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Linear regression uses the method of least squares to determine the best linear equation to describe a set of x and y data points. The method of least squares minimizes the sum of the square of the residuals - the difference between a measured data point and the hypothetical point on a line. The residuals must be squared so that positive and negative values do not cancel. Spreadsheets will often have built-in regression functions to find the best line for a set of data.
A common application of linear regression in analytical chemistry is to determine the best linear equation for calibration data to generate a calibration or working curve . The concentration of an analyte in a sample can then be determined by comparing a measurement of the unknown to the calibration curve. Linear Regression EquationsFor the linear equation: y = mx + b
Useful quantities:Slope:Intercept:Standard deviation of the residuals:Standard deviation of the intercept:Standard deviation of the slope:Standard deviation of a unknown read from a calibration curve: Where:
N is the number of calibration data points. L is the number of replicate measurements of the unknown. and is the mean of the unknown measurements. Related topics:data handling
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