Scatter Plot
Statistics & ProbabilityA 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. Each dot represents one data point, with one value on the x-axis and the other on the y-axis.
Example
Plot each student's hours studied on the x-axis and their test score on the y-axis. If dots drift upward from left to right, students who studied more tended to score higher.
Key Insight
Scatter plots help you see if two things tend to move together. A cloud of dots drifting up means a positive pattern; drifting down means a negative pattern; random cloud means no pattern.
Definition
A scatter plot graphs ordered pairs (x, y) for each observation, allowing visual detection of the direction, form, and strength of the relationship between two quantitative variables. Patterns can be linear or nonlinear, and outliers become visually obvious.
Example
A scatter plot of house size (x) vs. sale price (y) for 50 houses shows a positive linear trend: larger houses tend to cost more. A line of best fit can be drawn through the cloud of points.
Key Insight
Scatter plots reveal more than just correlation: they show nonlinearity, clusters, and outliers that a single correlation coefficient might mask.
Definition
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). Augmented scatter plots (e.g., with marginal distributions or contour overlays) provide richer distributional information.
Example
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
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.