
S
xx
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
)