6-25
u Calculation of the Correlation Coefficient (r), Coefficient of Determination
(r
2
) and Mean Square Error (MSe)
After the regression formula parameters on the regression calculation result screen, the
following parameters also appear on the display. The parameters that appear depend on the
regression formula.
Correlation coefficient (r)
Displayed following: linear regression, logarithmic regression, exponential regression, or power
regression calculation.
Coefficient of determination (r
2
)
Displayed following: linear regression, quadratic regression, cubic regression, quartic
regression, logarithmic regression, exponential regression, power regression calculation.
Mean square error (MSe)
Displayed following any regression calculation except Med-Med.
Depending on the regression calculation type, mean square error (MSe) is obtained using the
following formulas.
• Linear Regression (
ax + b ) .............
(
a + bx ) .............
• Quadratic Regression .....................
• Cubic Regression ...........................
• Quartic Regression .........................
• Logarithmic Regression ..................
• Exponential Regression (
a · e
bx
) .......
(
a · b
x
) ........
Se =
Σ
1
n – 2
i=1
n
(y
i
– (ax
i
+ b))
2
Se =
Σ
1
n – 2
i=1
n
(y
i
– (ax
i
+ b))
2
Se =
Σ
1
n – 2
i=1
n
(yi – (a + bxi))
2
Se =
Σ
1
n – 2
i=1
n
(yi – (a + bxi))
2
Se =
Σ
1
n – 3
i=1
n
(y
i
– (ax
i
+ bx
i
+ c))
2
2
Se =
Σ
1
n – 3
i=1
n
(y
i
– (ax
i
+ bx
i
+ c))
2
2
Se =
Σ
1
n – 4
i=1
n
(y
i
– (ax
i
3
+ bx
i
+ cx
i
+ d ))
2
2
Se =
Σ
1
n – 4
i=1
n
(y
i
– (ax
i
3
+ bx
i
+ cx
i
+ d ))
2
2
Se =
Σ
1
n – 5
i=1
n
(yi – (axi
4
+ bxi
3
+ cxi
+ dxi
+ e))
2
2
Se =
Σ
1
n – 5
i=1
n
(yi – (axi
4
+ bxi
3
+ cxi
+ dxi
+ e))
2
2
Se =
Σ
1
n – 2
i=1
n
(y
i
– (a + b ln x
i
))
2
Se =
Σ
1
n – 2
i=1
n
(y
i
– (a + b ln x
i
))
2
Se =
Σ
1
n – 2
i=1
n
(ln y
i
– (ln a + bx
i
))
2
Se =
Σ
1
n – 2
i=1
n
(ln y
i
– (ln a + bx
i
))
2
Se =
Σ
1
n – 2
i=1
n
(ln yi – (ln a + (ln b) · xi ))
2
Se =
Σ
1
n – 2
i=1
n
(ln yi – (ln a + (ln b) · xi ))
2
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