Raising the bar

Modeling a pair of random variables is very simple in Excel.

Modeling a pair of random variables - click to view video

Obviously, a pair of random variables is a more complex object than one variable, so be alert when you see one. The mathematical name for a pair of variables is a vector. Both components of the vector are constructed as normal variables, using a combination of a uniformly distributed variable and inverse cumulative distribution of a normal variable. On a scatterplot, we plot values of one variable against those of another. This definition is illustrated on the graph.

The simulation can be easily modified to obtain negatively correlated variables. Simulation of uncorrelated variables is a little trickier. If you just use the uniform distribution (the command is =rand()) in the first and second columns, the two columns will be uncorrelated. However, it is easy to construct variables which geometrically are correlated (say, follow a parabola on the scatterplot) but have the correlation close to zero. Elementary Statistics texts usually skip this detail.