Analyzing data using a standard curve – Bio-Rad Microplate Manager Software User Manual
Page 51
Analyzing Data Using a Standard Curve
43
A residual is the difference between an observed value of the response variable and
the value predicted by the regression line.
That is, Residual = observed y - predicted y.
The chi square value is a measure of how close the observed values are to the
calculated values. A chi value of zero means that the observed values are equal to the
calculated values. Likewise, small chi values indicate a good fit.
chi
2
= SQR(
Σ(y
i
-f(x
i
,
p
))
2
/(n-np))
For a set of data points (y
i
, x
i
);
y = f(x, p) where p is a set of parameters.
n is total number of values; np is total number of parameters
Correlation coefficient r is a slope of least square regression line for linear plots.
The correlation coefficient, r, is calculated for data pairs (x
i
, y
i
) with weighting
factors w
i
r = Σ w
i
(y
i
-Y
i
) (x
i
-X
i
) / (Σ w
i
(y
i
-Y)
2
)
1/2
(Σ w
i
(x
i
-X)
2
)
1/2
X = Σ w
i
x
i
/Σw
i
, Y = Σ w
i
y
i
/Σw
i
r = Σ w
i
Σw
i
x
i
y
i
- Σw
i
x
i
Σw
i
y
i
/ (Σw
i
Σw
i
x
i
2
-(Σw
i
x
i
)
2
)
1/2
(Σw
i
Σw
i
y
i
2
-(Σw
i
y
i
)
2
)
1/2
The r
2
(coefficient of determination) is often reported instead of r.
Back calc is the calculated concentration (x value) based on the calculated y value
for the curve.
OD is Optical Density (or Absorbance), the response values obtained from a reader
without pathlength correction. This is the logarithm (base 10) of the ratio of the
amount of incident light to the amount of light that passes through the sample.
Therefore an OD of 2.0 absorbs 10 times more incident light.
Weighted Average Concentration of Dilutions
The estimated error is calculated
S
y,pred
= SQR variance
y
= RMS (y)
If a sample has been analyzed in replicates, the mean response of n replicate
measurements will be more reliable than an individual measurement. The Standard
Error of the Mean (SEM) of the response y is
SEM
y
= s
y
/ SQR n