Using and Interpreting the Line of Best Fit
SAT Relevance: Line of best fit questions appear frequently on the SAT Math section — typically 2–4 questions per test. They test your ability to read scatterplots, interpret slope and y-intercept in context, and make predictions.
What Is a Line of Best Fit?
A line of best fit (also called a trend line or regression line) is a straight line drawn through a scatterplot of data points that best represents the overall trend of the data.
The equation of the line of best fit is written in slope-intercept form:
$$y = mx + b$$
- $m$ (slope) = the rate of change — how much $y$ changes for each 1-unit increase in $x$
- $b$ (y-intercept) = the predicted value of $y$ when $x = 0$
Key Skills the SAT Tests
- Interpreting slope in context — "For each additional year, the population increases by approximately 1,200."
- Interpreting the y-intercept in context — "The estimated starting salary is $32,000."
- Making predictions — Plugging in an $x$-value to find the predicted $y$-value (or vice versa).
- Identifying residuals — The difference between the actual data point and the predicted value: $\text{residual} = y_{\text{actual}} - y_{\text{predicted}}$
- Extrapolation vs. Interpolation — Predicting within the data range (interpolation) vs. outside it (extrapolation).
Interactive Visualization: Scatterplot with Line of Best Fit
The graph below shows a scatterplot of data points (blue dots) and the line of best fit (red line). Hover over the concepts to understand each component.
Interactive visualization — available in the full lesson