In a study to determine the effect of vehicle weight in tons (x1) and engine displacement in in3 (x2) on fuel economy in miles per gallon (y), these quantities were measured for ten automobiles. The...

In a study to determine the effect of vehicle weight in tons (x1) and engine displacement in in3 (x2) on fuel economy in miles per gallon (y), these quantities were measured for ten automobiles. The full quadratic model y = β0 + β1x1 + β2x2 + β3x2 1 + β4x2 2 + β5x1x2 + ε was fit to the data, and the sum of squares for error was SSE = 62.068. Then the reduced model y = β0 +β1x1 +β2x2 +ε was fit, and the sum of squares for error was SSE = 66.984. Is it reasonable to use the reduced model, rather than the full quadratic model, to predict fuel economy? Explain.