Answers to Exercises in: Review of Elementary Linear Regression Ideas Stat 640 Answer 1
y1 y2 . . . yn
=
1 x1 1 x2 . . . 1 xn
1
.
0 1
+
. . .
2
n
Answer 2 For the two-sample problem we have XX= n1 0 0 n2
n1 i=1
, y1i ,
n2 i=1
so (X X )1 is easy.
Answers to Exercises in: Vector Spaces and Projections Stat 640 Answer 1 (a) If we write a1 v 1 + a2 v 2 , we get (a1 , a1 , a1 , a2 , a2 , a2 ) , so we can describe this space as all vectors in IR6 for which the rst three elements are the same, and the l
Answers to Exersices in: Random Vectors Stat 640 Answer 1 We get: E (Y1 ) = 0, E (Y12 ) = 1, so var(Y1) = 1. Also, E (Y2 ) = 2, E (Y22 ) = 4.75, so var(Y2 ) = 0.75. Now, cov(Y1 , Y2 ) = .25, so cov(Y ) = Answer 2 The covariance of X and Y is zero. However
Answers to exercises in: The Gauss-Markov Theorem Stat 640 Answer 1 (a) The estimator is linear with a = (1/2, 1/2, 0, . . . , 0) and unbiased because E [(y1 + y2 )/2] = ( + )/2 = . (b) Linear but not unbiased. (c) The estimator is linear because it is a
Answers to exercises in: The Gauss-Markov Theorem Stat 640 Answer 1 The linear combination of parameters is dened by c = (1, 1, 0). Because the columns of the design matrix are orthogonal, we have (X X ) 1 .05 0 0 = 0 .05 0 . 0 0 .05
Therefore, c (X X )
Two- and Three-way ANOVA Models Stat 640 Two-way analysis of variance refers to a model with a continuous response and two categorical predictor variables. Of course, one way to approach this problem is to create a lot of dummy variables and do a regressi