ACJC Linear Regression Tutorial Q3

The height \(x\) cm and age \(y\) months for each of \(10\) children were measured.

The data can be summarized as follows:

\(\sum{\left( x-50 \right)}=60\), \(\sum{\left( y-20 \right)}=-20\),

\(\sum{{{\left( x-50 \right)}^{2}}}=450\), \(\sum{{{\left( y-20 \right)}^{2}}}=200\),

\(\sum{\left( x-50 \right)}\left( y-20 \right)=-100\).

Calculate the value of the linear product moment correlation coefficient for these \(10\) children. Based on your calculation, what can you say about the height and age of these children?