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Learn about the relation between random variables in a population and sample, estimation methods, least squares criterion, normality assumptions, and minimizing square residuals. Explore how Population Regression Functions (PRF) and Sample Regression Functions (SRF) are interconnected.
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2. Regression Analysis 2.1 Population and sample regression functions • PRF: relation between r.v.’s in population (unknown) • SRF: relation between r.v.’s in sample (we “estimate” it) To estimate means simply to calculate formula Criterion least squares (LS) minimization of sq. residuals We want the SRF to be as close as possible to the PRF, w/o knowing the latter! We will have to make assumptions on the distribution of ‘u’ (errors) normality