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=8200Determine the values of SccS_{cc}Scc and SctS_{ct}Sct.
Calculate the product moment correlation coefficient between c c\,c and ttt, giving your answer to 3 significant figures.
Interpret your result from part (b) in the context of the engineer's investigation.
