9231 P23 - Jun 2019 - Q10 - 12 marks
6113
The means and variances for a random sample of 8 pairs of values of \(x\) and \(y\) taken from a bivariate distribution are given in the following table.
| Mean | Variance | |
|---|---|---|
| \(x\) | 3.3125 | 3.3086 |
| \(y\) | 6.7375 | 7.9473 |
The product moment correlation coefficient for the sample is \(0.5815\), correct to 4 decimal places.
(i) Find the equation of the regression line of \(y\) on \(x\).
(ii) Test at the \(5\%\) significance level whether there is evidence of positive correlation between \(x\) and \(y\).
(iii) Calculate an estimate of \(y\) when \(x=6.0\) and comment on the reliability of your estimate.
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