**6.3 Linearity**

For any developed analytical method, standard curve is constructed to verify the linear relationship between the concentration and a characteristic parameter for a component such as peak area, peak height or peak ratio in chromatographic analysis or UV-absorption in spectrophotometry.

Most analytical methods are based on processes where the method produces a response that is linear and which increases or decreases linearly with analyte concentration. In other words, it is the ability of the method to elicit test results that directly proportional to the concentration of analyte within a given range.

Statistical application is important in evaluating calibration graphs in instrumental analysis. The equation of a straight line takes the form:

$$\mathbf{y} = \mathbf{a} + \mathbf{b}\mathbf{x} \tag{3}$$

Where a is the intercept of the straight line with the y axis and b is the slope of the line.

The statistical measure of the goodness of the fit of the line through the data is the correlation coefficient "r". It falls in the range −1 ≤ r ≥+1. Negative r-values indicate negative slope and vice-versa. It is important to note that calculated r-values can be sometimes misleading and a calibration curve must be physically plotted to ensure the shape of the plot. From the calculated regression line data, the concentration of the analyte can be estimated by interpolation. Each value of y is subjected to random error and likely an error in the slope and intercept values can occur. This can be resolved by calculating standard deviations of the slope (Sb) and intercept (Sa). Sb and Sa are obtained from a calculated statistic value Sy/x [29]. The values of Sb and Sa are used to calculate the confidence limits for the slope and intercept using a *t*-value at a desired confidence level, normally 95% level. These limits are important to indicate if there is a significant difference between these values and certain true values, which reflects the effect of random or systemic errors.
