Despite higher mortgage interest rates, housing construction has rebounded, increasing 3 1/2 percent in January from December, the commerce Department reported yesterday.

In separate reports also issued yesterday, Commerce said Americans' personal income rose nearly 1 percent in January, but their spending climbed even faster as savings dipped sharply; and the Federal Reserve Board said the nation's factories operated at a seasonally adjusted 80 percent of capacity last month compared with 79.8 percent in December and 79.4 percent in November.

The home-building figures showed that private housing, both singlefamily and multifamily, was started at what would amount to an annual rate of 1,585 million units, about 14 percent above January of last year. Housing starts in December had sagged a little more than 1 percent.

January's increase was entirely due to construction of apartment buildings. Construction of single-family homes decreased by 3 percent, while construction of apartment buildings with five or more units increased by nearly 18 percent.

At the same time, building permits, a reflection of future housing construction of single-family houses decreased by 5.4 percent.

Total personal income increased to a seasonally adjusted annual rate of $2.3 trillion last month, a gain of $21.3 billion, or 0.9 percent, over December, the Commerce Department reported. December's gain also had been 0.9 percent.

But while after-tax, or disposable, income rose 0.7 percent to a seasonally adjusted $1.93 trillion, personal spending rose 1.4 percent to an annual rate of $1.84 trillion, the report said. s

Savings sank 10.7 percent to an annual rate of $88.1 billion in January. The report said December's savings had been about 4.9 percent of the disposable income level for that month.

The personal income total was increased in January by a higher minimum-wage provision but was decreased by a higher base rate for Social Security taxes.

Other figures in the new report showed:

Wages and salaries rose 1.4 percent in January to a seasonally adjusted annual rate of $1.43 trillion.

Government transfer payments, such as old-age and health insurance benefits, rose 0.7 percent to an annual rate of $316.7 billion.

The unadjusted per capita aftertax income rose 0.7 percent to an annual rate of $8,061.

The Fed's breakdown of capacity utilization for January showed advanced processing industries at an adjusted 79.7 percent compared with 79.5 percent in December, primary processing industries at 80.9 percent compared with 80.7 percent and materials industries at 81.7 percent compared with 81.3 percent.