Questions: Find the Pearson correlation coefficient r for the given points. Round any intermediate calculations to no less than six decimal places, and round your final answer to three decimal places. (1,3),(2,5),(3,8),(4,6),(5,4),(6,10),(7,10)

Find the Pearson correlation coefficient r for the given points. Round any intermediate calculations to no less than six decimal places, and round your final answer to three decimal places.
(1,3),(2,5),(3,8),(4,6),(5,4),(6,10),(7,10)

Transcript text: Find the Pearson correlation coefficient $r$ for the given points. Round any intermediate calculations to no less than six decimal places, and round your final answer to three decimal places. \[ (1,3),(2,5),(3,8),(4,6),(5,4),(6,10),(7,10) \]

Solution

Solution Steps

Step 1: Calculate the Sums

Given that we have 7 data points, we first calculate the necessary sums for the Pearson correlation coefficient formula:

Sum of x values ($\sum x$): 28
Sum of y values ($\sum y$): 46
Sum of xy products ($\sum xy$): 211
Sum of x squared ($\sum x^2$): 140
Sum of y squared ($\sum y^2$): 350

Step 2: Apply the Pearson Correlation Coefficient Formula

Using the formula: \[ r = \frac{n(\sum xy) - (\sum x)(\sum y)}{\sqrt{[n\sum x^2 - (\sum x)^2][n\sum y^2 - (\sum y)^2]}} \] We substitute the calculated sums into the formula to find the Pearson correlation coefficient. The numerator of the formula is 189, and the denominator is 255.859.

Final Answer:

The Pearson correlation coefficient $r$ is 0.739.

Was this solution helpful?

Unhelpful

Helpful

Questions asked by other users

< Previous Next >

Thank you for your feedback.

Copied!