A marine biologist is investigating the relationship between water depth and the concentration of a specific dissolved mineral in a coastal lake. The concentration, c c\,c mg/L, was measured at various depths, d d\,d metres, below the lake surface. The results for a random sample of 8 measurements are summarised in the table below.
| Depth (d d\,d m) | 10 | 20 | 30 | 40 | 50 | 60 | 70 | 80 |
|---|---|---|---|---|---|---|---|---|
| Concentration (c c\,c mg/L) | 15.2 | 14.1 | 12.8 | 11.5 | 10.2 | 8.8 | 7.5 | 6.3 |
[You may use: ∑d=360\sum d = 360∑d=360, ∑c=86.4\sum c = 86.4∑c=86.4, ∑d2=20400\sum d^2 = 20400∑d2=20400, ∑dc=3345\sum dc = 3345∑dc=3345]
Calculate SddS_{dd}Sdd and SdcS_{dc}Sdc.
Find the equation of the least squares regression line of c c\,c on d d\,d in the form c=a+bdc = a + bdc=a+bd.
Give a practical interpretation of the gradient of your regression line in the context of this study.
A technician takes a measurement at a depth of 45 metres. Predict the mineral concentration at this depth.
A researcher suggests that at a depth of 150 metres, the mineral concentration will have decreased to less than 2.0 mg/L. Comment on the validity of this claim.
278 exam-style questions on CCEA A Level Maths 2.5 Data presentation and interpretation, covering 2.5.1 Data presentation and interpretation, 2.5.2 Data presentation and interpretation, 2.5.3 Data presentation and interpretation, 2.5.4 Data presentation and interpretation, 2.5.5 Data presentation and interpretation, 2.5.6 Data presentation and interpretation, 2.5.7 Data presentation and interpretation, 2.5.8 Data presentation and interpretation, 2.5.9 Data presentation and interpretation, and 2.5 Data presentation and interpretation. Each one has a worked solution and a mark scheme showing where the marks go.