Abstract
This chapter examines the least-squares estimation procedure; it is introduced through a regression example. The regression model format is applied to a broad class of problems including factorial experiments. The least squares regression model can also be expressed in matrix form. The best linear unbiased estimators are also identified with the help of theorems and examples. An ANOVA table can be constructed that partitions the total sum of squares into the sum of squares due to the overall mean and the sum of squares due to the residual. The lack of fit test requires replicate observations at one or more of the combinations of the x1, x2,..,xp-1 values. The model Y = Xβ + E suggests a general approach for writing the mean vector μ as Xβ for complete, balanced factorial experiments. It helps to find the distributions of the sums of squares and to construct a statistic to test the hypothesis.
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