An industrial chemist is studying the relationship between the UV intensity index, uuu, and the yield of a refined polymer, yyy grams. The chemist records the results for 12 different batches. The summary statistics are as follows:
∑u=84,∑y=156,∑u2=628,∑y2=2118 \sum u = 84, \quad \sum y = 156, \quad \sum u^2 = 628, \quad \sum y^2 = 2118 ∑u=84,∑y=156,∑u2=628,∑y2=2118 ∑uy=1146,Suu=40,Syy=90 \sum uy = 1146, \quad S_{uu} = 40, \quad S_{yy} = 90 ∑uy=1146,Suu=40,Syy=90Find the mean and variance of the recorded yields.
The chemist believes that increased UV intensity results in a higher polymer yield.
(i) Calculate the product moment correlation coefficient (PMCC) between uuu and yyy. (ii) State, with a reason, whether or not this value supports the chemist's belief.
Find the least squares regression line of yyy on uuu in the form y=a+buy = a + buy=a+bu. Give the values of aaa and bbb to 3 significant figures.
Estimate the yield when the UV intensity index is 9.2.
The coding z=5y−50z = 5y - 50z=5y−50 is used to transform the yield data.
Find an equation of the least squares regression line of zzz on uuu in the form z=c+duz = c + duz=c+du.
Find: (i) the variance of the transformed yields zzz. (ii) the product moment correlation coefficient between zzz and uuu.
278 exam-style questions on CCEA A Level Maths 2.5 Data presentation and interpretation, covering 2.5.1 Data presentation and interpretation, 2.5.2 Data presentation and interpretation, 2.5.3 Data presentation and interpretation, 2.5.4 Data presentation and interpretation, 2.5.5 Data presentation and interpretation, 2.5.6 Data presentation and interpretation, 2.5.7 Data presentation and interpretation, 2.5.8 Data presentation and interpretation, 2.5.9 Data presentation and interpretation, and 2.5 Data presentation and interpretation. Each one has a worked solution and a mark scheme showing where the marks go.