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# explan - Explanatory Variables in OLS...

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1 Explanatory Variables in OLS Regression [explanatory_vars_in_OLS_regr.doc] Part I. Options in conceptualizing the relation of the outcome variable to an explanatory variable, holding the other explanatory variables constant 1. Linear, independent (e.g., relationship of outcome variable “income” to education—i.e. slope—is the same at all levels of “education” & for “females- males”, holding the other explanatory variables constant; & the explanatory variables do not interact): first-order quantitative variable (e.g., income measured in thousands of dollars; the dummy variable for “gender” will test insignificant in this example). a. Check the sample size at each level of the quantitative explanatory variable. 2. Same slope coefficient but unequal y-intercept (e.g., same slope relationship of outcome variable “income” to “years of education” for females- males but females earn less than males): dummy variable (e.g., dummy variable “female” [or “gender”]: male=0 female=1). a. The sample size must be adequate in each category. If there are more than two categories, the largest category is commonly used as the “base” (or “reference” or “comparison”) category. 3. Critical thresholds (e.g., education is associated with a major increase in outcome variable income only at “one or more years of college” & higher, or only at “one or more years of college” [see increasing or decreasing effect ]): categorize “years of education” into appropriate categories for level of education (i.e. turn quantitative “years of education” into a categorical ordinal variable) (see also increasing or decreasing effect : in some such cases, squaring the explanatory variable or doing a log transformation may be an alternative option, though the former requires interval data & the latter ratio data with positive values).

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