Data Resources, Inc., one of the country's top economic forecasters, predicts real growth in the service industries will decline only slightly in 1979, despite a sizable slowdown in the economy as a whole.

So-called final consumer expenditures for services such as auto repair and health care, entertainment and communication are expected to rise 11.9 percent this year compared with 12.1 percent in 1978. Adjusted for inflation, growth in the service industry will be about 4 percent versus 4.5 percent last year. This is during a period when Data Resources foresees the gross national product sliding from 3.8 percent real growth to 2 percent and inflation running at 7.6 percent.

Service sector revenues and jobs are less affected by economic slowdowns than are those in manufacturing because people still have to get their laundry done and pay insurance premiums. In 1975, when the GNP dropped to minus 1.3 percent, total consumer services still rose 3.2 percent.

If there is a recession, certain less essential services may suffer, however. During the 1974-75 recession, retail trade, luxury restaurants and business consulting were some of the areas adversely affected. Automobile repairs and movie box office receipts grew, on the other hand, as people made their old cars last longer and avoided the more expensive forms of entertainment.

In its annual industrial outlook, the somewhat lower growth rates in 1979 for four out of seven selected services: advertising, auto repair and leasing, hotels and motels, and motion pictures.Franchising and personal services are expected to gain while total education outlays remain the same. But double-digit inflation could wipe out any gains for half of them.

(The Commerce Department figures for 200 industries are based on assumptions made before the word recession ever crossed the administration's lips. For the purposes of this study, the real 1979 GNP is assumed to be 3.8 percent GNP and the inflation rate 6.5 percent.)

Movies are expected to continue strong, though at a more moderate pace than in 1978, a record year. Total box office receipts reached about $4.1 billion in 1978, or a growth of 18 percent above 1977, whereas receipts are expected to grow another 16 percent this year to $4.8 billion.

Discount air fares and increased pleasure travel helped to make 1978 a record year for hotels and motels. Occupancy rates rose to between 75 and 77 percent and room rates went up, combining to produce revenues of $18.9 billion, a 14 percent rise over 1977. The outlook for 1979 is a 12 percent rise to $21.2 billion. Employment will increase about 4 percent.

Food service industry sales will top the $100 billion mark for the first time this year, according to Thad A. Eure Jr., president of the National Restaurant Association. One of the biggest growth areas will again be fast food restaurants, due to increase 13.3 per cent to $22 billion, whereas the rate of growth for all eating places is likely to slow marginally from 11.4 percent to 11 percent in 1979.

Automotive services will rise 11 percent to $27.6 billion in 1979, down from a 13 percent increase the previous year. As cars continue to become more sophisticated electronically, the cost of repairs will increase dramatically, said Dan Randell of the Automotive Sevice Council.

Franchising is expected to continue breaking records as fast food, real estate and employment chains continue to multiply. There will be a third more realty franchises this year, earning 27 percent more in commissions, or $2.9 billion. For the industry as a whole, this year will see a 9 percent gain to $299 billion for the distribution of products and services through franchises.