# What is the correlation coefficient with the following data points: (3, 9), (7, 10), (4, 1)?

**Solution:**

The correlation coefficient is a measure of the association between two variables. It is used to find the relationship is between data and a measure to check how strong it is.

r = [Σxy - (Σx Σy / n)] / √[(Σx^{2} - {(Σx)^{2}/n} (Σy^{2} - {(Σy)^{2} / n}]

We need to find xy, x^{2}, and y^{2} for these three points

For (3, 9) - xy = 27, x^{2 }= 9, y^{2} = 81

For (7, 10) - xy = 70, x^{2 }= 49, y^{2} = 100

For (4, 1) - xy = 4, x^{2 }= 16, y^{2} = 1

Σx = 14, Σy = 20, Σxy = 101, Σx^{2} = 74, Σy^{2} = 182

Applying this in the correlation coefficient formula for r, we get

r = [(101 - (14 × 20) / 3] / [(74 - (196 / 3)) (182 - (400 / 3))]

⇒ r = (101 - 280/3) / (74 - 65.333) (182 - 133.333)

⇒ r = 7.66 / (2.94) (6.98)

⇒ r = 0.37

You can use the correlation coefficient calculator to verify the answer.

The correlation coefficient with the following data points: (3, 9), (7, 10), (4, 1) is 0.37

## What is the correlation coefficient with the following data points: (3, 9), (7, 10), (4, 1)?

**Summary:**

The correlation coefficient with the given data points: (3, 9), (7, 10), (4, 1) is 0.37

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