Question

5. Rounded to three decimal places, what is the value of r for this data set?

Answer 1

The value of correlation coefficient (r) for the dataset is 0.981

What is correlation coefficient (r)?

The correlation coefficient (r) is used to determine the closeness and association of a scatter plot points.

The dataset is given as:

• x: 8  15  3  7  2  14
• y: 15  21  6  12  3  20

Using a graphing calculator, we have the following parameters:

X Values

• ∑x = 49
• Mean = 8.167
• ∑(X - Mx)2 = SSx = 146.833

Y Values

• ∑y = 77
• Mean = 12.833
• ∑(Y - My)2 = SSy = 266.833

X and Y Combined

• N = 6
• ∑(X - Mx)(Y - My) = 194.167

The correlation coefficient (r) is then calculated as:

$r = \frac{\sum{((x - My)(Y - Mx)) }}{ \sqrt{((SSx)(SSy))}}$

This gives

$r = \frac{194.167 }{ \sqrt{((146.833)(266.833))}}$

$r = 0.9809$

Approximate

$r = 0.981$

Hence, the value of correlation coefficient (r) for the dataset is 0.981

Read more about correlation coefficient at:

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