Line Graph
Statistics & ProbabilityA 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.
Example
Plotting a city's average monthly temperature from January to December creates a line graph. You can see which months are hottest and coldest.
Key Insight
The slope of the line tells the story: rising means increasing, falling means decreasing, flat means no change.
Definition
A line graph plots ordered pairs (x, y) and connects consecutive points with line segments. It is used to display trends in data over a continuous variable (usually time). Multiple lines on the same graph enable comparison of several groups or variables.
Example
A line graph tracking weekly quiz scores over a semester for two students shows how each student's performance changed and allows direct comparison. An upward trend indicates improvement.
Key Insight
The line between plotted points represents an assumption of a continuous trend. Be careful: the line does not mean values were measured at every point, only that there is a plausible trend connecting them.
Definition
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 {Xt}. Trends, seasonality, and cycles visible in the graph guide model selection (e.g., ARIMA models, exponential smoothing).
Example
A line graph of monthly retail sales shows an upward trend and regular seasonal spikes in December. An $\text{ARIMA}(1,1,1)(1,1,1)_{12}$ model captures both the non-stationarity (differencing) and seasonality.
Key Insight
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.