Question

Daily-Problem-3 Excel File Insert DrawPage Layout FormulasDataReview View Tell me what you want to do Calibri 11A A Clipboard Alignment E17 13 Use the sample data below to answer the following question. (See exercise 56 on page 157 of your textbook 1s 16problem.) 17 18 19 Correlation 23 17 21 23 29 Click to Grade Your Work 25 27 30 Daily Problem | % 粗寂. e圈臼@ew1归@ ← o

please show work

Answer 1

https://docs.google.com/spreadsheets/d/1rTFVr2J9CtCv2k60kgwCM2kkeGrmd3Gt4HRe_XEGqaU/edit?usp=drivesdk

$\bar{x} =\frac{1}{n}\Sigma x= 17.8$

And .$\bar{y} =\frac{1}{n}\Sigma y= 14.8$

Correlation coefficient

  $r=\frac{cov(x,y)}{\sqrt{var(x)var(y)}}$

  $Now, cov(x,y)=\frac{1}{n} \Sigma xy - \bar{x}\bar{y}$

= $\frac{1669}{5} - 14.8\times17.8=70.36$

  $Var(x)= \frac{1}{n}\Sigma x^2 - {\bar{x}}^2$

  $= \frac{1}{5}\times 1867- {17.8}^2=56.56$

Similarly .Var(y)= 93.36

So, correlation coefficient  $r = \frac{70.36}{\sqrt{56.56\times 93.36}}=0.9682$