rectstrapolate

To pull an answer completely out of your backside, with the air of authority suggesting that it was well researched and irrefutable.

Origin: A compound phrase derived from rect- (the sphincter from which worthless substances are magically produced) + extrapolate (to extend a trend, conclusion, or other information from existing data).

When asked about the daily sales figures, I rectstrapolated a prime number, a completely made-up figure that my boss took as gospel truth.