Performing regression calculations, U to view regression calculation results, Formulas – Casio ClassPad II fx-CP400 User Manual
Page 138
Chapter 7: Statistics Application
138
Performing Regression Calculations
You can use the procedures under “Overlaying a Regression Graph on a Scatter Plot” (page 134) to specify a
model formula, and determine and graph the regression formula for paired-variable data. The dialog box that
appears when performing these operations provides the coefficients, constant term, and other values for the
regression formula. You can also copy the regression formula to the Graph Editor window and perform residual
calculation (which calculates the distance between the regression model and an actual plotted point during
regression calculations).
u To view regression calculation results
1. On the [Calc] - [Regression] menu, select one of the regression calculation
commands (from [Linear Reg] to [Logistic Reg]).
• For information about regression calculation characteristics, see
“Regression graphs” (page 133).
2. On the dialog box that appears, specify the [XList] and [YList] names, and
select the [Freq] setting.
Model formula
3. Tap [OK].
• This displays the dialog box with the regression calculation results described below.
a
,
b
,
c
,
d
,
e
: coefficients of the model formula (shown at the top of the dialog box) corresponding to the
regression calculation
r
:
correlation coefficient (linear regression, logarithmic regression, exponential regression, and
power regression only)
r
2
:
coefficient of determination (except for Med-Med, sinusoidal regression, and logistic regression)
MSe
:
mean square error (except for Med-Med)
MSe
Formulas
Depending on the regression calculation type, mean square error (
MSe
) is obtained using the following
formulas.
Linear:
y
=
a
ؒ
x
+
b
:
;
Quadratic:
Quartic:
Exponential:
a
ؒ
e
b
ؒ
x
:
;
Power:
Sinusoidal:
y
=
a
+
b
ؒ
x
:
Cubic:
Logarithmic:
a
ؒ
b
x
:
Logistic:
u To copy a regression formula to the Graph & Table application
1. Perform steps 1 and 2 under “To view regression calculation results” (page 138).
2. On the dialog box that appears, tap the [Copy Formula] down arrow button, and then select the Graph &
Table line number (
y
1 through
y
20) to which you want to copy the formula.
3. Tap [OK].
• This copies the calculated regression expression to the line (
y
1 through
y
20) you selected.
Σ
1
n
– 2
i
=1
n
(y
i
– (ax
i
+ b))
2
Σ
1
n
– 3
i
=1
n
(y
i
– (ax
i
2
+ bx
i
+ c))
2
Σ
1
n
– 5
i
=1
n
(y
i
– (ax
i
4
+ bx
i
3
+ cx
i
2
+ dx
i
+ e))
2
Σ
1
n
– 2
i
=1
n
(ln y
i
– (ln a + bx
i
))
2
Σ
1
n
– 2
i
=1
n
(ln y
i
– (ln a + b ln x
i
))
2
Σ
1
n
– 2
i
=1
n
(y
i
– (a·sin (bx
i
+ c) + d ))
2
Σ
1
n
– 2
i
=1
n
(y
i
– (a + bx
i
))
2
Σ
1
n
– 4
i
=1
n
(y
i
– (ax
i
3
+ bx
i
2
+ cx
i
+ d ))
2
Σ
1
n
– 2
i
=1
n
(y
i
– (a + b ln x
i
))
2
Σ
1
n
– 2
i
=1
n
(ln y
i
– (ln a + (ln b)
ؒ x
i
))
2
Σ
1
n
– 2
1 + ae
–bx
i
C
i
=1
n
y
i
–
2