Does U.S. spending on science, space, and technology cause people to commit suicide?

No, it doesn't. There is no connection between spending on science, space, and technology and suicides by hanging, strangulation and suffocation, and no logical argument to think that there would be. So although this graph shows that the two things are correlated, it is an example of a spurious correlation:

(tylervigen.com)

If a very large number of monkeys randomly strike keys on a typewriter for a very large amount of time, one will eventually produce a Shakespeare play. And similarly, if you dig around in data enough, you will eventually find things that look to be connected, which obviously aren't.

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Another of my favorite examples of spurious correlation is usage of Internet Explorer versus the U.S. murder rate:

(chrisblattman.com)

And the number people who drowned by falling into a swimming-pool against the number of films Nicolas Cage appeared in:

(tylervigen.com)

Spurious correlations are the reason why having a consistent, logical theory is important. If you think one thing is being caused by another and have data to show the two are connected, to make a credible case you need to be able to explain why they are connected, and give a theory that makes testable predictions about the relationship between the two things.