Y Variable

The Y variable in regression analysis is the dependent variable, so named because it is conventionally depicted as the vertical (y) axis in a scatterplot showing the relationship between two variables. The Y variable represents the effect or outcome in a causeand-effect relationship, whereas X usually denotes the cause or independent variable. The Y variable is generally shown on the left-hand side of regression equations; therefore, it is sometimes referred to as a left-side variable. For example, a simple regression equation is often written as Y = a + bX + e. Figure 1 shows a hypothetical relationship between years of education and income, where income is the Y variable because it is presumed to be affected by how many years of education a person has.

Figure 1 Scatterplot With Y Variable Identified

In cross-tabulations of two variables, percentages are generally computed to determine the percentage of a given independent variable category that falls into each category on the dependent Y variable. In difference-of-means tests, the mean on the Y variable is computed within each category of the predictor variable, with a significance test to determine whether the obtained difference between the Y variable means is larger than expected on the basis of chance.

For example, in determining the relative contributions of different factors to a car’s gas mileage, its miles per gallon would be the Y variable, whereas its weight, number of engine cylinders, and age might be plausible predictor variables. In this case, the multiple regression model could be written as Y = a + bX + cW + dZ + e, where Y represents the dependent variable (gas mileage) and X, W, and Z represent the predictor variables.