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Unformatted text preview: c = ( 1 ,-1 ,-1 , 1 ). (a) Using the quadratic model E ( Y | X ) = β + β 1 X + β 2 X 2 , write L Q as a function of β 2 . Argue that a test of L Q = 0 is equivalent to a test of β 2 = 0. (b) Can you make the same argument about L Q for the cubic model E ( Y | X ) = β + β 1 X + β 2 X 2 + β 3 X 3 ? What conclusions can you reach about the test for a quadratic eﬀect? 1 3. Suppose we have a 3 by 3 table with the following set of observed sample responses. B 12,3 17 A 10,11 3 19, 16, 17 (a) For the additive model, are the population marginal means for A and B estimable? (b) Add the observations 6 and 12 to the (2,3) cell. Are the population marginal means for A and B estimable? Brieﬂy explain any diﬀerences between your two results. (c) Using the augmented data set, compare and contrast the Type III and Type IV hypotheses for the interaction model for A, B and AB. 2...
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- Spring '08
- Quadratic equation, Elementary algebra, Cubic function, Mathematics in medieval Islam