Understanding the nominal IV

3 thoughts on “Understanding the nominal IV”

  1. The term Regression defaultly reads Linear Regression (LR) rather than its historically original usage Regression Toward the Mean (RTM). As a lecturer in psychometrics, I have to answer careful students the distinction between these two Regressions.

    We have rather little difficulty to learn From Galton (1886) that RTM was to describe the non-trivial regressing of the conditionally predicted points (toward the unconditional population mean) relative to their respective given predictors. Those predicted points usually but not necessarily lie on a straight line, which was termed LR line. More researchers read LR line as that the series of means of sampled Y(s) will regress to the LR line, established by Central Limit Theorem. It is really misunderstanding for Galton while it is more likely the common understanding now.

    In the diagram, excluding the nominal IV Z, the blue is almost the conditional population mean of Y with respective given X, which is just the case that conditionally predicted points are not necessary on the LR (red, covered by green) line. Factually, the conditional mean blue points do not always regress toward the uncondional mean. For example, when X is just near to its unconditional mean zero, the corresponding blue point is farther From the Y's unconditional mean. At the same time, the conditional population mean of X with any given Y is just the vertical LR line Y=0.

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