Scatter diagrams, correlation and regressionAQA A-Level Maths: Mind map

Exam questions on Scatter diagrams, correlation and regression

1. A teacher records, for 25 students, the hours per week $h$ spent revising and the test score $s$ out of 100. The scatter diagram shows positive correlation and the regression line of $s$ on $h$ is $s=34+4.5h$. The values of $h$ range from 1 to 12.
   A student claims that revising for 30 hours a week would give a score of $34+4.5\times30$. Explain why this prediction is unreliable.2 marks
2. A scatter diagram shows the monthly sales of ice cream and the monthly number of beach rescues for 24 months in a seaside town. There is strong positive correlation between the two variables.
   A councillor proposes banning ice-cream sales to reduce the number of rescues. Comment on this proposal.2 marks
3. A scatter diagram shows the mass (kg) against the height (cm) of 60 adults. There is strong positive correlation overall, but the points form two distinct clusters: a lower cluster of 28 points and an upper cluster of 32 points. Further inspection shows that the lower cluster is the women and the upper cluster is the men.
   Explain why a single regression line fitted to all 60 adults could be misleading.3 marks