Question

The following sample observations were randomly selected:

X. 4. 5. 3. 6. 10

Y. 4. 6. 5. 7. 7

determine the correlation coefficient and the coefficient of determination

Answer 1

x values

$\sum =28$

Mean 5.6

$\sum(x-\mu)^2=SS_z=29.2$

Y values

$\sum=29$

Mean =5.8

$\sum(y-\mu)^2=SS_z=6.8$

X and Y combined

N=5

$\sum (x-M_x)(y-M_y)=10.6$

r calculation:

$r=\sum (x-M_x)(y-M_y)/\sqrt{(SS_x)(SS_y)}=10.6/\sqrt{29.2)(6.8)}=0.7522$

Coefficient of determination

$r^2=0.7522^2=0.5658$