8/9/2023 0 Comments Regress y on xbut teachers, writers and researchers often seem reluctant to abandon the terminology of dependent and independent. This preference goes back at least some decades: John Wilder Tukey often used the term response in writings in the 1960s and 1970s. The problem here has more symmetry and distinction between two kinds of variables is likely to be arbitrary if not meaningless.Īs far as terminology is concerned, we note that many would prefer some other term rather than DV or dependent variable. Yet again, and very much to the point, there are many problems in regression in which variables are on the same footing: properties of partners or siblings, two methods of measurement of ostensibly the same property, rainfall or temperature over time at two gauges or stations, and so on and so forth. That said, there are many examples in which predictive interest runs either way: if rainfall is a predictor of the response corn yield, so also we might use abundance of some taxon in reverse to predict temperature, rainfall or salinity of past environments. Most introductory courses and texts seem to use notation $y$ for dependent variable and $x$ for independent variable whenever there are many such independent variables, they can be distinguished by subscripts and/or denoted collectively as a matrix. The independent variable is then the cause or factor used to predict the response. Let's take it for the moment that at least in many situations, a dependent variable can be identified on substantive grounds as whatever is the outcome, response or effect which we are in practice interested in explaining or predicting in some way. This isn't much of a problem either: by the time people have learned about instrumental variables, they should be able to distinguish the two usages, at least in context. It's not at all old-fashioned to point out that among many economists, and some other social scientists, IV is now more likely to mean instrumental variable. IV is common, but not universal, shorthand for independent variable. It's probably old-fashioned to remind that DV has often been used to mean Deo volente, God willing, but those who know that and also some statistics seem unlikely to confuse or conflate those two meanings. Let's take that first.ĭV is common, but not universal, shorthand for dependent variable. The question prejudges another question, good terminology for the variables concerned. To belabor this point, one nice way of writing what a regression model estimates is the following:īetter options would be calling the "dependent" variable (Y): an outcome, a response, an output, and calling the "independent" variable (X): an input, a predictor, a regressor, a covariate, or an exposure. To this end, the mean of one variable conditional on another may be a flat response although the variables are indeed dependent (suppose the error of the Y varies according to X). Regression models estimate the conditional mean of the outcome as a function of one or more predictors. We only call the "X" (input variable) "independent" because it is considered fixed or given as part of an experimental design, or is representative of a population of interest. The mistake is that "dependence" (in the proper statistical sense) is commutative. However, this is such an egregious abuse of statistical language, many disciplines have abandoned such verbiage altogether. Traditionally speaking, one regresses the dependent variable (the Y, the outcome) on the independent variable (the X, the input). (beta coefficient) is the slope of the explanatory The explanatory (independent) variable(s) you are The dependent variable you are trying to predict
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