OCR S1 2012 January — Question 2

Exam BoardOCR
ModuleS1 (Statistics 1)
Year2012
SessionJanuary
TopicBivariate data
TypeDistinguish dependent and independent variables

2 In an experiment, the percentage sand content, \(y\), of soil in a given region was measured at nine different depths, \(x \mathrm {~cm}\), taken at intervals of 6 cm from 0 cm to 48 cm . The results are summarised below. $$n = 9 \quad \Sigma x = 216 \quad \Sigma x ^ { 2 } = 7344 \quad \Sigma y = 512.4 \quad \Sigma y ^ { 2 } = 30595 \quad \Sigma x y = 10674$$
  1. State, with a reason, which variable is the independent variable.
  2. Calculate the product moment correlation coefficient between \(x\) and \(y\).
  3. (a) Calculate the equation of the appropriate regression line.
    (b) This regression line is used to estimate the percentage sand content at depths of 25 cm and 100 cm . Comment on the reliability of each of these estimates. You are not asked to find the estimates.