* Domestic car sales roared out of the doldrums in mid-May, finishing 18.2 percent above last year's sales rate for the best showing in seven years for that period, the major auto makers said yesterday.

Analysts attributed the gains to consumer confidence in the economy and sales incentive programs such as cut-rate financing.

Compared with a year ago, GM sales were up 16.8 percent in the May 11-20 period, Ford sales were up 24.4 percent and Chrysler sales were 22.1 percent higher.

The seasonally adjusted annual rate of sales for the 10-day selling period was 9.5 million. Last year, the Big Three earned spectacular profits on sales of 7.9 million cars.

Among the four small producers, sales were up 2.8 percent at No. 4 American Honda Motor Co. Inc., up 6.2 percent at Volkswagen of America Inc. and down 32.6 percent at American Motors Corp.

Nissan Motor Corp. USA , which only recently began operations in Tennessee, sold about 600 cars in the period.

The daily sales rate was 33,501, the best for May 11-20 since 36,609 a day in 1978. For the year, sales were up 4.3 percent.