The decision by Americans to hunker down during the coronavirus pandemic has been heavily influenced by pronouncements from national and local leaders, according to data released Monday by the Centers for Disease Control and Prevention.

The report offers the most robust information to date showing the relationship between people’s behavior and official policies announced by the White House and local leaders.

The CDC used cellphone data from four cities — New York, San Francisco, Seattle and New Orleans — and correlated it with when governors, mayors and President Trump announced states of emergency, limits on mass gatherings, school closures and White House recommendations.

San Francisco offers perhaps the clearest illustration of the effect. The chart below shows how often people were leaving their homes, as tracked by their cellphones, after San Francisco County declared a state of emergency Feb. 25.

People’s movement started decreasing a few days after the declaration, but the two biggest drops came after the city closed schools and President Trump announced a 15-day national “pause,” including a nationwide recommendation against gatherings of more than 10 people.

Cities and states took action at different times so it is hard to compare one with another, but Trump’s 15-day pause is one universal data point that appears to have had a broad effect.

This has significant implications for how the nation moves forward and for assessing the country’s early stumbles during the pandemic.

Critics have said U.S. leaders should have moved sooner and more aggressively in imposing restrictions given events in China, Iran and Italy. That may have had a dramatic effect on stemming the exponential growth of cases in February and March.

The blame game has only intensified in recent days.

In a Sunday interview on CNN, Anthony S. Fauci, director of the National Institute of Allergy and Infectious Diseases, seemed to confirm that he and fellow health officials had recommended social distancing guidelines a month before Trump announced the guidance. “We make a recommendation,” Fauci said. “Often, the recommendation is taken. Sometimes, it’s not.”

By Sunday night, Trump had retweeted a call to “#FireFauci,” one of his top White House advisers on the coronavirus and a globally renowned epidemiologist.

At the same time, the president and his task force have fixated almost exclusively on plans to reopen the U.S. economy by the end of the month, though they haven’t detailed how they will do so without triggering another outbreak.

Health experts say ending the restrictions prematurely would be disastrous because the restrictions have barely had time to work, and because U.S. leaders have not built up the capacity for alternatives to stay-at-home orders — such as the mass testing, large-scale contact tracing and targeted quarantines used in other countries to suppress the virus.

The CDC data offers clues on the vital role social distancing has played in dramatically reducing infections and slowing the exponential growth of the virus. The small dotted line in the chart below represents the three-day average percentage change in San Francisco’s cumulative case count — a key measure of epidemic growth.

It is important to note that while the CDC data suggests strong correlations between when these public policies were announced and the drop in people’s mobility and changes in case counts, it does not prove it empirically and conclusively.

“The trends suggest, but cannot prove, a causal relationship,” the CDC report said.

To study how much people left their homes, CDC researchers used publicly aggregated, anonymized cellphone data provided by the company SafeGraph, which took users’ common nighttime locations — when they probably were sleeping at home — and tracked their movement within 150 square meters of that location.

Another interesting wrinkle is the order in which these public policy pronouncements were made. In all four cities, the emergency declaration came first and stay-at-home orders were often the last resort implemented.

In all four locations, emergency declarations didn’t appear to have much influence on mobility. The biggest declines seemed to require a combination of policies, such as limiting mass gatherings, closing schools and sending signals of seriousness from the White House.

Even after these policies, recommendations and orders were announced, many people did not stay at home — illustrating one continuing challenge in the country’s public health crisis. By April 1, New York City was still seeing 42 percent of people leaving home every day, with Seattle and San Francisco at about 50 percent and New Orleans at 58 percent.

Lena H. Sun contributed to this report.