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Unformatted text preview: Solution for hw9 1. A multiple cubic regression model with three independent variables was estimated on the basis of 40 sample points. The total corrected sum of squares was equal to 10000. The regression sum of squares was found to be 5000 with only linear terms included. When all quadratic terms (including interactions) were added, the regression sum of squares went up to 6000. When all cubic terms were added it further increased to 8000. a) Find the total number of coefficients in the full cubic model. b) Do the partial f-test to assess the contribution of the quadratic terms to the model. Do they contribute significantly at = 0 . 05? c) Do the partial f-test to assess the contribution of cubic terms. Is it significant at = 0 . 05? Solution: a) We can simply count terms: 4 linear (1 intercept and 3 slopes), 6 quadratic (3 squares and 3 interaction terms) and 10 cubic (3 cubes, 6 terms that have one square and one first power and the term x 1 x 2 x 3 ). The total number is 4 + 6 + 10 = 20.)....
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- Spring '08