ACT Math: Estimate Best-Fit Lines and Linear Regression

A best-fit line (regression line) is the line that passes closest to all the points on a scatterplot. You do not need to calculate it using formulas on ACT; you estimate visually. (1) Look at the scatter plot. (2) Imagine a line that has roughly equal numbers of points above and below it. (3) Identify two clear points the line passes through or nearly passes through. (4) Calculate slope using those two points. (5) Use point-slope form to write the equation. This visual method is 80% accurate and 90% faster than regression formulas, a huge advantage for time management.

Example: A scatter plot shows data trending upward. Visually, the best-fit line appears to pass through (0,2) and (4,10). Slope=(10−2)/(4−0)=8/4=2. Equation: y−2=2(x−0), so y=2x+2. Done in 45 seconds with no formulas.

Mistake 1: Picking the line that passes through the most points. (Not all points should be on the line; the line minimizes overall distance.) Mistake 2: Selecting unclear points for slope calculation. (Choose points with clear coordinates, not fractional positions.) Mistake 3: Forgetting to account for outliers. (Extreme points can distort your visual estimate; weight central points more heavily.) Avoid these three mistakes and your best-fit estimates will be accurate.

On your next practice test, sketch best-fit lines on scatterplots. Notice: most of your estimates will match the intended answer or be very close.

Find three ACT Math problems with scatterplots. For each, estimate the best-fit line visually. Write the equation using point-slope form. Check against the answer key. Your answers should be within 0.5 units of slope or y-intercept. This drill trains your visual estimation so that by test day, you can find best-fit lines in 45 seconds without formulas.

Do this drill once per week for two weeks. By test day, linear regression will feel intuitive.

One or two linear regression/best-fit questions appear on many ACT Math tests. Each is worth 1 point. Using visual estimation saves you 90 seconds total and earns you 2 correct answers. Time savings from visual estimation can improve your Math score by 1-2 points per test section by freeing up time for harder problems.

This week, learn the visual method. By test day, you will estimate best-fit lines faster than students calculating regression formulas.