This LaTeX document is available as postscript or asAdobe PDF.

ANSC*6370 QG and Animal Models
Fall 03 - Quiz 7 - Answers

1.

Given

$$E(\hat{\bf b}) = {\bf CX}'{\bf Xb} = \left( \begin{array}{rr... ...t_{1} \\ t_{2} \\ t_{3} \\ w_{1} \\ w_{2} \end{array} \right).$$

Determine if the following function, ${\bf K}'{\bf b}$ is estimable.

$$\left( \begin{array}{rrrrrrrr} 2 & 0 & 2 & 0 & 1 & 1 & 1 & 1 \\ 0 & 1 & -1 & -2 & 1 & 1 & 0 & 0 \end{array} \right){\bf b}.$$

Just show that ${\bf K}'{\bf CX}'{\bf X} = {\bf K}'$. This is true for this example, i.e. the function is estimable.

2.

Write out the LS equations directly from the table of numbers below. First number is the number of observations in a subclass and second number is the sum of the observations in that subclass. Margin totals are given.

Tail lengths, mm, of mice caught at cottage.

Sex of mice	YEARS				Row Totals
	2000	2001	2002	2003
Males	12,54	9,42	10,51	9,47	40,194
Females	8,34	11,50	10,46	11,41	40,171
Column Totals	20,88	20,92	20,97	20,88	80,365

The LS equations are

$$\left( \begin{array}{rrrrrrr} 80 & 40 & 40 & 20 & 20 & 20 & 2... ...65 \\ 194 \\ 171 \\ 88 \\ 92 \\ 97 \\ 88 \end{array} \right).$$

Students had to complete this question as homework. Assume that ${\bf y}'{\bf y} = 2000$, then construct the AOV table and test for sex and year effects.

An additional element was to include an interaction term between sex and year in the model. Set up new LS equations, solve and repeat the AOV testing for main effects and interaction effects.

	Without Interaction		With Interaction
Source	DF	SS	DF	SS
Total	80	2000.0000	80	2000.0000
Mean	1	1665.3125	1	1665.3125
Model	5	1674.9987	8	1680.7354
Sex	1	6.9487	1	6.8918
Year	3	3.0737	3	2.4975
Interaction			3	5.7366
Residual	75	325.0013	72	319.2646

This LaTeX document is available as postscript or asAdobe PDF.