Department of Statistics, UCLA

Regression analysis can imply a broader range of techniques that ordinarily appreciated. Statisticians commonly define regression so that the goal is to understand “as far as possible with the available data how the the conditional distribution of some response y varies across subpopulations determined by the possible values of the predictor or predictors” ( Cook and Weisberg, 1999: 27). For example, if there is a single categorical predictor such as male or female, a legitimate regression analysis has been undertaken if one compares two income histograms, one for men and one for women. Or, one might compare summary statistics from the two income distributions: the mean incomes, the median incomes, the two standard deviations of income, and so on. One might also compare the shapes of the two distributions with a Q-Q plot.