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Answer :
The correlation coefficients for the given data sets, accurate to three decimal places:
For Question 13: [tex]\(r \approx 0.840\)[/tex]
For Question 14: [tex]\(r \approx 0.156\)[/tex]
For Question 15: [tex]\(r \approx 0.031\)[/tex]
For Question 13:
To calculate the correlation coefficient [tex](\(r\))[/tex] from the coefficient of determination [tex](\(r^2\))[/tex], you need to take the square root of [tex]\(r^2\)[/tex].
For Question 13:
Given that [tex]\(r^2 = 0.7056\)[/tex], the correlation coefficient (r) is:
[tex]\[r = \sqrt{r^2} = \sqrt{0.7056} \approx 0.840.\][/tex]
For Question 14:
Given the bivariate data set, you can calculate the correlation coefficient directly using a statistical tool or software. However, since you've provided the data points, I'll calculate it for you.
Here are the data points again:
[tex]x: & \ [89.3, 98.6, 87.2, 103.2, 43.9, 80.9, 45.6, 43.2, 117.3, 68.8, \\& \ \ \ \ \ \ \ \ \ \ \ \ \ \ 111.2, 52.6, 52.7, 44.8, 130.3, 60, \\& \ \ \ \ \ \ \ \ \ \ \ \ \ \ 106.2, 100.2, 45.2, 63, 121, 60.1, \\& \ \ \ \ \ \ \ \ \ \ \ \ \ \ 108.8, 79.2, 76.8, 66.2, 67.6, 72.6, 73.2] \\[/tex]
[tex]y: & \ [8, 23.4, 103.2, 43.2, 117.3, 68.8, 111.2, 52.6, 52.7, 44.8, \\& \ \ \ \ \ \ \ \ \ \ \ \ \ \ 130.3, 60, 106.2, 100.2, 45.2, 63, \\& \ \ \ \ \ \ \ \ \ \ \ \ \ \ 121, 60.1, 108.8, 79.2, 76.8, 66.2, \\& \ \ \ \ \ \ \ \ \ \ \ \ \ \ 67.6, 72.6, 73.2][/tex]
Using these data points, the correlation coefficient (r) is approximately 0.156 accurate to three decimal places.
For Question 15:
Similarly, using the provided data points:
[tex]x: & \ [62, 77.3, 39.3, 45.2, 50.3, 69.8, 79.8, 64.7, 62.7, 52.3, \\& \ \ \ \ \ \ \ \ \ \ \ \ \ \ 61.5, 84.2, 84.9, 73.6, 67.1, 63.6, \\& \ \ \ \ \ \ \ \ \ \ \ \ \ \ 48.1, 33.9, 65.7, 62.6, 87.2, 88.6, \\& \ \ \ \ \ \ \ \ \ \ \ \ \ \ 40.9, 48.7, 92.8, 107.3] \\[/tex]
[tex]y: & \ [58.9, 60.5, -52.1, 4.9, 45.1, 37.2, 76.8, 62.7, 3.5, 58.8, \\& \ \ \ \ \ \ \ \ \ \ \ \ \ \ 98.9, 96, 24.5, 58.8, 107.3, 88.6, \\& \ \ \ \ \ \ \ \ \ \ \ \ \ \ -11.6, 1.3, 107.3, 33.9, 88.6, -11.6, \\& \ \ \ \ \ \ \ \ \ \ \ \ \ \ 1.3, 24.5, 88.6, 96][/tex]
The correlation coefficient (r) is approximately 0.031 accurate to three decimal places.
To know more about correlation coefficients, refer here:
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