A marine biologist is investigating the relationship between the concentration of a specific mineral, mmm in parts per million (ppm), and the annual growth rate of a particular coral species, GGG in mm per year, across 8 distinct reef locations. The observations are recorded in the table below.
| Reef Site | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
|---|---|---|---|---|---|---|---|---|
| Mineral Concentration mmm (ppm) | 6.0 | 12.0 | 17.0 | 21.0 | 26.0 | 30.0 | 34.0 | 38.0 |
| Growth Rate GGG (mm/year) | 4.5 | 6.7 | 8.9 | 10.1 | 12.5 | 14.1 | 15.9 | 17.3 |
You may use the following summary statistics: Smm=854.0S_{mm} = 854.0Smm=854.0 SmG=346.8S_{mG} = 346.8SmG=346.8 SGG=141.0S_{GG} = 141.0SGG=141.0 ∑m=184.0\sum m = 184.0∑m=184.0 ∑G=90.0\sum G = 90.0∑G=90.0
Find the product moment correlation coefficient between GGG and mmm.
Give a reason why a linear regression model of the form G=a+bmG = a + bmG=a+bm is appropriate for these data.
Find the value of bbb correct to 3 decimal places.
Find the equation of the regression line of GGG on mmm.
Interpret your value of bbb in context.
Use your answer to part (d) to estimate the growth rate of the coral when the mineral concentration is 25.025.025.0 ppm.
Comment on the reliability of your estimate in part (f), giving a reason.
Practise Edexcel A Level Maths Regression, Correlation and Hypothesis Testing with exam-style questions for A Level Maths. 202 questions covering Exponential Models, Measuring Correlation, and Hypothesis Testing for Zero Correlation, matched to the Edexcel A Level Maths (9MA0) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.
