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Calculate the Pearson correlation coefficient on paired data and comment on the significance.
\nrebelmaths
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\nCouple | $\\var{obj[0]}$ | $\\var{obj[1]}$ | $\\var{obj[2]}$ | $\\var{obj[3]}$ | $\\var{obj[4]}$ | $\\var{obj[5]}$ | $\\var{obj[6]}$ | $\\var{obj[7]}$ |
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Wife $(X)$ | \n$\\var{r1[0]}$ | \n$\\var{r1[1]}$ | \n$\\var{r1[2]}$ | \n$\\var{r1[3]}$ | \n$\\var{r1[4]}$ | \n$\\var{r1[5]}$ | \n$\\var{r1[6]}$ | \n$\\var{r1[7]}$ | \n
Husband $(Y)$ | \n$\\var{r2[0]}$ | \n$\\var{r2[1]}$ | \n$\\var{r2[2]}$ | \n$\\var{r2[3]}$ | \n$\\var{r2[4]}$ | \n$\\var{r2[5]}$ | \n$\\var{r2[6]}$ | \n$\\var{r2[7]}$ | \n
The answers to all parts are given on revealing.
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Husband $(Y)$ | \n$\\sum y=\\;$[[2]] | \n$\\sum y^2=\\;$[[3]] | \n
Also find $\\sum xy=\\;$[[4]].
\nHence calculate the correlation coefficient $r$ correct to 3 decimal places:
\n$r=\\;$[[5]]
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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}}\\]
\nNote that $n$ is the number of data points. In this case $\\var{n}$
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