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NEW YORK — Investors are starting to believe that the stock market is on the verge of another big rally.

The Dow Jones industrials rose almost 103 points Tuesday, their biggest gain in more than two weeks. The day’s economic news was tepid as the National Association of Realtors reported a drop in homes sales last month that wasn’t as steep as forecast. But analysts said many investors, after seeing the Dow at new highs for 2010, were afraid of missing out on further gains.

The report on housing was typical of recent economic numbers that have been somewhat better than expected but that still point to a weak economy. Sales of previously occupied homes fell 0.6 percent last month to an annual rate of 5.02 million. The drop was less than expected.

For now, the sales numbers aren’t hurting hopes that the economy can recover even if the housing market is still sluggish. The Commerce Department is expected to report new-home sales for February today. A month ago, investors shrugged off an 11.2 percent drop in that reading.

The market’s continuing advance has been welcome, but analysts are divided over whether stocks have run too far or if they have more to gain because of improvements in the economy. The recent gains have been mild in contrast to those of 2010 when triple-digit gains in the Dow were frequent as the index soared higher from a 12-year low.

Even many traders who have doubts about how solid the advance is, expect it to continue until something pops the optimistic mood.

“You can’t deny the trend. Definitely the trend is higher,” said Doreen Mogavero, president of brokerage Mogavero, Lee & Co. in New York. She said investors are optimistic about the health of corporate earnings for the January-March quarter.

“Things seem to be moving along in the right direction. So, to that end, I think people are feeling better.”

But Mogavero is cautious because the advance has come on light trading volume, which signals that not many investors are willing to put money into the market.

The Dow rose 102.94, or 1 percent, to 10,888.83, its biggest point and percentage gain since March 5. The Dow has risen 10 of the past 11 days and is at its highest level since Sept. 26, 2008.

The Standard & Poor’s 500 index rose 8.36, or 0.7 percent, to 1,174.17. It also stands at an 18-month high.

The Nasdaq composite index rose 19.84, or 0.8 percent, to 2,415.24, a 19-month high.

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