biochrom Libra S21 - Least Squares Regression Analysis and Linearity

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26 Libra S21/S22, English Issue 02 - 04/2004
Least squares regression analysis and linearity
The slope (or best straight line) and intercept in a kinetics assay or standard curve
determination is calculated from a least squares linear regression of the data. The
following equations are used, where n is the number of data points:
Slope
xynxy
xxnx
=
−
−
∑∑∑
∑∑∑
2
()
Intercept y x slope n=−
∑
∑
*/
Linearity is an estimate of the “goodness of fit” of the least squares linear regression
analysis, a perfect fit being 100%. It is used in both the Reaction Rate and Standard
Curve modes, and is expressed by a coefficient of determination (r
2
), calculated
using the following equation:
() () () ()
∑∑∑∑
∑
∑
∑
−−
−
=
2
2
2
2
*100
ynyxnx
xynyx
Quality