In the typical regression problem, as in most problems in applied statistics, researchers have available for analysis a sample of observations from some real or hypothetical population. Based on the results of their analysis of the sample data, they are interested in reaching decisions about the population from which the sample is presumed to have been drawn. It is important, therefore, that the researchers understand the nature of the population in which they are interested. They should know enough about the population to be able either to construct a mathematical model for its representation or to determine if it reasonably fits some established model. A researcher about to analyze a set of data by the methods of simple linear regression, e.g. should be secure in the knowledge that the simple linear regression model is, at least, an approximate representation of the population. It is unlikely that the model will be a perfect portrait of the real situation, since this characteristics is seldom found in models of practical value. A model constructed so that it corresponds precisely with the details of the situation is usually too complicated to yield any information of value. On the other hand, the results obtained from the analysis of data that have been forced into a model that does not fit are also worthless. Fortunately. however, a perfectly fitting model is not a requirement for obtaining useful results. researchers, then, should be able to distinguish between the occasion when their chosen models and the data are sufficiently compatible for them to proceed and the case where their chosen model must be abandoned.
Assumptions of Regression Model
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