Regression Methodology: Correlation, Meta-Analysis, Confidence Intervals, and Reliability

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Abstract
This article reviews the methodological problems associated with the assessment of the relation between two variables. Regression is defined in terms of conditional means and variances so as to bring out the close relationship between correlation and analysis of variance. Sampling error is treated from the point of view of meta-analysis; i. e., the problem of cumulating results across studies and the flaw in the statistical significance test in that context. Error of measurement is treated in terms of equations for attenuation, and we give corrections for attenuation bias in the correlation, slope, and intercept of the regression model.

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