Trend line
A trend line is a plotted line that summarizes the direction or relationship of measured values across an ordered variable.
Statistics Slam Dunk
A regression line is a fitted line that summarizes the predicted relationship between variables in a regression model.
- How it is used
- Visualizes trends and compares correlations in sports and automobile data through annotated scatterplots and line charts.
- How deep it goes
- Defines fitting and slope interpretation, demonstrates ggplot2 implementation, and notes confidence intervals without deriving regression mathematics.
- Examples
- Uses NBA salaries and win shares, points and wins, automobile mileage, and Milwaukee Bucks possession trends.
- What you can do after
- Apply it via ggplot2 by adding geom_smooth(method = lm) to plotted numeric data and controlling confidence bands with se.
Grokking AI Algorithms, Second Edition
A regression line is a fitted straight-line model representing the relationship between a dependent variable and an independent variable.
- How it is used
- Uses a straight-line model to predict a dependent variable from an independent variable.
- How deep it goes
- Works through means, deviations, squared distances, slope, intercept, plotting, and R² testing without theoretical proofs.
- Examples
- Uses carat-and-price diamond data, scaled feature values, plotted endpoints, calculation tables, and a Python fitting function.
- What you can do after
- Build it from scratch, calculate its slope and intercept, plot predictions, and evaluate accuracy on unseen data.
Read how Grokking AI Algorithms, Second Edition explains trend line →
Statistics Every Programmer Needs
A regression line is a straight-line representation of the relationship between a dependent variable and an independent variable in a linear regression model.
- How it is used
- Models a linear relationship between predictors and responses for prediction and relationship measurement.
- How deep it goes
- Explains parameters, residual minimization, multiple-predictor geometry, and R-squared but defers broader diagnostics.
- Examples
- Uses plotted x-y observations, a fitted line, positive and negative relationships, neutral relationships, and R-squared.
- What you can do after
- Evaluate linear fit by reading predicted values, residual differences, relationship direction, and R-squared.
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Everyday Data Visualization
A line in a visualization that represents the direction or pattern of change in plotted data.
- How it is used
- Frames a visualization’s main insight as a narrative of change, especially through peaks and subsequent declines.
- How deep it goes
- Explains peaks and falls as climax and falling action, stopping short of mathematical construction or implementation.
- Examples
- Uses rhino-poaching data from 2007–2016, emphasizing its near-century-fold rise, 2014 peak, and later decline.
- What you can do after
- Evaluate/understand how a plotted trend communicates a central insight and whether improvement represents a complete resolution.
Related concepts
- falling actionused by · The narrative element after the climax that shows consequences unfolding and tension decreasing before the ending.
- geom_smooth() functionproduced by · The ggplot2 geom_smooth() function adds a smoothed trend or fitted-model layer to a plot.
- line plotpart of · A line plot is a chart that connects ordered data values with line segments to show changes, relationships, or trends.
- squared lossmeasured by · Squared loss is the square of the difference between a predicted or fitted value and its target or observation, often summed across data points.
- linear regressionproduced by · Linear regression is a statistical modeling method that estimates a continuous response as a linear combination of predictor variables and fitted coefficients.
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