Golfer Tiger Woods, engulfed in speculation over his private life after a car accident in the middle of the night, apologized Wednesday for “transgressions” in a statement that apparently addressed allegations he had extra-marital relationships. Woods, the world's No. 1 golfer and a married father of two young children, said in a statement published on his website that “I have not been true to my values and the behavior my family deserves.” He did not directly address the allegations of infidelity. “I have let my family down and I regret those transgressions with all of my heart,” Woods said. Companies whose endorsements have helped make Woods perhaps the world's richest athlete, with a fortune estimated at $1 billion, said they were standing by him. The golfer suffered facial cuts and bruises when he ran his Cadillac SUV into a fire hydrant and a tree while pulling out of the driveway of his home in Windermere, Florida at around 2 A.M. last Friday. The time of the accident and Woods' refusal to meet with police to answer questions about it triggered a storm of speculation. Media outlets have reported Woods, 33, has had extra-marital relationships with at least three women. The Florida Highway Patrol closed its investigation into the accident Tuesday and issued a traffic ticket to Woods for careless driving, saying Friday's accident was his fault but that no criminal charges would be brought. It said there were no claims of domestic violence made during its investigation. Some media reports had speculated that the accident followed a dispute in the Woods household. Woods issued the statement on his website the morning after US Weekly magazine reported that Jaimee Grubbs, a 24-year-old cocktail waitress from California, claimed to have had a 31-month affair with Woods and said she had saved hundreds of text messages to prove it. The report was accompanied by a recording of a voicemail message purported to be from Woods to Grubbs in which he warns her to delete her name from her voicemail because his wife had gone through his phone and could be calling her. “I am not without faults and I am far short of perfect. I am dealing with my behavior and personal failings behind closed doors with my family. Those feelings should be shared by us alone,” Woods said in his statement, adding that “personal sins should not require press releases and problems within a family shouldn't have to mean public confessions.” Several days ago, the National Enquirer tabloid had said Woods had a relationship with Rachel Uchitel, whom the paper described as a “New York City party girl.” Uchitel has denied any such relationship. A third publication, Life & Style magazine, reported Woods had been seeing Kalika Moquin, a marketing manager for a Las Vegas nightclub. The magazine said she “neither confirmed nor denied an affair with Tiger.” The conspicuous absence of tournament host Woods from this week's Chevron World Challenge was a major talking point for the players as they prepared for Thursday's opening round. US Open champion Lucas Glover described Woods's absence as unfortunate but said he fully understood the world No. 1's decision to stay at home this week.