Analysis of relationship between dependent and independent variable
The
following example deals with about 100 adults, in whom we
have measured length (X-axis, the origin is not at 0 cm) and
inspiratory vital capacity (IVC, Y-axis). It is intuitively
clear that generally taller persons will have a larger IVC.
Body dimensions will determine lung size, and not the other
way around; hence length is the independent and IVC the dependent
variable. Typically data cluster like a torpedo-like cloud
of data points, as in the figure. We can fit a line by eyeballing,
but there are formal statistical techniques to do this. What
these techniques achieve is to describe how differences in
the dependent variable can be explained by differences in
the independent variable: we perform regression of y on x.