When the calibration curve is linear, the slope is a measure of sensitivity: how much the signal changes for a change in concentration. A perfect line would have an R 2 value of 1, and most R 2 values for calibration curves are over 0.95. For a simple single regression, R 2 is the square of the correlation coefficient (r) and provides information about how far away the y values are from the predicted line. With a linear regression analysis, an R 2 value, called the coefficient of determination, is given. Linear regression is typically performed using a computer program and the most common method is to use a least squares fitting. However, not all curves are linear and sometimes to get a line, one or both set of axes will be on a logarithmic scale. Many calibration curves are linear and can be fit with the basic equation y=mx+b, where m is the slope and b is the y-intercept. Ideally a few concentrations above and below the expected concentration sample are measured. The range of concentrations of the calibration curve should bracket that in the expected unknown sample. Thus, many calibration curves are made in a sample matrix that closely approximates the real sample, such as artificial cerebral spinal fluid or artificial urine, but may not be exact. In practice, running calibration samples in the same matrix as the unknown is sometimes difficult, as the unknown sample may be from a complex biological or environmental sample. A sample matrix is the components of the sample other than the analyte of interest, including the solvent and all salts, proteins, metal ions, etc. To be completely accurate, the standard samples should be run in the same matrix as the unknown sample. Thus, care must be taken when making the initial solution.Ĭalibration curves can be used to predict the concentration of an unknown sample. The disadvantage is that any errors in solution making-pipetting, massing, etc.-get propagated as more solutions are made. The advantage is that only one initial solution is needed. The next sample is made from the previous dilution, and the dilution factor is often kept constant. With serial dilutions, a concentrated sample is diluted down in a stepwise manner to make lower concentrations. Another method for making many different concentrations of a solution is to use serial dilutions. However, that can take a lot of starting material and be time consuming. When making solutions for a calibration curve, each solution can be made separately. The calibration curve can be used to calculate the limit of detection and limit of quantitation. Typically the response is linear, however, a curve can be made with other functions as long as the function is known. The data are then fit with a function so that unknown concentrations can be predicted. For more accuracy and to understand the error, the response at each concentration can be repeated so an error bar is obtained. Generally, a set of standard samples are made at various concentrations with a range than includes the unknown of interest and the instrumental response at each concentration is recorded. Jill Venton - University of VirginiaĬalibration curves are used to understand the instrumental response to an analyte and predict the concentration in an unknown sample.
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