Scatter Plot
A scatter plot displays pairs of values as individual points on a coordinate plane to reveal relationships between two variables.
Definition
A scatter plot is a graph with dots showing the relationship between two sets of numbers, where each dot represents one data point, with one value on the x-axis and the other on the y-axis. It graphs ordered pairs (x, y) for each observation, allowing visual detection of the direction, form, and strength of the relationship between two quantitative variables, and patterns can be linear or nonlinear, with outliers becoming visually obvious. Formally, a scatter plot visualizes the joint distribution of bivariate data (X, Y); regression diagnostics use scatter plots of residuals vs. fitted values to check model assumptions (linearity, homoscedasticity), and augmented scatter plots (e.g., with marginal distributions or contour overlays) provide richer distributional information.
Example
Plotting each student's hours studied on the x-axis and their test score on the y-axis, dots drifting upward from left to right suggest that students who studied more tended to score higher. A scatter plot of house size (x) vs. sale price (y) for 50 houses might show a positive linear trend, with a line of best fit drawn through the cloud of points. A partial regression plot (added-variable plot) shows the relationship between one predictor and the response after partialing out the effects of all other predictors, enabling interpretation in multiple regression.
Key Insight
A cloud of dots drifting up means a positive pattern, drifting down means a negative pattern, and a random cloud means no pattern; scatter plots reveal more than just correlation, showing nonlinearity, clusters, and outliers that a single correlation coefficient might mask. Anscombe's quartet demonstrates that four datasets with nearly identical summary statistics (mean, variance, correlation) can have dramatically different scatter plots, underscoring the indispensability of graphical analysis.