Answer
(a) See the picture below.
(b) $r=0.440$
(c) There is a moderate positive linear relation between x and y.
Work Step by Step
(b) $x ̅=\frac{0+5+7+8+9}{5}=5.8$
$s_x=\sqrt {\frac{(0-5.8)^2+(5-5.8)^2+(7-5.8)^2+(8-5.8)^2+(9-5.8)^2}{5-1}}=3.5637$
$y ̅=\frac{3+8+6+9+4}{5}=6$
$s_y=\sqrt {\frac{(3-6)^2+(8-6)^2+(6-6)^2+(9-6)^2+(4-6)^2}{5-1}}=2.5495$
$r=\frac{Σ(\frac{x_i-x ̅}{s_x})(\frac{y_i-y ̅}{s_y})}{n-1}=\frac{(\frac{0-5.8}{3.5637})(\frac{3-6}{2.5495})+(\frac{5-5.8}{3.5637})(\frac{8-6}{2.5495})+(\frac{7-5.8}{3.5637})(\frac{6-6}{2.5495})+(\frac{8-5.8}{3.5637})(\frac{9-6}{2.5495})+(\frac{9-5.8}{3.5637})(\frac{4-6}{2.5495})}{5-1}=0.440$
(c) The scatter diagram looks like Figure 4 (c) on page 194. $r\approx0.4$ indicates a moderate positive linear relation.
