Question

The following model (M) was proposed for testing whether there was a significant interaction between two predictor variables X1 and X2. y = β0 + β1x1 + β2x2 + β3x2^2 + β4x1x2 + ε. The regression ANOVA table for the model without interaction is the following: df SS MS F Significance F Regression 3 7474.7333 2491.5778 846.1803 2.8653e-08 Residual 6 17.6667 2.945 Total 9 7492.4 The regression ANOVA table for the full model is the following: df SS MS F Significance F Regression 4 7487.7803 1871.9451 2026.1339 3.3025e-08 Residual 5 4.6197 0.9239 Total 9 7492.4 (1) Do the data provide sufficient evidence to support the model without interaction instead of the full model? Use α = 0.05. Show all necessary calculations before explaining your answer. (2) Repeat the appropriate steps in part (1) using α = 0.01. (3) Do we obtain the same conclusions in parts (1) and (2)? Explain your answer.

          The following model (M) was proposed for testing whether there was a significant interaction between two predictor variables X1 and X2. y = β0 + β1x1 + β2x2 + β3x2^2 + β4x1x2 + ε. The regression ANOVA table for the model without interaction is the following: 
df SS MS F Significance F 
Regression 3 7474.7333 2491.5778 846.1803 2.8653e-08 
Residual 6 17.6667 2.945 
Total 9 7492.4 

The regression ANOVA table for the full model is the following: 
df SS MS F Significance F 
Regression 4 7487.7803 1871.9451 2026.1339 3.3025e-08 
Residual 5 4.6197 0.9239 
Total 9 7492.4 

(1) Do the data provide sufficient evidence to support the model without interaction instead of the full model? Use α = 0.05. Show all necessary calculations before explaining your answer. 
(2) Repeat the appropriate steps in part (1) using α = 0.01. 
(3) Do we obtain the same conclusions in parts (1) and (2)? Explain your answer.

Added by Connor H.

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