Linear Regression; Regression Coefficient And Estimated Value Calculation; Quadratic Regression - Casio fx-50F User Manual

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
Regression Formula
Constant Term a
Regression Coeffi cient b
Correlation Coeffi cient r
Estimated Value
Estimated Value

Quadratic Regression

Command
Regression Formula
Constant Term a
Regression Coeffi cient b
Regression Coeffi cient c
However,
Sxx Sxx
Sxy Sxy
Command
Estimated Value
Estimated Value
Estimated Value
a =
b
r
a =
b =
c =
Σx Σx
2 2
( ( ) )
Σx Σx
i i
2 2
= = – –
i i
n n
. Σy . Σy
Σx Σx
( (
Σx Σx i i i i
y y
= = – –
i i i i
n n
1
1
2
2
Calculation Formula
Σy – b . Σx
i i
n
n . Σx – Σx . Σy
y
i i i
=
n . Σx
Σx
2 2
– ( )
i i
n . Σx
y
i i
=
n . Σx
Σx
2 –
( )
{
i i
y – a
=
b
= +
x
a b
Calculation Formula
Σy Σx
( )
i i
– b – c
n n
xy .
2 2 2
x x x
S S – S
xx .
2 2
x x
S S – (S
y .
2
x xx
S S – S
xx .
2 2
x x
S S – (S
Σx Σx
2 2 3 3
Sxx Sxx
= =
i i
Σx Σx
2 2 2 2
Sx Sx x x
= =
i i
) )
Σx Σx
2 2 2 2
Sx Sx y y
= =
i i
Calculation Formula
2
– b + b – 4c
=
2c
– b – b 2 – 4c
=
2c
= a + bx + cx 2
E-47
i
. Σy
– Σx
i i
n . Σy
Σy
2 2 – 2
( )
}{ }
i i
Σx
2
( )
i
n
y .
2
xx
S
2 2
xx
)
xy .
2
xx
S
2 2
xx
)
Σx Σx Σx Σx
. .
2 2
( ( ) )
i i i i
– –
n n
Σx Σx
2 2 2 2
( ( ) )
i i
4 4
– –
n n
. Σy . Σy
Σx Σx
2 2
( ( ) )
i i i i
y y
– –
i i
n n
a – y
( )
a – y
( )