* Strong data may boost odds Fed will reduce stimulus
* Builders rally after Lennar results, data
* Walgreen slips after earnings, Netflix down on downgrade
* Indexes up: Dow 0.7 pct, S&P 0.8 pct, Nasdaq 0.5 pct
NEW YORK, June 25 (Reuters) - U.S. stocks rose solidly on Tuesday, partially recovering from recent steep declines as strong data pointed to improvements in the economy.
Equities were volatile for much of the session, as the data initially raised concerns about central bank stimulus, but analysts said a rebound was due coming off a large drop in Monday's session, which itself followed the worst week for the S&P 500 since April.
"Everyone panicked after the Fed, but the fear is starting to come out of the system now. Investors are realizing that the Fed is still a long way from raising rates," said Mark Foster, who helps manage $600 million at Kirr Marbach & Co in Columbus, Indiana.
The recent downturn in markets started after Fed Chairman Ben Bernanke last week said the Fed's stimulus program may be scaled back this year if the economy improves, placing traders in a paradoxical situation where good data could indicate less stimulus, which would in turn be a threat to growth.
Data on durable goods orders and new home sales in May, and consumer confidence in June, all topped analysts' expectations. The April Case/Shiller report on home prices also was above forecasts.
Housing stocks were among the strongest of the day, surging on the data as well as because Lennar Corp posted strong results and the company pointed to a "solid housing recovery." The stock rose 1 percent to $35.34 while peer homebuilder PulteGroup Inc was up 3.9 percent at $19.02. The PHLX housing sector index climbed 1.7 percent.
The Dow Jones industrial average was up 95.22 points, or 0.65 percent, at 14,754.78. The Standard & Poor's 500 Index was up 11.58 points, or 0.74 percent, at 1,584.67. The Nasdaq Composite Index was up 16.45 points, or 0.50 percent, at 3,337.21.
While the S&P is up 11 percent in 2013, the recent trend has been negative, with the benchmark index dropping below both its 14-day and 50-day moving averages, seen as signs of near-term market direction. It is down about 2.6 percent in June.
"The market trend has turned to the downside. It is now easier to sell rallies than to buy dips," said Donald Selkin, who helps oversee $3 billion in assets as chief market strategist at National Securities in New York. "If we close lower today, that would be a big blow to the bulls."
The S&P on Monday closed at its lowest level since April 22 after China's central bank said the country's banks need to do a better job of managing their cash and due to continued worries about a reduction in stimulus from the U.S. Federal Reserve.
On Tuesday, the People's Bank of China said it would not press banks too hard in its efforts to curb easy credit and prevent a possible banking crisis.
Carnival Corp jumped 4.4 percent to $34.68 after the cruise ship operator named a new chief executive and affirmed its full-year profit outlook.
On the downside, Walgreen Co slumped 7.6 percent to $44.38 as the worst performer on the S&P 500 after reporting weaker-than-expected results, citing slow front-end sales and a challenging economy.
Netflix Inc fell 2.1 percent to $211 after Bernstein downgraded the stock to "underperform."
Barnes & Noble Inc tumbled 18.5 percent to $15.33 after the largest U.S. bookstore chain reported its quarterly net loss more than doubled.