Analytical Chemistry

the values of a, the intercept on the y-axis, and b, the slope, can be computed from equations (2.17) and
(2.18) respectively. Commonly a and b are referred to as regression coefficients.

In the evaluation of equation (2.16) it is appropriate first to calculate b (equation (2.18)) and then a
(equation (2.17)).

Example 2.8

A series of measurements obtained in the preparation of a calibration curve for an analytical method is
shown in Table 2.7. From equations (2.18), (2.17) and (2.16)

Table 2.7 Calibration data obtained in the assessment of a new method of analysis

Analyte concentration (ppm) Signal (arbitary units)

3.0 1.4

4.0 1.5

5.0 2.2

6.0 2.4

8.0 3.1

9.0 3.2

10.0 3.2

11.0 3.9

12.0 4.1

14.0 4.7

15.0 4.5

16.0 5.2

17.0 5.0

n = 13

The final 'best fit' calibration curve can be seen at Figure 2.9. Note the limitations on the use of the
lower, extrapolated, portion of the curve. The line obtained will always pass through the centroid of all

the points, i.e. the point on the graph corresponding to. A further aspect is the uncertainty
associated with the values of a and b. These may be estimated in terms of the variability of x and y.