Thermo BioMate 3 series User Manual

Appendix C - Calculations
C-5 BioMate 3 Operator’s Manual
Calculations
Table 3 Calculations for Software
Calculation Calculation(s) Graphs
Standard Curves
Partial sums
Linear regression
(general case)
Linear regression
through zero
Segmented model
SX = Σ x
i
SY = Σ y
i
SXX = Σ x
i
2
SYY = Σ y
i
2
SXY = Σ x
i
y
i
SQX = Σ (x
i
- x
_
)
2
= N
*
SXX - SX
2
SQY = Σ (y
i
- y
_
)
2
= N
*
SYY - SY
2
SSXY = Σ (x
i
- x
_
)(y
i
- y
_
) = N
*
SXY - SX
*
SY
where: x
i
= concentration of i
th
standard
y
i
= absorbance of i
th
standard
N=number of standards
A = A(c)
where: A = absorbance
c = concentration
A(c) is defined by an equation of the form
A(c) = a
4
c
4
+ a
3
c
3
+ a
2
c
2
+ a
1
c + a
0
where: a
0
= Y-axis intercept
a
1
…a
4
= coefficients
The coefficients are computed using the least
squares method.
A= a
1
* (c)
where: A = absorbance
c = concentration
a
1
= slope
The slope is calculated as
a
1
= SXY
SXX
This model requires:
• Slope is not equal to zero
• At least one standard data point with
concentration not equal to zero
The segmented model requires:
• Data for at least two standard data points
with different concentrations and
absorbances
• Slopes of all segments must be
ascending (positive) OR descending
(negative)

Thermo BioMate 3 series Specifications

General

Brand	Thermo
Model	BioMate 3 series
Category	Measuring Instruments
Language	English