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Valentin [98]
3 years ago
13

Compute the correlation coefficient for the data set. (2,19), (3,22), (4,26), (5,20), (6,35), (7,30), (9,40), (10,42), (11,35)

Mathematics
1 answer:
lakkis [162]3 years ago
4 0

Answer:

The correlation coefficient  of the data is 0.8679.

Step-by-step explanation:

The formula to compute the correlation coefficient is:

r(X,Y)=\frac{n\cdot \sum XY-\sum X\cdot \sum Y}{\sqrt{n\cdot\sum X^{2}-(\sum X)^{2}}\times \sqrt{n\cdot\sum Y^{2}-(\sum Y)^{2}}}

From the data provided compute the values of ∑ XY, ∑ X, ∑ Y, ∑ X² and ∑ Y².

The values are computed in the table below.

Compute the correlation coefficient as follows:

r(X,Y)=\frac{n\cdot \sum XY-\sum X\cdot \sum Y}{\sqrt{n\cdot\sum X^{2}-(\sum X)^{2}}\times \sqrt{n\cdot\sum Y^{2}-(\sum Y)^{2}}}

            =\frac{(9\times 1893)-(57\times 269)}{\sqrt{(9\times 441)-(57)^{2}}\times \sqrt{(9\times 8635)-(269)^{2}}}\\\\=\frac{1704}{\sqrt{720\times 5354}}\\\\=0.86788895\\\\\approx 0.8679

Thus, the correlation coefficient  of the data is 0.8679.

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