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Variance

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One assumption about the errors in multiple-regression model is that they possesses constant variance. Every residual (error) has the same variance, and the variance does not depend on anything (thus making it constant). This is also called homoscedasticity.

 ***

            Ever since Sherlock returned a week ago, John never strayed far from him.

            Not that he had before, generally, but there had been times before Sherlock faked his death (Faked his death! thought John, Stupid, infuriating, unreliable—[heartbreaking, he also thought, but there was no more thinking about that just now]—git!) that John was away for a time, in another city, sometimes in another country, or Sherlock left for a distant case while John did some locum work in London. But now, just now, just for now, anyway, for the time being, and probably it would go away eventually, such things did, didn’t they—John stayed close. It was probably distressingly predictable, his usual distance from Sherlock.

            “You can occasionally be more than three meters from me,” Sherlock finally said from the window, letting his violin bow rest against the strings. It figured he’d catch on eventually. Well, really, it figured he’d catch on first. “I know you’re worried I’ll disappear again, but I can firmly reassure you that I shall not.” His voice dipped a little, quivered a little, as he made his promise—or was that the bow brushing the strings, confusing John’s ears?

            “Yeah, well,” John couldn’t keep from clenching his fists—just a little—at the memory of Sherlock’s return—most particularly at the rather fantastic and well-deserved wallop he’d given Sherlock about three seconds after he processed what had happened, why this man who looked so much like Sherlock was suddenly in his flat. He’d paused after that blow, too, with Sherlock doubled over against the wall, and clenched his fists. He had, maybe, been thinking about whether he ought to just keep Sherlock pinned up against that wall—but then Sherlock had stood up and brushed himself off and John shook the thought out of his head, because he wasn’t, well—he wasn’t. “Forgive me if I don’t quite believe every bloody thing you say.”

            “It’s actually two point nine.”

            “What?”

            “Meters. That you stay from me, all the time. Well—since you punched me, anyway.” Sherlock rubbed his jaw, apparently replaying that moment himself. “At the flat, at crime scenes—you’d be two point nine meters from me in the cab if you could do.”

            “Oh,” said John, because—well. He hadn’t really been thinking about it all that much. The distance he stayed had just seemed like a pretty good distance to keep. Close enough to keep Sherlock from doing something really stupid again, far enough that John didn’t get tempted to…whatever he was thinking of doing before, with his clenching fists and Sherlock doubled over against the wall. “I hadn’t really put that much thought into it.”

            “How very homoscedastic of you.”

            “I’m not ga—” John started, and then frowned. “What?”

            “Homoscedasticity, John. The property of constant variance.”

            “Variance?”

            “It’s like error, John.” Sherlock set down his violin and moved rather closer than John’s two-point-nine meter rule of thumb had put him. Rather closer. Rather sort of a lot closer, in kind of a very much right there way. Close in sort of a hands-inches-from-John’s-hips way, in a manner of speaking. Or in an exact way of speaking. “In this case, the error would be defined as your distance from me.”

            “Um,” John said, because…well. What else was there? “That’s an error, is it?”

            “I’m well aware you’re not gay, John,” Sherlock somehow continued to reduce the variance despite the already minute space between them. “But simply being capable of being attracted to women doesn’t mean you can’t want to be homoscedastic a little closer to me.”

            “Right,” John breathed, which was really all he needed to do anyway for the message to reach Sherlock’s ears. He could probably blink it in morse code against Sherlock’s cheek at this point.

            “Do you understand what I mean?” Now Sherlock had bowed his head, so that he was speaking almost against John’s lips. The warm air of Sherlock’s words against John’s lips slipped down through his throat and hit the pit of John’s stomach and then continued down, down, down, gaining heat, gaining momentum.

            John licked his lips. In exiting his mouth, his tongue almost touched Sherlock. “Think so,” he mouthed, and tilted his chin up…

            ...and reduced the variance to zero in what was overall a very pleasant way, with pressing lips and sliding tongues and fingers in belt loops and hands up shirts, teeth on tendons and nails in skin.

            True, John couldn’t stay this close to Sherlock all the time…but maybe constant variance was overrated.