2.	Compute Pearson’s Product Moment Correlation for the following data:

Individuals	A	    B	    C   	D	     E	      F	G	    H	     I	    J
Data A	   34  22	   10	   11	    23	20	16	18	21	15
Data B	  12	 23	   21	   24	     10	   30	   28	   29	   32	    25
 
2.	Compute Pearson’s Product Moment Correlation for the following data:

To compute Pearson's Product Moment Correlation Coefficient (often denoted as \( r \)), we can use the following formula:

\[
r = \frac{n\sum{(XY)} - \sum{X}\sum{Y}}{\sqrt{[n\sum{X^2} - (\sum{X})^2] [n\sum{Y^2} - (\sum{Y})^2]}}
\]

Where:
- \( X \) and \( Y \) are the two data sets.
- \( n \) is the number of data points.
- \( \sum{XY} \) is the sum of the product of corresponding data points.
- \( \sum{X} \) and \( \sum{Y} \) are the sums of the data sets \( X \) and \( Y \), respectively.
- \( \sum{X^2} \) and \( \sum{Y^2} \) are the sums of the squares of the data sets \( X \) and \( Y \), respectively.

Given the dataTo compute Pearson's Product Moment Correlation Coefficient (often denoted as \( r \)), we can use the following formula:

\[
r = \frac{n\sum{(XY)} - \sum{X}\sum{Y}}{\sqrt{[n\sum{X^2} - (\sum{X})^2] [n\sum{Y^2} - (\sum{Y})^2]}}
\]

Where:
- \( X \) and \( Y \) are the two data sets.
- \( n \) is the number of data points.
- \( \sum{XY} \) is the sum of the product of corresponding data points.
- \( \sum{X} \) and \( \sum{Y} \) are the sums of the data sets \( X \) and \( Y \), respectively.
- \( \sum{X^2} \) and \( \sum{Y^2} \) are the sums of the squares of the data sets \( X \) and \( Y \), respectively.

Given the 

\[
\text{Data A} = [34, 22, 10, 11, 23, 20, 16, 18, 21, 15]
\]
\[
\text{Data B} = [12, 23, 21, 24, 10, 30, 28, 29, 32, 25]
\]

Let's calculate \( r \) step by step.The Pearson's Product Moment Correlation Coefficient \( r \) for the given data is approximately \(-0.463\). 

This negative value indicates an inverse relationship between Data A and Data B, meaning that as values in Data A increase, values in Data B tend to decrease, and vice versa.

Would you like more details on the calculation process or further explanation? Here are some related questions that might interest you:

1. How do you interpret the value of the Pearson correlation coefficient?
2. What is the significance of a negative Pearson correlation coefficient?
3. How does Pearson correlation differ from other types of correlation?
4. Can Pearson correlation be used for non-linear relationships?
5. What are the limitations of using Pearson's correlation coefficient?

**Tip:** Always plot your data when analyzing correlations to visually assess the relationship.

Learn how to compute Pearson’s Product Moment Correlation Coefficient using step-by-step calculations. Understand the relationship between Data A and Data B with detailed statistical analysis.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation