Marine biologists are investigating the relationship between the depth of a lake, DDD (metres), and the dissolved oxygen concentration, CCC (mg/L). For a sample of n=12n = 12n=12 measurements, the biologists code the data using the variables x=D−123x = \frac{D - 12}{3}x=3D−12 and y=C−50.5y = \frac{C - 5}{0.5}y=0.5C−5. The summary statistics for the coded data are as follows:
∑x=24Sxx=110∑y=48Syy=260∑xy=−12\sum x = 24 \quad S_{xx} = 110 \quad \sum y = 48 \quad S_{yy} = 260 \quad \sum xy = -12∑x=24Sxx=110∑y=48Syy=260∑xy=−12
Calculate the product-moment correlation coefficient between xxx and yyy. Give your answer to 3 decimal places.
Write down the value of the product-moment correlation coefficient for DDD and CCC.
A researcher suggests that deeper water contains lower levels of dissolved oxygen.
State, with a reason, whether or not the researcher's suggestion is supported by these data.
Practise Edexcel A Level Maths Regression, Correlation and Hypothesis Testing with exam-style questions for A Level Maths. 100 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.