3. Twenty pairs of observations are made of two variables \(x\) and \(y\), which are believed to be related. It is found that $$\sum x = 200 , \quad \sum y = 174 , \quad \sum x ^ { 2 } = 6201 , \quad \sum y ^ { 2 } = 5102 , \quad \sum x y = 5200 .$$ Find

1. the product-moment correlation coefficient between \(x\) and \(y\),
2. the equation of the regression line of \(y\) on \(x\). Given that \(p = x + 30\) and \(q = y + 50\),
3. find the equation of the regression line of \(q\) on \(p\), in the form \(q = m p + c\).
4. Estimate the value of \(q\) when \(p = 46\), stating any assumptions you make.