10 For a random sample of 6 observations of pairs of values \(( x , y )\), where \(0 < x < 21\) and \(0 < y < 14\), the following results are obtained.
$$\Sigma x ^ { 2 } = 844.20 \quad \Sigma y ^ { 2 } = 481.50 \quad \Sigma x y = 625.59$$
It is also found that the variance of the \(x\)-values is 36.66 and the variance of the \(y\)-values is 9.69 .
- Find the product moment correlation coefficient for the sample.
- Find the equations of the regression lines of \(y\) on \(x\) and \(x\) on \(y\).
- Use the appropriate regression line to estimate the value of \(x\) when \(y = 6.4\) and comment on the reliability of your estimate.