Answer :
Final answer:
There is a strong positive linear relationship between x and y, with a correlation coefficient of approximately 0.874.
Explanation:
To draw a scatter diagram of the given data, we plot the x-values on the horizontal axis and the y-values on the vertical axis:
X: 2, 4, 6, 6, 7
Y: 4, 8, 10, 13, 20
Now, let's plot these points on a graph:
From the scatter diagram, we can observe that there is a general positive trend between x and y. As x increases, y tends to increase as well.
To compute the correlation coefficient, we need to calculate the sums and products of x and y:
n = 5
Σx = 2 + 4 + 6 + 6 + 7 = 25
Σy = 4 + 8 + 10 + 13 + 20 = 55
Σxy = (2 * 4) + (4 * 8) + (6 * 10) + (6 * 13) + (7 * 20) = 222
Σx^2 = (2^2) + (4^2) + (6^2) + (6^2) + (7^2) = 135
Σy^2 = (4^2) + (8^2) + (10^2) + (13^2) + (20^2) = 909
Now, we can use the formula to calculate the correlation coefficient:
r = (nΣxy - ΣxΣy) / sqrt((nΣx^2 - (Σx)^2)(nΣy^2 - (Σy)^2))
r = (5 * 222 - (25 * 55)) / sqrt((5 * 135 - (25)^2)(5 * 909 - (55)^2))
After evaluating the above expression, we find that the correlation coefficient, r, is approximately 0.874.
Since the correlation coefficient is positive and close to 1, we can conclude that there is a strong positive linear relationship between x and y.
Learn more about scatter diagram and correlation coefficient here:
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