This "employment protection index" is a measure of things like legal requirements for advance notice of layoffs and severance pay, and the degree of regulation of temporary employment contracts, where 0 means "little regulation" and 100 means "highly regulated."

In a graph:

For those with knowledge of statistics, the line in the graph is a regression line of the unemployment rate on the employment protection index.

The regression suggests that for every 10 points of increase in the employment protection index, the unemployment rate increases by about 0.4 points. However, variation in the EPI explains only 7% of the variation in unemployment rates, so it's not a very tight fit, as the graph indicates.

For what it's worth, this seems to indicate that labor regulations play some role in increasing unemployment, but there is little evidence for the overwhelming effects of labor market reregulation suggested by the "party line." For example, (taking the regression literally for a moment) if Germany were to deregulate its labor markets to Irish levels, the data indicate that doing so would knock only about 1.5 points off of the unemployment rate, which would be far from solving the whole German unemployment problem. And even that is probably an overestimate.

Here are some more sophisticated analyses along the same lines:

(1) Unemployment and Labor Market Institutions: The Failure of the Empirical Case for Deregulation, by Dean Baker, Andrew Glyn, David Howell, and John Schmitt

The authors conclude that the statistical evidence for the supposed beneficial effects of labor market deregulation is not strong:

[T]he evidence [for "the widespread belief that rigidities generated by labor market institutions lie at the heart of the unemployment crisis"] is far from conclusive. [T]here is no simple relationship
between any of the labor market institutions and the unemployment rate.

Furthermore, there is more than one path to low unemployment rates:

Countries with very different institutional frameworks have managed to achieve unemployment rates substantially below the OECD average. While the United States and United Kingdom stand out as countries that have achieved low rates of unemployment with relatively weak labor market protections, the OECD also includes examples of countries that have achieved comparable results - Austria, Denmark, Netherlands, Norway, and Sweden - with high levels of labor-market protections. A complete and convincing analysis of the relationship between labor-market institutions and unemployment must be able to explain the success of these more regulated countries as well.

(2) The Role of Shocks and Institutions in the Rise of European Unemployment, by Olivier Blanchard and Justin Wolfers

The authors conclude that labor market regulations do matter, but only in conjunction with macro-economic "shocks" (such as oil price increases, the post-1970 slowdown in productivity growth, shifts in labor demand, and so forth). Neither shocks nor institutions alone can explain both the rise in unemployment and current differences in unemployment rates across countries. This is because there is not enough differences in the degree of "shocks" across countries to explain current differences in unemployment rates, while many of the labor market institutions blamed for poor labor market performance actually pre-date the rise in unemployment.

And here is some historical data on the evolution of labor market protections across countries: