Scatterplots and association

What does a scatterplot show?

What is meant by a positive association between two numerical variables?

What is meant by a negative association between two numerical variables?

List the three main features used to describe association in a scatterplot.

Explain the difference between a strong association and a weak association.

What does it mean if a scatterplot has a nonlinear association?

What is a line of good fit used for?

Explain why interpolation is usually safer than extrapolation.

Why should an outlier in a scatterplot be investigated before it is ignored?

Why does association between two variables not automatically prove causation?

A scatterplot of study time and test score shows points rising from left to right and clustered close to a straight line. Describe the association using direction, strength and form, then write one cautious interpretation.

A scatterplot of car age and resale price shows a downward pattern, but the points are spread widely. Describe the association and explain what the spread suggests about using age alone for prediction.

Construct a labelled scatterplot for these data pairs: (1, 42), (2, 45), (3, 47), (4, 51), (5, 54), (6, 56). Describe the association and suggest a reasonable real-world context.

For the data pairs (2, 30), (4, 42), (6, 51), (8, 61), estimate a line of good fit by eye. Use it to predict y when x = 5 and state why this is interpolation.

The same line of good fit from observed x-values 2 to 8 is used to predict y when x = 30. Explain why this prediction is risky.

A scatterplot shows a curved U-shaped pattern between temperature and electricity use. Explain why saying “there is no association” may be wrong, even if the association is not linear.

A dataset about height and jumping distance has one point far above the main cluster. Give three possible explanations for the outlier and explain how each should be handled.

A report claims that ice-cream sales cause sunburn because both increase during summer. Explain the association, identify a possible confounding variable and rewrite the conclusion correctly.

A data scientist examines a scatterplot before building a prediction model. Explain what the scatterplot can reveal about a numerical feature, and name two things it cannot prove on its own.

Create your own bivariate dataset with at least six ordered pairs. Draw or describe the scatterplot, identify direction, strength and form, note any outlier, and write a careful conclusion in context.