* U.S. market loses some of its early gains
* China cuts interest rate for second time in two months
* Apple up 5.1 pct, Best Buy jumps 15.48 pct
* Nine of the 10 major S&P sectors higher
* Indexes up: Dow 1.95 pct, S&P 1.81 pct, Nasdaq 2.49 pct (Updates to late afternoon trade)
By Noel Randewich
Aug 25 (Reuters) - Wall Street rallied on Tuesday as investors bought beaten-down stocks a day after fears about China's economy sent the market into its worst slump in four years.
Investors drove prices sharply higher from the opening bell but caution set in by the afternoon due to lingering concerns that a slowdown in China could hobble global growth, even after the country's central bank cut interest rates on Tuesday for the second time in two months.
"(It's) just investor confusion," said Art Hogan, chief market strategist at Wunderlich Securities in New York. "They are trying to figure out what the slowdown in China means to the global economy," he said.
Monday's pummeling pushed the S&P 500's valuation down to about 15 times expected earnings, compared to around 17 for much of 2015 and just above a 10-year average of 14.7, according to Thomson Reuters StarMine.
"We had a panic yesterday. As people get back in the market, they're questioning what everything is worth, said Brian Battle, director of trading at Performance Trust Capital Partners in Chicago.
While U.S. stocks appeared relatively cheap to some investors, others were waiting for positive economic data from China, said Xavier Smith, investment director at Centre Asset Management.
"Only when we see that will the rallies be sustainable."
The move by China's central bank came after Chinese stocks slumped 8 percent on Tuesday, on top of an 8.5 percent drop on Monday.
The Nasdaq composite index led stocks higher with a 2.49 percent rise, fueled by a 5.1 percent jump by Apple's .
The iPhone maker's stock had slumped as much as 13 percent on Monday, when the Dow Jones industrial average fell more than 1,000 points in its biggest intraday fall ever and the S&P 500 recorded its worst day since 2011.
Even with Tuesday's gains, the Dow and the S&P were on track for the their worst monthly losses since February 2009 and the Nasdaq headed for its steepest drop since November 2008.
JPMorgan cut its forecast for its year-end target for the S&P 500 to 2,150 from 2,250.
At 2:52 p.m., the Dow Jones industrial average was up 309.18 points, or 1.95 percent, at 16,180.53 and the S&P 500 was 1.81 percent higher at 1,927.48.
The Nasdaq Composite added 112.56 points to 4,638.81.
Earlier, the S&P rose as much 2.9 percent, the Dow as much as 2.8 percent and the Nasdaq as much as 3.6 percent.
Data on Tuesday showed U.S. consumer confidence increased to a seven-month high in August.
Nine of the 10 major S&P sectors were higher in afternoon trading, with the consumer discretionary index's 2.3 percent rise leading the advancers, helped by Amazon's 4 percent rally.
New U.S. single-family home sales rebounded in July, adding to evidence of underlying strength in the economy that could allow the Federal Reserve to raise interest rates this year.
Among the big gainers, Facebook was up 4.5 percent and Netflix jumped 8.6 percent.
Best Buy jumped 15.48 percent after the owner of the biggest U.S. electronics chain reported an unexpected increase in quarterly sales.
Advancing issues outnumbered decliners on the NYSE by 2,304 to 786. On the Nasdaq, 1,996 issues rose and 835 fell.
Underscoring the delicacy of Tuesday's rally, the S&P 500 index showed just one new 52-week high and 12 new lows, while the Nasdaq recorded seven new highs and 83 new lows. (Additional reporting by Tanya Agrawal, Saqib Iqbal Ahmed in New York,)