linear correlation coefficient r if given x: 10, 8, 11, 4, 7, 3, 9 y: 7, 5, 8, 3, 5, 2, 7

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Answer 1

n=7, ∑x=52, ∑y=37, ∑x²=440, ∑y²=225, ∑xy=314,

(x̄=7.43, ȳ=5.29) r=0.9845. This correlation coefficient shows that there is a very good relationship between the x and y values, that is, when plotted, the graph of y against x is almost a straight line. As x increases so does y increase. (If you tabulate the x and y values you can confirm that the given sums are correct. Excel is useful in this exercise.)

correlation coefficient, r=(n∑xy-∑x∑y)/(√[(n∑x²-(∑x)²)(n∑y²-(∑y)²)]. Plug in the statistics as shown to get r.

∑ means sum of. For example, ∑xy means the sum of the product of paired x and y values; ∑y means the sum of all the y values.