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

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Textbook 1990g the strength of relationships. Because they provide a way of em- pirically identifying how a variable is affected by other variables, regression methods have become essential in a wide range of fields, including the social sciences, engineering, medical research and business. Of the various method

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Tests and Confidence Regions,his chapter we consider such testing problems. In the second part of the chapter we shall study the related issue of determining confidence intervals and regions. In the last section we return to testing.

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Indicator Variables,inly be concerned with using them as independent variables. In general, their use as dependent variables in least squares analysis is not recommended. Nonetheless, we shall consider the topic further in the final section of this chapter.

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The Normality Assumption,ld; 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 assumptions actually holds and what, if anything, we can do if it does not. This chapter is devoted to the normality assumption.

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Variable Selection,cing the number of variables often reduces multicollinearity. Still another reason is that it lowers the ratio of the number of variables to the number of observations, which is beneficial in many ways.

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*Biased Estimation, the variances of the estimates of .. There are several other methods of estimation which are also based on trading off bias for variance. This chapter describes three of these: principal component regression, ridge regression and the shrinkage estimator.

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1431-875X s are valuable for at least two purposes: making predictions and judging the strength of relationships. Because they provide a way of em- pirically identifying how a variable is affected by other variables, regression methods have become essential in a wide range of fields, including the social scie

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Introduction,uences of our actions and to manipulate our environment. Most relationships we know of are based on empirical observations. Although some relationships are postulated on theoretical grounds, usually the theories themselves were originally obtained from empirical observations. And even these relation

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Multiple Regression,rst to simple regression, which we considered in Chapter 1, and then to multiple regression. Alter that. we shall derive formulae for least. squares estimates and present properties of these estimates. These properties will he derived under the Gauss-ldarkov conditions which were presented in Chapte

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Tests and Confidence Regions,ts we may even be interested in seeing whether all the independent variables together have any effect on the response variable. In the first part of this chapter we consider such testing problems. In the second part of the chapter we shall study the related issue of determining confidence intervals