The Federal Reserve chairman says that the central bank will raise interest rates. How will this affect prices of food, housing, and oil?

The central bank has overwhelming influence over the
United States economy.  Their control over interest rate fluctuation has a huge effect
over how virtually every business conducts themselves (to say nothing of the consumers).
 That said, in short, interest rates are like a pressure valve for the economy.  For
example, in your question, if the fed were to raise interest rates it will change the
prices of all three markets that you have listed.  First, the housing market will slow
down.  If the interest rate is raised, this will discourage people from taking out new
loans for new homes (it will by definition cost them more).  Therefore, we could expect
other subsquent changes to related markets, like construction or the lumber industry.
 For the other two industries, food and oil, you could also see a negative impact over
the long run.  Businesses, just like people, take out loans from banks to help run their
business.  With a higher interest rate on tap; farms will be less inclined to take out
new loans... less likely to purchase more land, plant more crops... then the laws of
supply and demand will swing into action... a lower food supply will invariably lead to
a higher food price.  With oil, you could expect the same effect... drilling oil takes
money... again with a steeper interest rate, oil companies will be less inclined to take
out new loans to operate.