## Error free data

Suppose we have a set of data comprising two related variables. As an example we take the cm and the inch: 1 inch = 2.54 cm, the two variables are linearly related. We compute the number of centimeters for 1, 2, 3 ... 10 and put these in a graph with inches on the X-axis and centimeters on the Y-axis. The X-axis comprises the independent variable (inch), the Y-axis the dependent variable. We use a calculator, and as no measurements are performed there are no measurement errors either. Obviously the data are on a straight line which passes through the origin. The relationship can be described in mathematical form:

Y = a + b·X

where

Y is in cm, X in inch

a is the intercept, the value of Y when X = 0; in this case a = 0.

b is the slope, in this example 2.54.