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Methodology: Tutorials and spreadsheets for the bottom‐up evaluation of the uncertainty of measurements based on least square calibrations were developed. Scope: Measurement based on least square calibration of analytical instrumentation. Definition of the calibration interval
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The least squares regression line is the line that minimizes the sum of the squares (d1 + d2 + d3 + d4) of the vertical deviation from each data point to the line (see figure below as an example of 4 points). Figure 1. the standard deviation ¾x is the square root of the variance: ¾x = v u u t 1 N XN n=1 (xi ¡x)2: (2.4) Note that if the x’s have units of meters then the variance ¾2 x has units of meters 2, and the standard deviation ¾x and the mean x have units of meters. Thus it is the standard deviation that gives a good measure of the deviations of the x’s around their mean.
The least-squares method provides the closest relationship between the dependent and independent variables by minimizing the distance between the residuals, and the line of best fit, i.e., the sum of squares of residuals is minimal under this approach. Hence the term “least squares.” Examples of Least Squares Regression Line
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