The battered economy got its first dose of good news in a long time yesterday when the Commerce Department announced that housing units were being started at an annual rate of more than 1.4 million in November, a 26 percent increase over October's rate.

Generally, a pickup in homebuilding is a necessary prelude to an economic recovery. A rise in construction of single-family homes, small apartment buildings and bigger multifamily dwellings triggers improvements in other industries such as appliances, furniture and textiles.

Secretary of Commerce Malcolm Baldrige said yesterday's report "confirms that this key sector is in a solid recovery." He said the pickup is due to declining interest rates, and lower rates should stimulate other industries as well.

While the housing industry is recovering, a Federal Reserve Board report yesterday showed that the rest of the industrial economy remains in the grip of a severe recession.

The central bank said that industries were operating at only 67.8 percent of total capacity in November, 0.5 percentage point below October and the lowest level of so-called capacity utilization in the post-World War II period.

At the depths of the harsh 1975 recession--until the current decline, the worst recession the economy had experienced since the Great Depression of the 1930s--capacity utilization fell to 69 percent.

Alan Greenspan, former chairman of the Council of Economic Advisers and now head of the consulting firm Townsend-Greenspan Inc, said the low level of factory utilization is making companies hold back on spending for modernization and expansion. Business investment spending will be crucial to an econonic recovery as well.

Greenspan said that, because industry is producing so little, there is "no incentive to replace a nonoperating high-cost facility with a nonoperating low-cost facility."

Nevertheless, Greenspan said the upturn in homebuilding--the industry began a mild recovery last year--is welcome. If the United States is to have an economic recovery in the near term, housing will have to lead it, Greenspan said.

Donald H. Straszheim, vice president of Wharton Econometric Forecasting Associates, called the sharp increase in housing starts the "best news the economy has had in years."

Not only did housing starts jump 26 percent in November, but permits authorizing construction at some point in the future were issued at a seasonally adjusted annual rate of 1.24 million in November, 6 percent more than in October.

Both housing starts and permits are more than 65 percent higher than in November 1981.

Straszheim said that housing is recovering faster than expected--indicating there is a strong demand for housing that is being stimulated by declining rates. He said mortgage rates can be expected to decline another 2 percentage points by the end of 1983, which should boost housing construction further.

The Labor Department also reported that the number of workers filing initial claims for unemployment insurance fell from 598,000 to 590,000, the lowest weekly total since early August. The number was 654,000 two weeks ago.

The Labor Department figure suggests that layoffs are slowing down, an indication that, while the overall economy may not be getting better yet, it is not getting sicker as fast as it has been.

For example, while fewer workers are being laid off, even fewer are finding new jobs. While initial claims for benefits declined, the total number of workers collecting unemployment insurance grew by 123,000 last week. The unemployment rate, at 10.8 percent last month, still is expected to pierce the 11 percent level in December.