SMB.Splinesp.96sol.Greek

SMB.Splinesp.96sol.Greek - 1 terms in the cross product so...

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Splines HW p. 96 problem solutions 1. a. 4 parameters total = 3 for the quadratic + 1 for the jump from A to B b. E(y) = 0 + 1 x 1 + 2 x 1 2 + 3 x 3 where x 3 = 1 if B, 0 otherwise 2. a. 4 parameters total = 2 for the line below 5 + 1 for the jump at 5 +1 for the jump from A to B b. E(y) = 0 + 1 x 1 + 2 x 4 + 3 x 3 where x 3 = 1 if B, 0 otherwise; x 4 = 1 if x1 >= 5, 0 otherwise 3. a. 8 parameters total = [3 for the quadratic below 8 + 1 for the new slope of the connected line] x 2 for an entirely unrelated same quant. model for each of levels of A and B b. The hard part is the model for A. Once we have that, we just add the most general qualitative model and take products of these two parts to get the eight parameters. For the model for just A, we start with the line above 8 and then add in first and second order terms without jumps to this below 8. I prefer x 1 2 -8 2 rather than (x 1 -8) 2 since the latter expression then has x
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Unformatted text preview: 1 terms in the cross product so that later when we test that for example the model is just two connected lines at 8, testing the beta =0 for the quadratic term may have an effect on the x 1 linear term. Of course, when there are several ways to write the models, ultimately it depends for our purposes on what we are going to be asked to test and can we test it by testing a subset of betas = 0. If not, we may have to reparameterize! For just the part with A, how about + 1 x 1 + 2 (x 1-8)x 4 + 3 (x 1 2-8 2 )x 4 , then for E(y) we would just have our usual way of writing most general model where this Is the model with quantitative variables alone: E(y) = + 1 x 1 + 2 (x 1-8)x 4 + 3 (x 1 2-8 2 )x 4 + 4 x 3 + 5 x 1 x 3 + 6 (x 1-8)x 4 x 3 + 7 (x 1 2-8 2 )x 4 x 3 where x 3 = 1 if B, 0 otherwise; x 4 = 1 if x1 <= 8, 0 otherwise...
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