Sir Francis Galton, in the late $1800$s$,$ was the first to introduce the statistical concepts of regression and correlation. He studied the relationships between pairs of variables such as the size of parents and the size of their offspring.

Data similar to that which he studied are given below, with the variable $x$ denoting the height $($in centimeters$)$ of a human father and the variable $y$ denoting the height at maturity $($in centimeters$)$ of the father's oldest son. The data are given in tabular form and also displayed in the Figure $1$ scatter plot. Also given is the product of the father's height and the son's height for each of the fifteen pairs. $($These products, written in the column labelled $"x{y}^{\text{'}\text{'}},$ may aid in calculations.$)$

$\backslash$table$[[\backslash$table$[[$Height of$],[$father$,x$