Does private whois registration significantly affect your Google rankings?

I have a high quality content site that was consistently growing the last three months. The backlinks are from authority sites.

Just a few days after I changed my whois registration to private, my Google rankings almost completely dropped (over 90%) all of a sudden.

I have checked Webmaster Tools and don't see any evidence of any competitor doing negative SEO (no bad backlinks).

I'm completely confused as to what might have triggered this as the only change done to the site was the private whois information.

Panda changes can take time - so the possibility exists that changes hit at the same time as your whois registration. To learn about what panda 4.0 meant to many sites, take a look at this MOZ change history for details.

While old, in 2006 Matt Cutts made a comment regarding private registration:

“…When I checked the whois on them, they all had “whois privacy protection service” on them. That’s relatively unusual. …Having whois privacy turned on isn’t automatically bad, but once you get several of these factors all together, you’re often talking about a very different type of webmaster than the fellow who just has a single site or so.”

Nothing finite, but having private domains has the smell / potential that the site has "something to hide" so if you care about SEO / SEM, I wouldn't make it private.