Chapter 296: The Regression Equation

Captain Ma went out to investigate, and the few people left in the tiny bathroom calmed down slightly, each lowering their heads to attend to their tasks.

Jiang Yuan also lowered his head to think.

For him, the preliminary phase of the case was essentially complete. The judgment of the time of death did show discrepancies, but that wasn't the issue—it might even help solve the case.

Of course, based on Jiang Yuan's experience, even without this skill, a case of this scale could likely be cracked by other clues once Captain Ma returned from his investigation.

Jiang Yuan was thinking to reset his thoughts.

Comrade Ye Tianhe was a bit noisy.

As a forensic pathologist himself, Jiang Yuan now understood that Ye Tianhe simply outputted his conclusions too often and wasn't used to being questioned.

Forensic pathologists held relatively high status at crime scenes—this referred to professional authority.

Usually, once a forensic pathologist gave an estimated time of death, no detective would ask: "Did you miscalculate?"

Even detective captains lacked the professional competence and confidence to make such judgments. At most, they'd only bully new forensic pathologists.

Laypeople judged forensic pathologists by whether they stood unmoved before corpses and unmoved by stench—satisfied with that, they'd only ask about love life or family matters.

Professional exchanges among forensic pathologists were rarely intense.

Especially for grassroots forensic pathologists, either they received support and recognition from higher-level pathologists, in which case their word was final,

or their own expertise was low and their confidence weak, so they never entered into heated debates.

Ye Tianhe was actually a relatively strong forensic pathologist.

As a forensic pathologist for the provincial capital's criminal investigation brigade, Ye Tianhe might seem easygoing, but he didn't fully accept technical guidance even from provincial bureau pathologists.

So most of the time, Ye Tianhe operated with one-way output and rarely underwent verification.

In normal cases, when Ye Tianhe arrived at the scene as a forensic pathologist, examined the body, and reached a conclusion, detectives wouldn't question him; even peers who were confident enough wouldn't surpass him much in ability, and their methods and conclusions would be nearly identical.

As for the truth of the case, feedback wouldn't come immediately, nor would it necessarily be accurate; even if the conclusion turned out to be flawed—off by a few hours, or even days—forensic pathologists easily comforted themselves.

In fact, using only rectal or liver temperature to determine time of death, most regression equations had an initial accuracy of only about 85% or 90%; an error of one or two hours was routine.

So it wasn't so much that Jiang Yuan and Ye Tianhe had conflicting opinions, but that their standards weren't on the same level.

Ye Tianhe simply hadn't faced such direct, face-to-face challenges in a while.

After calming down, Ye Tianhe quickly realized it himself and smiled at Jiang Yuan: "Jiang Yuan, did I just get tangled up in your logic? I was talking about body temperature and using rectal temperature to estimate time of death, and you brought up rigor mortis, corneal opacity, and all sorts of other things." Jiang Yuan eased the tension: "I came in too hurriedly, flustered. You're right—other factors yield different time-of-death estimates than body temperature, so body temperature alone seems abrupt." Ye Tianhe nodded, but his understanding was superficial.

After all, forensic pathologists always used body temperature when possible for time-of-death estimation.

Because body temperature was easier to quantify—whether rectal, liver, or surface temperature, a thermometer would give a precise reading.

A precise temperature, plugged into a regression equation—even a simplified one—produced a highly accurate time-of-death estimate.

For detectives using this data—whether from the Changyang City Criminal Investigation Brigade or the Ningtai County Criminal Investigation Team—

for bodies found that day, precision within two or three hours, or for bodies found days later, precision to morning, afternoon, or evening, was more than sufficient.

Jiang Yuan's time estimate was excessively precise—unconventional.

Ye Tianhe's inability to understand was normal.

Jiang Yuan had no time to lecture him: "If conditions allow, performing a chemical analysis of the eyeball could yield a relatively accurate conclusion, since red blood cell rupture and potassium ion accumulation are largely unaffected by temperature." Ye Tianhe replied: "Maybe. But the time difference is too large." "I agree," Jiang Yuan said. "Under normal weather and environmental conditions, such a large discrepancy is unconventional."

"Mm."

"I think this is likely due to the suspect fabricating the scene."

Ye Tianhe froze, his gaze immediately falling on the bathtub beside the bathroom. "How?" he asked.

Based on his forensic experience, his first thought was the bathtub.

Water immersion greatly affects temperature—many times more than air does. Thus, estimating time of death for a body in water differs significantly from estimating it for a body on land.

If ice were added to the water or it was heated, the discrepancy could be enormous.

Ye Tianhe stepped forward again to examine the body, then shook his head: "No signs of water contact."

"We could reverse-calculate using the multiple regression equation."

Jiang Yuan took out his notebook, writing as he spoke: "Assume rectal temperature is y, and environmental temperature, clothing or covering, body substrate, ventilation, humidity, gender, age, body type, and cause of death are a, d, e, f, g, h respectively. With given coefficients, the equation is: y = 44. 52 - 0. 11a + 0. 88b + 0. 35c + 0. 36d + 0. 63e + 0. 64f + 0. 49g + 0. 19h."

Earlier, Ye Tianhe had been bothered that Jiang Yuan hadn't measured rectal temperature or provided data—he'd just stated a number outright.

Now, hearing Jiang Yuan cite precise figures, he fell into confusion again.

As Jiang Yuan plugged in numbers and calculated, he continued: "The key here is quantifying a, d, e, f, g, h—for example, cause of death can be simply quantified by blood loss: massive hemorrhage can be assigned a value of 2. The husband has an alibi." "What kind of alibi?" Jiang Yuan asked. Alibis could theoretically be faked, especially by those who favored perfect murders; endless hypothetical discussions sometimes led to such ideas.

Captain Ma shook his head: "The alibi is solid. The husband works for an outsourced internet company. His workstation has cameras, his computer logs are recorded, the office building has entry/exit cameras, and if he leaves his seat too long, his phone alerts. Unless the company is massively falsifying records, it's impossible."

"Then it must be someone else." Jiang Yuan nodded.

Captain Ma hesitated, then whispered: "Maybe we shouldn't pin the time of death so tightly." "I've double-checked—the time of death isn't problematic," Jiang Yuan said.

"Double-checked?" Captain Ma asked.

Jiang Yuan tore off the calculation page from his notebook and handed it to Captain Ma.

Captain Ma saw a sea of letters and numbers, then gave a pure human smile: "I shouldn't have asked."

"This multiple regression equation is hard to reverse-calculate, but someone definitely fabricated the crime scene and disrupted the body's temperature." Jiang Yuan did the calculations only to clarify his thinking.

Now his thoughts were clear; he no longer needed to look at the numbers. He muttered to himself: "Either the victim was drugged—requiring a toxicology test—or someone altered the body or its surrounding environment. This family's bathroom is small; if temperature and humidity were raised for two or three hours to a high enough level, it's possible. But—"

Jiang Yuan glanced at Forensic Pathologist Ye and Captain Ma: "If it were high temperature and high humidity, we should've sensed it when we entered."

Ye Tianhe shook his head slightly: "I walked here for forty minutes."

"Didn't the responding officers mention anything? Ask Captain Ma?"

Captain Ma grunted, immediately pulling out his phone to ask.

Soon, he put his phone down and shook his head: "Neither of the responding officers noticed anything unusual."

"Then… ask the husband?" Jiang Yuan hesitated slightly.

Captain Ma frowned: "This… unless we're certain, I think we should hold off for now? Suppose someone really fabricated the scene and created high temperature and humidity—yet now there's none of that, meaning they removed it beforehand. Could this be a seasoned criminal? They sneaked in, committed the crime, then left."

He was merely going along with Jiang Yuan; from Captain Ma's perspective, such a complex case rarely occurred, and seasoned criminals never made cases this messy.

"If they came in, they might've left traces," Jiang Yuan said, standing up. "I'll help sweep the scene. Forensic Pathologist Ye, will you take the body back for autopsy?"

"Alright."

The group no longer dawdled, returning to their tasks in the bathroom.

Jiang Yuan changed clothes, replaced his gloves, put on his specialized goggles, and began inspecting the scene starting from the bathroom.

Everything seemed to fall into proper order.

Just like before.

Captain Ma and Wan Baoming simultaneously exhaled, then exchanged a glance and smiled.

Just as they felt at ease, Jiang Yuan's voice came again: "This family uses smart home systems—the bathroom's air conditioner, shower heater, and ventilation can all be operated remotely."

—to proceed with inspection