Fitting Linear Models pp 8-25 | Cite as

# The Linear Model

## Abstract

Suppose that we are to analyze *n* measurements or observations *y*_{ i } to see how they depend upon *q* other sets of measurements or observations *F*_{l} … *F*_{ q } If *F*_{ j } is considered *quantitative*, we will refer to it as a *variate*. If *F*_{ j } is considered *qualitative*, we will refer to it as a *factor*, and use the notation *n*_{ j } to denote the number of levels of *F*_{ j }. (In other words, *n*_{ j } is the number of classes into which *F*_{ j } divides the *n* measurements *y*.) In the balance of this report, we will deal almost exclusively with *analysis of* *variance* models, that is, models in which all the *F*_{ j } are factors. Models in which some of the *F*_{ j } are variates will be referred to as *analysis of covariance* models. We will use the phrase *factorial design* to describe any experiment in which all (or nearly all) of the combinations of the factors *F*_{l} … *F*_{ q } are of interest. Depending on the nature of the factors or the design, a *nested* model might well be appropriate in such a design.

### Keywords

Manifold Covariance Folk## Preview

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