Connect the Dots

Learning Focus

Describe association in scatterplots, use a line of best fit, and interpret residuals.

Big idea

A scatterplot shows two numerical variables.

• Positive association: both tend to increase. Negative: one increases as the other decreases.
• Correlation $r$ is between $-1$ and $1$; the sign gives direction, the size gives strength.
• A line of best fit predicts $y$ from $x$.
• Residual = actual $-$ predicted.
• Association is not causation.

Worked example

Line of best fit: $\hat y=2.5x+40$ (score vs. hours studied).

At $x=8$: $\hat y=2.5(8)+40=60$.

If a student's actual score is $72$ when the model predicts $68$, the residual is $72-68=4$.

Takeaways

• Describe direction and strength.
• Residual = actual $-$ predicted.
• Correlation does not mean cause.