353Multivariate Models
10.5 EXERCISES
Exercise 10.1
Assume two uncorrelated variables X
1
and X
2
with the sample means 1.5 and 2.3, respectively, and
sample variances 0.2, 0.3, respectively. Assume a dependent variable Y with sample mean of 4.0
and that covariance of Y with X
1
and X
2
are 0.25 and 0.12, respectively. Calculate the coefcients of
linear multiple regression.
Exercise 10.2
Repeat the previous exercise but assume that X
1
and X
2
are correlated with covariance of 0.5. Discuss
the differences in results with respect to the results of the previous exercise.
Exercise 10.3
Suppose that a multivariate regression model has two dependent variables Y
1
and Y
2
and four inde-
pendent variables X
1
, X
2
, X
3
, X
4
. Determine the dimensions for matrices