Answer
(a) See the picture below.
(b) $r=0.896$
(c) There is a positive linear relation between x and y.
Work Step by Step
(b) $x ̅=\frac{2+4+6+6+7}{5}=5$
$s_x=\sqrt {\frac{(2-5)^2+(4-5)^2+(6-5)^2+(6-5)^2+(7-5)^2}{5-1}}=2$
$y ̅=\frac{4+8+10+13+20}{5}=11$
$s_y=\sqrt {\frac{(4-11)^2+(8-11)^2+(10-11)^2+(13-11)^2+(20-11)^2}{5-1}}=6$
$r=\frac{Σ(\frac{x_i-x ̅}{s_x})(\frac{y_i-y ̅}{s_y})}{n-1}=\frac{(\frac{2-5}{2})(\frac{4-11}{6})+(\frac{4-5}{2})(\frac{8-11}{6})+(\frac{6-5}{2})(\frac{10-11}{6})+(\frac{6-5}{2})(\frac{13-11}{6})+(\frac{7-5}{2})(\frac{20-11}{6})}{5-1}=0.896$
(c) The scatter diagram looks like Figure 4 (b) on page 194. $r\approx0.9$ indicates a strong positive linear relation.