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Calculate the Pearson correlation coefficient on paired data and comment on the significance.

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rebelmaths

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It is well known that similarity in attitudes, beliefs and interests plays an important role in interpersonal attraction. A researcher developed a questionnaire which was completed by 8 married couples. One question sought to place each individual on a 20 point scale in which low scores represent liberal attitudes and high scores represent conservative attitudes. The data were:

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Couple$\\var{obj[0]}$$\\var{obj[1]}$$\\var{obj[2]}$$\\var{obj[3]}$$\\var{obj[4]}$$\\var{obj[5]}$$\\var{obj[6]}$$\\var{obj[7]}$
Wife $(X)$$\\var{r1[0]}$$\\var{r1[1]}$$\\var{r1[2]}$$\\var{r1[3]}$$\\var{r1[4]}$$\\var{r1[5]}$$\\var{r1[6]}$$\\var{r1[7]}$
Husband $(Y)$$\\var{r2[0]}$$\\var{r2[1]}$$\\var{r2[2]}$$\\var{r2[3]}$$\\var{r2[4]}$$\\var{r2[5]}$$\\var{r2[6]}$$\\var{r2[7]}$
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The answers to all parts are given on revealing.

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Wife $(X)$$\\sum x=\\;$[[0]]$\\sum x^2=\\;$[[1]]
Husband $(Y)$$\\sum y=\\;$[[2]]$\\sum y^2=\\;$[[3]]
\n

Also find $\\sum xy=\\;$[[4]]. 

\n

Hence calculate the correlation coefficient $r$ correct to 3 decimal places:

\n

$r=\\;$[[5]]

\n

 

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\\[r=\\frac{n\\Sigma xy -\\Sigma x \\Sigma y}{\\sqrt{n\\Sigma x^2-(\\Sigma x)^2}\\sqrt{n\\Sigma y^2-(\\Sigma y)^2}}\\]

\n

Note that $n$ is the number of data points. In this case $\\var{n}$

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