Reading Graphs

There’s a blog, Political Calculations, which is immensely satisfying to a highly political data junkie such as myself.  So it’s a good blog, but the proprietor really hoses his interpretation of this graph:

The graph in question

[government spending] has literally “gone vertical” during the last two years.
In mathematical terms, that’s the sort of thing you see when you divide any number by zero. Applied to the chart above, that means that the relationship between the change in total government spending and the typical income earned by an American household from year-to-year is now “undefined.”

The problem is that this is a bivariate graph, and the concept of slope in terms of dy over dx does not apply.  More precisely, it has little meaning, and manifestly does not mean what it does in the graph of a function of x.

One might as well divide by color.

Notice that in the line segment leading to the most recent data point, it actually moves a small way “backward”, that is to the left, while it continues its march up the page.  You can’t do this with a function, but this is a parametric graph of two independent variables.

So the alarmed tone and if you’ll excuse the term, hyperbolic conclusions drawn by the author are unjustified.  At least, the justification he gives are not true.  This is an informative graph, but in this case, “vertical” means nothing.

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