The matrix representation of the general linear statistical model is studied through the implication, distribution, and partitioning of quadratic forms and their probability distributions. Estimation of parameters in the linear model by methods of maximum likelihood and least squares will be presented along with the accuracy and precision of these estimators. Estimability in both the full rank and less than full rank models is introduced. The test statistic for the general linear hypothesis is derived, and its distribution is determined under an assumption of normally distributed errors for both the null and a general alternative hypothesis. Sufficient examples are given to show its application to tests on means as well as in ANOVA and ANOCOVA. Students prepared in basic statistical methods and theory, and matrix algebra are eligible to take this course.
BMTRY 701, 707