Question 3

QUESTION 3 [16] The following model (M) was proposed for testing whether there was a significant interaction be- tween two predictor variables X1 and X2. y = Pot Bix1+ B2x2+ 83x2+ P4x1x2+c. (M) 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 2.8653 x 10- 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 3.3025 x 10-8 Residual 5 4.6197 0.9239 Total 9 7492.4 (3.1) Do the data provide sufficient evidence to support the model without interaction instead of the full model? Use a = 0.05. Show all necessary calculations before explaining your answer. (10) (3.2) Repeat the appropriate steps in part (3.1) using a = 0.01. (4 ) (3.3) Do we obtain the same conclusions in parts (3.1) and (3.2)? Explain your answer. (2)