## Linear Regression: Spectrophotometric determination of Mn

For users of the Mathcad browser:
wmc-rl1.mcd (7 KB, ver. 5.0)In the
spectrophotometric determination of manganese (as permanganate) a linear
dependence of the absorbance for a given concentration range is
obtanied:

*c*/(mmol/L) | 0.186 | 0.459 | 0.728 | 0.906 | 1.094 | 1.351 | 1.647 | 1.838 |

*A* | 0.092 | 0.202 |
0.321 | 0.401 |
0.498 | 0.602 | 0.731 | 0.820 |

The formula for this linear
dependence can be written as *y=b*x+a*, where *y*
corresponds to the absorbance and *x* to the concentration
(or **A=b*c+a**). The parameters *b* and *
a*, are the slope of the line and the intercept with the
ordinate, respectively.

In MathCAD, the data series are defined as
vectors (one-column matrices). The syntax for the slope and the
intercept, as well as the correlation of the two sets of data is simple,
as illustrated in the following example:

The unknown concentrations of samples can be determined from

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