In a study to determine the effect of vehicle weight in tons (x 1 ) and engine displacement in in 3 (x 2 ) on fuel economy in miles per gallon (y), these quantities were measured for ten automobiles The full quadratic model y 0 1 x 1 2 x 2 3 x 2 1 4 x 2 2 5 x 1 x 2 was fit to the data, and the sum of squares for error was SSE 62 068 Then the reduced model y 0 1 x 1 2 x 2 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

Question: In a study to determine the effect of vehicle weight in tons (x 1 ) and engine displacement in in 3 (x 2 ) on

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 + β₃x²₁+ β₄x²₂+ 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.

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