AP Statistics Scatterplots and Correlation Worksheet Solutions (PDF)

(a) Explanatory: absences; response: final exam score. (b) Explanatory: mileage; response: price.

As study hours increase, scores increase. The points follow a straight pattern closely and there are no outliers.

Positive, linear, strong association; r = 0.934 with no unusual points.

(a) As temperature rises, heating costs fall: negative, roughly linear. (b) More sleep, fewer mistakes: negative. (c) Height rises quickly then levels off: positive, curved.

(a) negative linear; (b) negative; (c) positive and curved.

The points fall steadily with very little scatter.

r is about -0.994, closest to -0.98: strong and negative.

\(r=\frac{1}{4}(3.098)=0.775\).

r = 0.775, a fairly strong positive linear association.

The sign is negative and the size is moderately strong.

There is a moderately strong, negative, linear association: cities with warmer winters tend to have lower heating costs.

Changing units is a linear transformation of each variable. z-scores do not change.

r = 0.62; correlation has no units and is unchanged by linear changes of units.

The formula multiplies z-scores, and multiplication is commutative.

0.45.

The correlation is close to zero because the pattern is curved, not linear.

No: there is a strong curved relationship. r measures only linear association.

The point (8, 40) lies far from the trend, so it weakens the linear pattern.

r falls from 0.934 to 0.179. Correlation is not resistant to outliers.

A third variable could drive both.

No. Hot, sunny weather is a lurking variable: it increases both ice cream sales and sunburns.

Strength depends on how tightly points cluster around a line, not on the slope.

No. A steep cloud of widely scattered points has a weak r, and a nearly flat tight line has r near 1 or -1 in absolute value.

Strength depends on |r|: 0.8, 0.3, 0.95, 0.1.

0.1, -0.3, 0.8, -0.95.

Scores decrease steadily as screen time rises.

Negative, linear, very strong; r = -0.996.

The explanatory variable is on the x-axis.

Hours of exercise on the x-axis; a negative association is expected (more exercise, lower resting heart rate).

Together, the clusters line up from lower left to upper right even if each has a weak trend inside it.

The combined r is stronger than within each cluster; the lurking variable is age. Describe the clusters as an unusual feature.

r = 0.87 is strongly positive.

There is a strong, positive linear association. Correlation alone does not show that changes in x cause changes in y.

The new point is far from the existing pattern (far above the line).

r will likely decrease, because the point adds vertical scatter around the linear trend.

Use direction, form, strength, unusual features, and context.

There is a moderately strong, positive, linear association between average income and average rent in these cities; one city with very high income and rent is an unusual point.

Mileage is used to explain 5K time. More weekly mileage usually lowers the time.

Explanatory: weekly mileage. Negative association; for runners at a similar level r would be weak, closer to 0, because other factors matter more.