Abstract: This chapter considers linear parameterization of a conditional expectation, which is called the linear regression. It starts with the basic ideas, presents the definitions, treats some examples, considers the relationship between a linear regression and a linear quasi-regression, and deals with uniqueness of a linear parameterization and the identification of the regression coefficients. The chapter focuses on two parameterizations of a discrete conditional expectation. It presents a theorem on the invariance of regression coefficients and a theorem on the existence of a linear regression if the regressand and the regressors have a joint multivariate normal distribution. Much empirical research uses some kind of regression in order to investigate how the conditional expectation values of one random variable depend on the values of one or more other random variables. The chapter introduces the concept of a regression as a special case of a factorization of a conditional expectation in which the regressor X is numerical.
Publication Year: 2017
Publication Date: 2017-03-10
Language: en
Type: other
Indexed In: ['crossref']
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