Linear Models and Bivariate Data

Imagine tracking the exact number of hours a group of middle school students spends practicing algebra problems, and pairing each time with their respective scores on a final exam. You are no longer looking at a single, isolated list of grades; you are examining bivariate measurement data, which consists of observations of two different quantitative variables for each subject. To make sense of this paired information, you plot it. A scatterplot is a graphical representation used to display bivariate quantitative data on a coordinate plane. The rule of mapping is strict and logical: the independent driver, or the explanatory variable, is plotted along the horizontal x-axis, while the measured outcome, or the response variable, is plotted along the vertical y-axis. By mapping data this way, we transform a chaotic spreadsheet into a visual narrative.