Line Graph
A line graph displays data points connected by lines, showing how a quantity changes over time or another continuous variable.
Definition
A line graph shows how something changes over time: points are plotted and connected by a line, making it easy to see whether values went up, down, or stayed the same. It plots ordered pairs (x, y) and connects consecutive points with line segments, used to display trends over a continuous variable (usually time), and multiple lines on the same graph enable comparison of several groups or variables. Formally, a line graph is a visual representation of a time series or functional relationship; in time series analysis, line graphs display realizations of a stochastic process $\{X_t\}$, and trends, seasonality, and cycles visible in the graph guide model selection (e.g., ARIMA models, exponential smoothing).
Example
Plotting a city's average monthly temperature from January to December creates a line graph showing which months are hottest and coldest. A line graph tracking weekly quiz scores over a semester for two students shows how each student's performance changed and allows direct comparison, with an upward trend indicating improvement. A line graph of monthly retail sales showing an upward trend and regular seasonal spikes in December might be modeled with an $\text{ARIMA}(1,1,1)(1,1,1)_{12}$ model, capturing both non-stationarity (differencing) and seasonality.
Key Insight
The slope of the line tells the story: rising means increasing, falling means decreasing, flat means no change, but the line between plotted points represents an assumption of a continuous trend, not proof that values were measured at every point. Decomposing a time series into trend, seasonality, and residual (e.g., STL decomposition) allows each component to be modeled separately, leading to more accurate forecasts than treating the series as a whole.