Respuesta :
The expresion for the correlation coefficient is :
[tex]r=\frac{n\Sigma xy-\Sigma x\Sigma y}{\sqrt[]{\mleft\lbrace n\Sigma x^2-(\Sigma x)^2\}\mleft\lbrace n\Sigma y^2-(\Sigma y)\mright?^2\mright\rbrace}}[/tex]summation of x = 5 + 7 + 10 + 15 + 19
Summation of x = 56
Summation of y = 19 + 17 + 16 + 12 + 7
Summation of y = 71
Summation of prodcut xy
[tex]\begin{gathered} \Sigma xy=5\times19+7\times17+10\times16+15\times12+19\times7 \\ \Sigma xy=687 \end{gathered}[/tex]Summation of x^2 = 25 + 49 + 100 + 225 + 361
Summation of x^2 = 760
Summation of y^2 = 361 + 289 + 256 + 144 + 49
Summation of y^2 = 1099
Substitute tha value in the expression of correlation coefficient
[tex]\begin{gathered} r=\frac{n\Sigma xy-\Sigma x\Sigma y}{\sqrt[]{\mleft\lbrace n\Sigma x^2-(\Sigma x)^2\}\mleft\lbrace n\Sigma y^2-(\Sigma y)\mright?^2\mright\rbrace}} \\ r=\frac{5(687)-56\times71}{\sqrt[]{\mleft\lbrace5(760)-(56)^2\}\mleft\lbrace5(1099\mright)-(71\mright)^2}} \\ r=\frac{541}{\sqrt[]{\begin{cases}3800-3136\}\mleft\lbrace5495-5042\mright\rbrace\end{cases}}} \\ r=\frac{541}{\sqrt[]{300792}} \\ r=\frac{541}{548.44} \\ r=0.985 \end{gathered}[/tex]Answer: A) Correlation coefficient is 0.985
