Question

Calculate coefficient and coorelation

X- 4 7 8 9 10 14 18

Y- 2 3 4 5 6 7 8

Answer 1

X	Y	X2	Y2	XY
4	2	16	4	8
7	3	49	9	21
8	4	64	16	32
9	5	81	25	45
10	6	100	36	60
14	7	196	49	98
18	8	324	64	144
$\sum _{}^{}\mathrm{X}=70$	${\sum }_{}^{}\mathrm{Y}=35$	${\sum }_{}^{}{\mathrm{X}}^2=830$	${\sum }_{}^{}{\mathrm{Y}}^2=203$	${\sum }_{}^{}\mathrm{XY}=408$

$$\begin{gathered} \overline{\mathrm{X}}=\frac{70}{7}=10 \\ \overline{\mathrm{Y}}=\frac{35}{7}=5 \\ \mathrm{r}=\frac{{\sum }_{}^{}\mathrm{XY}-\mathrm{N}\overline{\mathrm{X}}\overline{\mathrm{Y}}}{\sqrt{{\sum }_{}^{}{\mathrm{X}}^2-\mathrm{N}({\overline{\mathrm{X})}}^2}\sqrt{{\sum }_{}^{}{\mathrm{Y}}^2-\mathrm{N}({\overline{\mathrm{Y})}}^2}} \\ =\frac{408-7\times 10\times 5}{\sqrt[]{830-7\times (10{)}^2}\sqrt{203-7\times (5{)}^2}}=\frac{408-350}{\sqrt{130}\sqrt{28}}=\frac{58}{11.40\times 5.29}=0.96 \end{gathered}$$