Scatter Plots and Trend Lines

What does a scatter plot show?

A scatter plot displays two variables as points on an x-y plane. The pattern reveals the relationship: positive (up-right), negative (up-left), or no correlation (random cloud).

Trend lines

A trend line (line of best fit) summarizes the relationship. It's computed using least squares regression: $\hat{y} = mx + b$.

Interpreting the scatter

• Positive correlation: Points trend upward. As $x$ increases, $y$ tends to increase. (Height vs weight, study time vs grades.)
• Negative correlation: Points trend downward. As $x$ increases, $y$ tends to decrease. (Price vs demand, age of car vs value.)
• No correlation: Random scatter. No trend. (Shoe size vs GPA.)

The equation tells a story

If height vs weight gives $\hat{y} = 2.3x - 80$: for every 1 cm increase in height, weight increases by about 2.3 kg on average.

Try it in the visualization

Points are plotted with the trend line. The equation, $r$-value, and $R^2$ are displayed. Toggle residuals to see the vertical distances minimized by the line.