What does Rex Reagan have in common with Teddy Roosevelt, Grace Coolidge and Queen Wilhelmina?

They've all seen Abraham Lincoln's ghost.

And they're not alone. Plenty of others -- both White House residents and their guests -- claimed they "felt" Lincoln's presence through the years.

Winston Churchill hated to sleep in the Lincoln Bedroom and usually slipped across the hall when he could. Lady Bird Johnson told Liz Carpenter, then her press secretary, of feeling Lincoln's presence when she sat watching a television special on Lincoln's life one spring night. Dwight Eisenhower told his press secretary, James Haggerty, that he often felt Lincoln's presence. And Harry Truman once told of being awakened by two knocks on his bedroom door, but when he opened it, no one was there.

Now, on the eve of the 177th anniversary of Abraham Lincoln's birth, White House ghostbusters may be on the verge of solving the mystery. Rex Reagan is sniffing around. His mistress has confirmed that he occasionally goes to the threshold of the Lincoln Bedroom, where he barks but never goes in.

That's the same mistress who shortly after moving into the White House noticed that a contemporary painting of Lincoln in the Lincoln Bedroom always seemed to be askew. Nancy Reagan straightened it, only to find it hanging crooked the next time she went into the room. One day, she mentioned it to a White House maid.

"Oh," said the maid, "he's been here again."

This father-daughter act was slightly different.

"Some of you may think it a little unfair to catch her off guard like this," said the father, looking not the least bit remorseful, "but let me assure you, she's been doing this to me all my life."

"Are we even now?" asked the equally unremorseful daughter, wiping her lipstick off his cheek.

They were President Reagan, the surprise guest, and Maureen Reagan, the guest of honor he was surprising last night at a reception celebrating her role as U.S. representative to the United Nations Commission on the Status of Women. Assistant Secretary of State Alan L. Keyes hosted the party at the State Department. He got an assist from Secretary of State George Shultz, who praised Maureen for excelling at "multilateral diplomacy" at the women's conference in Nairobi, Kenya, last summer.

Reagan was also laudatory. He said every time he read how the American delegation in Nairobi might be outsmarted, "I'd think to myself, 'Somebody out there sure doesn't know my daughter' . . . To Nancy and me, she's someone we love dearly but also someone whom we recognize is the extraordinary individual she is."

Maureen heads for Vienna on Feb. 24 to "begin the process of implementing" the "hard-won strategies and dreams" at Nairobi.

"We are determined that what happened in Nairobi will not end in Nairobi," she told the 250 guests, who included Reagan aides, members of the Cabinet and several foreign ambassadors.

Ron Reagan's "Saturday Night Live" debut left 'em laughing at the White House, or so says Nancy Reagan's press secretary.

The Reagans didn't stay up to see the show, but Elaine Crispen said they saw it Sunday on videotape.

"They had never seen the show before, but as far as Ron was concerned, they were delighted at how good he was on stage, how at ease he was," Crispen said.

First Son Ron comes by his stage presence naturally enough. But in addition to having show biz parents, he did a stint in the Joffrey Ballet's junior corps before turning to free-lance writing. As host of NBC's "Saturday Night Live" over the weekend, he unabashedly went before the cameras wearing white undershorts and a hot pink shirt and strumming a broom guitar with appropriate rock gyrations in a parody of the movie "Risky Business."

The Reagans just thought it was "that kind of show," said Crispen. "They weren't offended. They thought the whole thing was funny."

Nancy Reagan's copy of First Daughter Patti Davis' highly autobiographical novel, "Home Front," arrived yesterday at the White House. The first lady apparently had no plans to stay up all night reading it.

"I imagine she'll pack it into her bag for the ranch," Crispen said.

The Reagans leave tomorrow for their Santa Barbara ranch. The president will return to the White House on Saturday, but Mrs. Reagan won't be back until next week because, among other things, she's going to the wedding of Doug Wick and Lucy Fisher in Los Angeles on Sunday. Doug is the son of U.S. Information Agency Director Charles Z. Wick and his wife Mary Jane.

Crispen said she doesn't know what Mrs. Reagan's plans are for Monday, or whether she might go house-hunting in Los Angeles. The first lady has already seen a half-dozen houses, but so far nothing she decided she wants to buy.

Crispen said friends keep Mrs. Reagan informed about what comes onto the market. But the press secretary thinks the first lady isn't in a hurry to find something because she and the president have adequate accommodations at the moment, both here and in California.

"I don't think they need a house to move into until they leave the White House," Crispen said.

Five and a half years and two presidential elections after a friend first commissioned it from Lenox, Jimmy Carter's presidential china has found a table to call home. Not at the White House, obviously, but at the Carter Library and Study Center, due to open at Emory University this fall.

Rosalynn, you'll remember, never got around to ordering the Carter china in time to take delivery at the White House. She wasn't the only first lady who thought her husband would have a second term; Jacqueline Kennedy, Pat Nixon and Betty Ford didn't order china either.

But all's well that ends well -- and is paid for by Carter friends. With its two-inch presidential seal, etched gold bands and "Carter green" border, this 36-place ivory dinner set is as fit for a king as anything the Reagans have at the White House. And kingly guests there well might be.

"Remembering Camp David, my feeling is that when there is a dispute between nations, President Carter hopes to discuss it at the center and come up with a common agenda," said Set Charles Momjian, whom Carter named as a U.S. representative to the United Nations in 1978-79 and who spearheaded the drive to buy the china.

Meanwhile, in the current issue of House and Garden, Carter writes about his and Rosalynn's involvement with Habitat for Humanity, the "ecumenical effort" intended to provide "decent housing for poor people in need" without state or federal assistance.

Apparently, it's only the beginning of the Carters' determination to spread the word. In collaboration now on a book titled "Habitat for Humanity," they are taking turns at writing the chapters.

Rosalynn, of course, has already finished the first one.

Betty Ford was in town last week and, never one to miss a chance to plug the drug and alcohol treatment center bearing her name, she popped in to congratulate a longtime friend on his new job -- Health and Human Services Secretary Otis R. Bowen. The former first lady, who is about to write a sequel to her autobiography, used to give Bowen's predecessor, Margaret Heckler, periodic updates on the Betty Ford Center at Rancho Mirage, Calif. This visit, she also wanted to discuss the center's prospects for treating Medicare patients.

Before coming here, the Fords were in Winston-Salem, N.C., for the baptism of Michael and Gail Ford's newest daughter. Mike Ford is associate dean of students at Wake Forest University, where Betty also delivered the Founders Day convocation at Wake Forest Chapel.

In Washington she stayed with daughter and son-in-law Susan and Charles Vance and their two daughters. Susan arranged a luncheon for her mother, inviting some of the Fords' former Alexandria neighbors. Those who RSVPd by telephone heard a well-rehearsed recitation that began, "Good morning. Who's this? Just a minute. I'll put you on hold."

An obviously proud grandmother later identified the voice as that of Tyne Vance, 5. As for the recitation, "that's her job," explained Betty Ford.