The regression line of \(y\) on \(x\), obtained from a random sample of 6 pairs of values of \(x\) and \(y\), has equation
$$y = 0.25 x + k$$
where \(k\) is a constant. The values from the sample are shown in the following table.
| \(x\) | 4 | 5 | 7 | 8 | 10 | 14 |
| \(y\) | 5 | 8 | \(p\) | 7 | \(p\) | 9 |
- Find the value of \(p\) and the value of \(k\).
- Find the product moment correlation coefficient for the data.
- Test, at the \(5 \%\) significance level, whether there is evidence of positive correlation between the variables.
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