Prices of crude oil have been steadily rising over the last two years (The Wall Street Journal, December 14, 2010). The monthly data on price per gallon of unleaded regular gasoline in the United States from January 2009 to December 2010 were available. Three trend models were created starting with t = 1 and the following output was generated. Using the cubic trend equation, which of the following would be the forecast for the price of regular unleaded gasoline for January 2011?
A) $3.00
B) $3.09
C) $3.175
D) $3.22

Question

Prices of crude oil have been steadily rising over the last two years (The Wall Street Journal, December 14, 2010). The monthly data on price per gallon of unleaded regular gasoline in the United States from January 2009 to December 2010 were available. Three trend models were created starting with t = 1 and the following output was generated.  Using the cubic trend equation, which of the following would be the forecast for the price of regular unleaded gasoline for January 2011?
A) $3.00 
B) $3.09 
C) $3.175 
D) $3.22

Quizplus · Accepted Answer

The cubic trend equation is y = -0.0001x^3 + 0.1091x^2 - 96.901x + 22185, where x = time in months starting with January 2009. To find the forecast for January 2011, we substitute x = 25 (since January 2009 is month 1 and January 2011 is month 25) into the equation: y = -0.0001(25)^3 + 0.1091(25)^2 - 96.901(25) + 22185 = $3.175. Therefore, the forecast for the price of regular unleaded gasoline for January 2011 is $3.175.

Prices of Crude Oil Have Been Steadily Rising Over the Last