Building Linear Models from Data

What you’ll learn

• Check first differences before fitting, compare candidate lines by their balance of points, ask the model both questions, and state its domain of validity.
• A line of best fit summarizes linear trend in a scatter plot; it is a model, not a perfect match.
• Slope and intercept must carry units from the context (dollars per mile, points per game).
• Interpolation is safer inside the data range; extrapolation beyond the cloud needs caution.
• Outliers pull hand-drawn lines; investigate before deleting points.
• Model equations use $\hat{y}$ or words like "approximately" to show uncertainty.