The home price index (HPI) produced by Integrated Asset Services’ (IAS) saw a 1.2% monthly increase from May to June, the Denver-based default servicer announced Tuesday. While on its fourth consecutive month of gains, the IAS360 HPI — which tracks monthly changes in median sales prices of US detached single-family homes — is still down 16.7% from its June 2007 high. It fell 2.6% in the first three months of 2009, but has increased 2.7% since then. IAS also broke down its HPI in the four US census regions. The index was up in all four regions — 1.8% in the Midwest, 1.9% in the Northeast, 1.2% in the South, and 0.4% in the West. Of the country’s top 10 Metropolitan Statistical Areas (MSA), only Las Vegas (-1.8%) and Denver (-0.1%) declined in the month-over-month. Boston and Chicago followed increases in May with improvements of 2.9% and 1.3%, respectively, along with three of California’ biggest MSAs — Los Angeles (2.2%), San Francisco (1.7%) and San Diego (1.4%). Write to Austin Kilgore.