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)] / √[(Σx² - {(Σx)²/n} (Σy² - {(Σy)² / n}]

We need to find xy, x², and y² for these three points

For (3, 9) - xy = 27, x² = 9, y² = 81

For (7, 10) - xy = 70, x² = 49, y² = 100

For (4, 1) - xy = 4, x² = 16, y² = 1

Σx = 14, Σy = 20, Σxy = 101, Σx² = 74, Σy² = 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