Strong housing and earnings reports helped stocks rebound from their worst day of the year. The Dow rose 157.58 points on Tuesday, winning back more than half of its loss a day earlier. The S&P 500 logged its second-best day of the year. Home construction topped 1 million last month, the highest level since June 2008. Robust earnings from companies including Coca-Cola also propelled the market higher. Worries about an economic slowdown in China led to a drop in prices for oil, copper, and other commodities, causing mining and energy stocks to fall. Gold, which was at the epicenter of Monday’s sell-off, rose 1.9 percent to $1,387.40 an ounce.