* Sales of new homes are seen rising by about 6.7 percent to a 320,000 unit annual rate in June from 300,000 in May. Sales plummeted 32.7 percent in May to the lowest since record-keeping started in 1963. Forecasts from 57 economists polled by Reuters range from 290,000 to 350,000 units.

* Standard & Poor's/Case-Shiller 20-city home price index is seen up 4.0 percent year-over-year in May, compared with a 3.8 percent rise in April. The 26 economists in a Reuters poll estimate a rises ranging from 2 percent to 5.1 percent.

* The 20-city index likely rose 0.2 percent in May from April, seasonally adjusted, with forecasts from 13 economists spanning between a 0.6 percent drop and a 0.5 percent gain. Unadjusted, prices likely rose 0.3 percent, with nine forecasts between a 0.4 percent drop and 0.8 percent rise.

FACTORS TO WATCH

New home sales likely rose about 6.7 percent in June, but the advance would come from record lows set in the wake of the homebuyer tax credit expiration on April 30.

Tax credits of up to $8,000 pulled sales forward into the spring at the expense of summer sales.

Applications to buy homes hover just above 13-year lows, according to the Mortgage Bankers Association, even though mortgage rates are at record lows and prices remain about 30 percent below peaks set four years ago.

The National Association of Home Builders sentiment index in July sank to a 15-month low in the tax credit hangover. The sales retreat has turned out to be longer than expected because of the sluggish recovery in the broader economy, particularly in employment, the NAHB and other economists said.

As for home prices, the S&P/Case-Shiller 20-city index is seen up 4.0 percent in May from a year earlier, compared with a 3.8 percent annual increase reported for April, a Reuters survey found.

Prices in May likely climbed but at a slower pace than in April. The 20-city index is seen up 0.2 percent, seasonally adjusted, and up 0.3 percent unadjusted, compared with April gains of 0.4 percent and 0.8 percent, respectively.

MARKET IMPACT

The biggest surprise for the markets would be data showing that the U.S. housing market can avert a double dip.

Granted, this leg down in housing is likely to be tame, with single-digit price declines widely expected after a period of stability induced by the tax incentives.

Evidence of a small rise from a deep floor in new home sales and a sideways pattern in prices would reinforce the widespread view that housing will bounce around the bottom until employment improves and foreclosures subside.

(Reporting by Lynn Adler; polling by Bangalore Polling Unit)