A national home price index from Calfornia-based CoreLogic increased 7.5 percent in 2012, the largest increase since 2006.

The index is based on repeat sales. This year, CoreLogic projects home prices nationally to rise 6 percent due to greater affordability fueling steady demand, a lower level of real estate owned (REO) sales and a low inventory of unsold homes, the company said.

Total home sales nationwide rose 11 percent to 3.2 million, with new sales rising 3 percent to nearly 300,000.

REO sales dropped more than 20 percent to 600,000, the third annual consecutive decline. Short sales were up 23 percent to 370,000 units, the highest level since the real estate downturn began.

Serious delinquencies declined by nearly 300,000 loans in 2012, which drove the seriously delinquent rate down to 6.9 percent, from 7.4 percent in 2011. Since the January 2010 peak, serious delinquencies have declined by 1 million loans.

Massachusetts home sales through November totaled 93,219, up 24 percent from the same period a year before, according to CoreLogic. The stock of foreclosures in Massachusetts is down 19 percent from the peak of the downturn, according to CoreLogic.