Matrix Algebra Examples Exercises
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Exercises

Suppose we are analyzing a set of 4 samples. The first two samples are from a treatment group A and the second two samples are from a treatment group B. This design can be represented with a model matrix like so:
X < matrix(c(1,1,1,1,0,0,1,1),nrow=4) rownames(X) < c("a","a","b","b") X
## [,1] [,2] ## a 1 0 ## a 1 0 ## b 1 1 ## b 1 1
Suppose that the fitted parameters for a linear model give us:
beta < c(5, 2)
Use the matrix multiplication operator,
%*%
, in R to answer the following questions:What is the fitted value for the A samples? (The fitted Y values.)

What is the fitted value for the B samples? (The fitted Y values.)

Suppose now we are comparing two treatments B and C to a control group A, each with two samples. This design can be represented with a model matrix like so:
X < matrix(c(1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,1,1),nrow=6) rownames(X) < c("a","a","b","b","c","c") X
Suppose that the fitted values for the linear model are given by:
beta < c(10,3,3)
What is the fitted value for the B samples?

What is the fitted value for the C samples?