US housing starts increased in April, adding to evidence that residential real estate is gradually recovering after a yearlong slump. Beginning home construction rose 2.2% to a 1.4 million annualized rate, according to government data released Wednesday. Single-family homebuilding increased 1.6% to the highest level this year, entirely due to a jump in the West. Starts of apartment buildings and other multifamily projects also rose. Applications to build, a proxy for future construction, fell 1.5% to an annualized rate of 1.42 million units. Permits for one-family dwellings, however, increased to a seven-month. …Builders are taking advantage of an historically low supply of existing homes for sale and some are offering financing incentives to ease affordability constraints amid budding demand for new houses. That helps explain why homebuilder sentiment currently stands at a 10-month high.