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2.5.10 Correlation as closeness to a straight line (A-level only)

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Question 83

A civil engineer investigates the relationship between the concentration of a chemical additive, ccc (grams per litre), and the setting time of a high-performance concrete, ttt (minutes). A random sample of 50 batches was analysed, and the following summary statistics were obtained:

∑c=450,∑c2=4275,∑t=7200,∑ct=63650,Stt=8200 \sum c = 450, \quad \sum c^2 = 4275, \quad \sum t = 7200, \quad \sum ct = 63650, \quad S_{tt} = 8200 ∑c=450,∑c2=4275,∑t=7200,∑ct=63650,Stt​=8200
a.

Determine the values of SccS_{cc}Scc​ and SctS_{ct}Sct​.

[2]
b.

Calculate the product moment correlation coefficient between c c\,c and ttt, giving your answer to 3 significant figures.

[2]
c.

Interpret your result from part (b) in the context of the engineer's investigation.

[1]

2.5.10 Correlation as closeness to a straight line (A-level only) Questions

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