An ecologist is studying the impact of soil salinity, sss (measured in mS/cm), on the maximum growth height, hhh (measured in cm), of a particular marsh grass. Data collected from 10 different sites are plotted on a scatter diagram. For 9 of these sites, the data points exhibit a strong negative linear correlation. However, the 10th site, labeled 'Site Omega', is located at (48,82)(48, 82)(48,82), which is positioned significantly above the trend line observed in the other 9 sites.
State why Site Omega might be considered an outlier in this context.
For the other 9 sites, the following summary statistics were calculated:
Sss=648.2,Shh=392.5,Ssh=−415.8 S_{ss} = 648.2, \quad S_{hh} = 392.5, \quad S_{sh} = -415.8 Sss=648.2,Shh=392.5,Ssh=−415.8Calculate the product moment correlation coefficient, rrr, for these 9 sites. Give your answer to 3 significant figures.
If Site Omega were included in the calculation of the product moment correlation coefficient for all 10 sites, state what effect this would have on the value of rrr.
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.
