Question

Question is in image

Answer 1

The expresion for the correlation coefficient is :

`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}}`

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

`\begin{gathered} \Sigma xy=5*19+7*17+10*16+15*12+19*7 \\ \Sigma xy=687 \end{gathered}`

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

`\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*71}{\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=(541)/(548.44) \\ r=0.985 \end{gathered}`

Answer: A) Correlation coefficient is 0.985