Consider all the 11 observations in the table below. The data is from a 2 factor factorial experiment. Factor 2 Factor 1 1 2 3 1 14 8 7 2 10 19 6 3 --- 17 22 4 3 9 10 1.1 Write down the equation of the general model without an interaction term for this data. 1.2 Write down the equation of the general model with the interaction term for this data. (4) (4) 1.3 Write down the normal equations for the no interaction model in part 1.1. 1.4 Find the solutions to the normal equations for the no interaction model in part 1.1. (8) (8)
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Step 1: Let $y_{ij}$ denote the observation for the $i$th level of factor 1 and the $j$th level of factor 2. Show more…
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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.
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The accompanying data file contains 20 observations on the response variable y along with the predictor variables x1 and x2. a. Estimate a regression model with the predictor variables x1 and x2, and then extend it to also include the interaction variable x1x2. What is the estimated regression coefficient for the predictor variable x1 and x2 in both models? (Negative values should be indicated by a minus sign. Round your answers to 4 decimal places.) X1 X2 Model 1(no interaction) Model 2 (interaction) b-1. Which is the preferred model for making predictions? b-2. Use the preferred model to predict y. (Round coefficient estimates to at least 4 decimal places and final answer to 2 decimal places.) Predictor Variables Predicted Y X1 = 30, x2 = 10 X1 = 30, X2 = 20 y x1 x2 37 22 33 51 32 35 57 30 25 42 28 22 28 21 17 87 34 9 64 27 33 52 30 19 45 28 34 56 28 5 31 21 32 34 21 12 38 28 16 84 34 13 44 23 29 54 28 15 31 22 13 35 29 22 66 26 14 72 38 21
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Hi All, Please assist with the following difficult question from my past paper
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