Not very much until I know the source of the data and whether I can actually trust it. However, it's certainly not inconceivable that such a correlation might be highly misleading. Here are two simple thought experiments to illustrate this.
1. Suppose that in every country, in every year GDP growth is exactly proportional to government spending the previous year. In other words, spending more produces immediate GDP gains. And suppose that government spending generally changes quite slowly, within certain limits.
Then low spending at the start of a decade will correlate with increasing spending over the decade (because of regression to the mean) and therefore with increasing GDP growth over the decade (because of the assumed relationship between spending and GDP growth). So we'll get a graph rather like that one despite the fact that the real relationship between spending and GDP growth is positive.
2. Suppose that GDP growth is entirely independent of government spending, and that it depends on some other characteristics of a country; that high-growth countries tend also to be rich ones (as they would, having grown faster in the past); that all countries would (with equal patterns of taxation and government spending) have roughly equal levels of inequality, so that poorer countries have more really poor people; and that government spending is dominated by attempts to give the poorest people a decent life.
Then the poorer countries will spend more, because they have more people who need government assistance to keep out of severe poverty; they will also have less growth (by our assumptions); so we'll see a correlation like the one in the graph, even though there is (by assumption) no causal relationship between government spending and GDP growth.
Of course these are both likely to be much simpler than the truth. But then, so is the model you're implicitly relying on if you point to the graph and say "see, government spending inhibits growth" without further analysis. (That model would be something like: GDP growth is purely a function of government spending over the previous decade, and nothing else.)
I'd say that there's a lot more variables that you didn't control.
It seems fair to say that a big contributor to our economic success in the 50's and 60's was due to every other first world nation having been reduced to rubble in the 1940s.
Manufacturing and innovation in Japan and Europe didn't really roar back until the late 60s and 70s.
1. Suppose that in every country, in every year GDP growth is exactly proportional to government spending the previous year. In other words, spending more produces immediate GDP gains. And suppose that government spending generally changes quite slowly, within certain limits.
Then low spending at the start of a decade will correlate with increasing spending over the decade (because of regression to the mean) and therefore with increasing GDP growth over the decade (because of the assumed relationship between spending and GDP growth). So we'll get a graph rather like that one despite the fact that the real relationship between spending and GDP growth is positive.
2. Suppose that GDP growth is entirely independent of government spending, and that it depends on some other characteristics of a country; that high-growth countries tend also to be rich ones (as they would, having grown faster in the past); that all countries would (with equal patterns of taxation and government spending) have roughly equal levels of inequality, so that poorer countries have more really poor people; and that government spending is dominated by attempts to give the poorest people a decent life.
Then the poorer countries will spend more, because they have more people who need government assistance to keep out of severe poverty; they will also have less growth (by our assumptions); so we'll see a correlation like the one in the graph, even though there is (by assumption) no causal relationship between government spending and GDP growth.
Of course these are both likely to be much simpler than the truth. But then, so is the model you're implicitly relying on if you point to the graph and say "see, government spending inhibits growth" without further analysis. (That model would be something like: GDP growth is purely a function of government spending over the previous decade, and nothing else.)