Construction of new housing jumped 15 percent last month to an annualized rate of 1.83 million units, the highest level since January of 1984, the Commerce Department reported yesterday.

At the same time, the Federal Reserve Board reported that the operating rate of the nation's factories, mines and utilities rose to 81.9 percent of capacity, up from 81.7 percent in December, but remained below the record levels of last summer.

The Reagan administration obviously was pleased with the economic picture, particularly in housing.

Commerce Secretary Malcolm Baldrige attributed the surge to lower interest rates that are "boosting new housing construction and stimulating sales of existing homes." He said, "Residential construction should make a positive contribution to economic growth in the current quarter and in all of 1985."

The White House issued a statement calling housing a "historic barometer of economic growth" and adding: "Right now that barometer is rising. Housing and the economy are off to good starts."

Interest rates have indeed been falling. The average commitment rate for a 30-year, fixed-rate mortgage was 12.9 percent last week, according to a survey by the Federal Home Loan Mortgage Corp., down from more than 14.5 percent in July.

But in light of that, many experts in the field found the numbers somewhat puzzling. Construction starts in single-family homes and buildings of two to four units declined slightly, while the figures for buildings of five or more units climbed a whopping 76 percent, accounting for the entire overall increase.

James Christian, chief economist of the U.S. League of Savings Institutions, said he was "a little surprised that single-family starts were down even that little bit. The market fundamentals look pretty good."

In addition to lower interest rates, Christian pointed to steady improvements in personal income and added that "it looks like the economy is growing again."

"I would really look for a fairly decent spring . . . good solid production," he said.

Michael Sumichrast, chief economist of the National Association of Home Builders, noted that seasonal factors can magnify changes disproportionately in the winter when the actual numbers are small. "You really have to wait for the three-month data to tell anything," he said.

But he added that he views the Commerce figures as "excellent numbers, much better than I would have guessed three months ago." And he said the NAHB's own surveys of builders' views are "the best in eight years . . . . Builders are very, very optimistic."

Analysts also were not certain why multifamily construction increased so much. Sumichrast said he thinks builders were implementing unused permits that had piled up in the preceding months. Christian noted that the multifamily starts were concentrated in the West, where vacancy rates are lower. "Most are based in market fundamentals," he said.

Warren Lasko, executive vice president of the Mortgage Bankers Association of America, said that while "we can only conjecture about what is going on," his association has noted "remarkable" levels of housing bond financing in the West, particularly in Alaska and California.

"The spurt in financing could underlie the spurt in starts in January," he said.

In any case, Lasko added, "it doesn't appear likely that the January figures will be sustained." He noted that permit figures paint "the opposite picture," one that is "more like the picture we are going to see as months go by," though he said "we could see some pickup in single-family" starts.

The Commerce Department said permits were issued last month at an annual rate of 1.66 million units, 2 percent above the December rate.

The Fed's capacity-utilization figures showed production gains for mines and utilities, while the rate for manufacturing plants was unchanged from december.

Mines operated at 75.2 percent of capacity, compared with 74.9 in December, while utilities reached 84.3 percent, compared with 82.8 percent the previous month. Manufacturing plants ran at 82.1 percent of capacity. The peak overall level for the recovery occurred last July, when plant use hit 82.7 percent.