Data Interpretation • Topic 6 of 6

Scatterplots

A scatterplot shows paired data as points, one axis per variable, revealing the relationship between them. If the points trend upward left-to-right the variables have a positive association; downward is a negative association; no pattern means no association. The closer the points lie to a straight line, the stronger the association. A line of best fit (trend line) summarises the pattern and lets you predict a y-value from an x-value by substituting into its equation. On the SAT, expect to identify the type of association, read or use a line of best fit, and make predictions — substitute carefully and follow the trend.

A scatterplot with a positive trend and a line of best fitScatterplotxy

✅ Solved examples

1. Points rise from left to right close to a line. What association is this?
An upward trend means a positive association.
2. A line of best fit is y = 5x + 10. Predict y when x = 4.
y = 5(4) + 10 = 30.
3. As a car’s age rises, its value falls. What association?
One up while the other down is a negative association.
4. Line of best fit y = 3x + 2. Find y at x = 6.
y = 3(6) + 2 = 20.

✏️ Practice — try these, take hints as needed

1. Points scatter with no clear direction. What association?
No pattern means…
—
—
No association.
2. Line of best fit y = 2x + 7. Predict y at x = 5.
Substitute x = 5.
2(5) + 7.
—
17.
3. Hours studied vs score: points rise to the right. Association?
Upward trend.
—
—
Positive.
4. Line of best fit y = 4x + 1. Find y at x = 3.
4(3) + 1.
—
—
13.
5. Points lie very close to an upward line. Is the association weak or strong?
Closeness to the line sets strength.
Very close → …
—
Strong (positive).

📝 Topic test — 8 questions

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