Trend Lines: Predictions & Equations

Predicting with the line

To predict $y$ for some $x$: find that $x$ on the horizontal axis, go straight up to the trend line, then straight across to the $y$-axis. Use the height of the line, not the height of a nearby data point — the line is the pattern, and predictions come from the pattern.

In the scatter plot below the points scatter on both sides of the straight trend line. To predict, you follow the line, not the dots.

Predictions are estimates. The trend line says what the data tends to do, so a prediction of $16$ means about $16$, not exactly $16$.

Writing the equation

Read a trend line the same way you read any line. The $y$-intercept $b$ is where the line crosses the $y$-axis. The slope $m$ comes from two points that sit on the line, using $\displaystyle \frac{y_2 - y_1}{x_2 - x_1}$. Pick spots where the line crosses grid intersections — the data points themselves usually do not sit on the line.

Always check the sign of the slope against the picture. A line that falls from left to right must have a negative slope, and it goes with a negative association in the data.

Working backward from a prediction

Sometimes you know the output and need the input — the trend line predicts $19$ free throws, so how many hours of practice is that? Substitute the known value for $y$ in the equation and solve for $x$. It is a two-step equation from there.

Worked examples

Try one yourself

Common questions