A broad coalition of diverse groups - including Sears, Roebuck & Co., the National Association of Manufacturers, American Conservation Union, Common Cause and two of Ralph Nader's groups - yesterday endorsed legislation to reduce federal regulation of the airlineindustry.

"Reduced federal control over domestic airline fares and routes is essential to building a stronger air transportation system which serves all segments of the public," members of the coalition said in letters to every senator. "Inflexible an danticompetitive regulaion by the Civil Aeronautics Board raises the cost of air travel to consumers and inhibits the profitability of airlines."

The letter's 11 signers suggested that the issue of airline regulatory reform is a test of the ability and willingness of Congress to deal with the overall issue of regulatory reform, not just airlines.

Legislation to reduce the CAB's hold over the industry has been endorsed by President Carter and has been the subject of extensive hearings by the Senate Aviation Subcommittee which is expected to begin marking up a bill soon. Little has happened in the House so far.

The letter sent yesterday is apparently just the beginning of what many in the coalition said would be an extensive lobbying effort on behalf of the legislation.

Many members of the coalition yesterday expressed surpris and pleasure that they were able to get together. "There is some amount of culture shock, but we do all agree on this issue," said Tim Rich, a spokesman for Sears.

He nonted that Sears generally has supported deregulation efforts in transportation - especially railroads - and though they have "no direct immediate economic interest" in airline regulation," the principles are the same.

"In the course of the years, all of these groups have developed similar positions on this one issue, so the coalition is a pretty natural development," Rich said.

Tim Engel, research director of the American Conservative Union, yesterday said his group plans to send out mailings to the membership and to distribute fliers to travelers at airports, as well as to lobby on the Hill. "The senators have been deluged with mailings from the airlines and their unions," he said. "I don't think they know much about broad support there is for this measure and we hope to show them."

Other signers of the letter were officials of the American Association of Retired Persons, Public Interest Economics Group, Congress Watch, Aviation Consumer Action Project; National Taxpayers Union, National Consumers Congress and the Cooperative League of the U.S.A.