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QUADRATIC FORMS AND THEIR DISTRIBUTIONS
ESTIMATION IN THE LESS THAN
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ANOVA assumed chi-squared random variables column Computing Supplement conditional inverse confidence interval contrast data of Example data of Exercise degrees of freedom denote diagonal distributed random vector eigenvalues estimator for a2 expressed F ratio F test Find fixed effects follows a noncentral full rank model given H0 is true Hence idempotent interaction intercept least squares estimator less than full levels of factor linear model linear unbiased estimator multivariate normal random n x k matrix noncentral chi-squared distribution noncentrality parameter nonsingular nonsingular matrix normal equations normal random variable normally distributed random null hypothesis one-way classification model orthogonal matrix partitioned positive definite prediction interval proof quadratic form random vector real numbers reduced model regression sum reparameterized residual result sample Section Show shown simple linear regression solution SSRes sum of squares symmetric matrix test H0 test statistic testable Theorem two-factor design variance-covariance matrix vector with mean Verify y'Ay