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# hw3 - Stat 511 Due 11am Monday Jan 31 Homework 3 Spring...

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Stat 511 Homework 3 Spring 2011 Due: 11am, Monday Jan 31 1. Consider a factor effects model for a 2-way ANOVA with 2 levels (a and b) of temperature and 2 levels of pressure (A and B). The table of cell means is: Pressure Temp. A B a μ aA μ aB b μ bA μ bB Please answer EACH of the following in two ways: in terms of cell means, and in words, e.g. the mean for pressure A, averaged over temperatures. OR, tell me the quantity is non-estimable. (a) If no constraints are put on the parameter vector, the β vector and X matrix are: μ α 1 α 2 β 1 β 2 αβ 11 αβ 12 αβ 21 αβ 22 1 1 0 1 0 1 0 0 0 1 1 0 1 0 1 0 0 0 1 1 0 0 1 0 1 0 0 1 1 0 0 1 0 1 0 0 1 0 1 1 0 0 0 1 0 1 0 1 1 0 0 0 1 0 1 0 1 0 1 0 0 0 1 1 0 1 0 1 0 0 0 1 What quantity is estimated by β 1 ? What quantity is estimated by αβ 11 ? (b) If ’set last to zero’ constraints are used, the β vector and X matrix are: μ α 1 β 1 αβ 11 1 1 1 1 1 1 1 1 1 1 0 0 1 1 0 0 1 0 1 0 1 0 1 0 1 0 0 0 1 0 0 0 What quantity is estimated by β 1 ?

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