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9231 P22 - Nov 2018 - Q9 - 11 marks
6136

For a random sample of 5 observations of pairs of values \((x, y)\), the equation of the regression line of \(y\) on \(x\) is \(y=4.2+c x\) and the equation of the regression line of \(x\) on \(y\) is \(x=10.8+d y\), where \(c\) and \(d\) are constants. The product moment correlation coefficient is -0.7214 and the mean value of \(x\) is 7.018 .
(i) Test at the 5\% significance level whether there is evidence of non-zero correlation between the variables.

(ii) Find the values of \(c\) and \(d\).

(iii) Use an appropriate regression line to estimate the value of \(x\) when \(y=3.5\), and comment on the reliability of your estimate.

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