Titlebook: Regression Analysis; Theory, Methods, and Ashish Sen,Muni Srivastava Textbook 1990 Springer-Verlag New York Inc. 1990 Bootstrapping.Estimat

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Indicator Variables, We have already encountered such variables in Example 2.2, p. 31. They have a wide range of uses which will be discussed in this chapter. We shall mainly be concerned with using them as independent variables. In general, their use as dependent variables in least squares analysis is not recommended.

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The Normality Assumption,ditional assumption that the errors and, therefore, the dependent variables were normally distributed. In practice, these assumptions do not always hold; in fact, quite often, at least one of them will be violated. In this and the next four chapters we shall examine how to check whether each of the

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Unequal Variances,re. These conditions can be checked and if we find that one or more of them are seriously violated, we can take action that will cause at least approximate compliance. This and the next few chapters will deal with various ways in which these G-M conditions can be violated and what we would then need

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Transformations, The actual relationship may not be a linear function of the .’s and sometimes not even of the .’s. In some such cases we may still be able to do linear regression by . (i.e., using functions of) the independent and/or the dependent variables.

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Multicollinearity,ditions, These conditions only assure us that least squares estimates will be ‘best’ for a given set of independent variables; i.e., for a given . matrix. Unfortunately, the quality of estimates, as measured by their variances, can be seriously and adversely affected if the independent variables are

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*Biased Estimation,can lead to bias. Obviously, the general principle is that it might be preferable to trade off a small amount of bias in order to substantially reduce the variances of the estimates of .. There are several other methods of estimation which are also based on trading off bias for variance. This chapte

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Multicollinearity, closely related to each other. This situation, which (with a slight abuse of language) is called ., is the subject of this chapter and is also the underlying factor that motivates the methods treated in Chapters 11 and 12.