What does interpolation mean?

• predicting within the measured x range
• joining pairs of recorded points
• predicting beyond the measured x range
• measuring how closely points follow a line

A park records more filled paddling pools and more sunburn cases in summer. Which is a possible shared explanation?

• Pool filling directly increases sunburn.
• Hot, sunny weather could affect both counts.
• Sunburn directly increases the number of filled pools.
• Different totals mean the logs cannot be compared.

A fitted line predicts 17.6 visitors at a target inside its measured range. Report the estimate to the nearest whole visitor.

A line of best fit is y = 90 - 3x, and the data covers x from 4 to 15. What does the line predict when x = 8?

Recorded x values range from 5 to 12. The fitted line is drawn across an axis from 0 to 20. Which interval is the measured data range?

• 5 to 12, from the recorded x values
• 0 to 20, from the axis ends
• 0 to 12, from zero to the last recorded x value
• 5 to 20, from the line's end

A line fitted to adult runners covers 2 to 14 training runs. Someone uses it for a child doing 7 runs. What check is still needed?

• Whether 7 lies within 2 to 14, since that alone establishes suitability for any runner.
• Whether substitution is correct, since the model's original population does not affect its use.
• Whether the adult model is suitable for children.
• Whether drawing the adult line farther supplies the missing observations about children.

A study's data covers x from 10 to 50. A prediction is made at x = 80. How far beyond the data is it?

If two quantities rise together, one of them must be causing the other.

A line fits height data for babies aged 0 to 12 months closely. At age 30 years it predicts 4 metres. Which limitation does this illustrate?

• The infant records must contain an error because a fitted line cannot otherwise give an unrealistic adult height.
• A childhood trend need not continue unchanged into adulthood.
• Checking the arithmetic justifies the adult prediction when the fit during infancy was close.
• The measured age range extends to every age where the equation can be evaluated, whether or not it was observed.

Sam needs a better-supported prediction for 20 training runs, but the log covers 2 to 14. Which action supplies relevant new evidence?

• Treat the model's prediction at 20 as a new observation.
• Use the prediction at 14 instead.
• Record suitable runners near 20 runs, then reassess the model.
• Repeat the existing calculations more precisely, without recording runners near the new target.