Solve the Pearson's correlation and coefficient from the following data: x=17,13,12,15,16,14,16,16,18,19

Y=94,73,59,80,93,85,66,79,77,71

Pearson's correlation coefficient \( r \) is calculated using the formula:

\[
r = \frac{n\sum xy - (\sum x)(\sum y)}{\sqrt{[n\sum x^2 - (\sum x)^2][n\sum y^2 - (\sum y)^2]}}
\]

Where:  
- \( x \) and \( y \) are the given data points  
- \( n \) is the number of data points  
- \( \sum x \) and \( \sum y \) are the sums of \( x \) and \( y \) values  
- \( \sum xy \) is the sum of the product of corresponding \( x \) and \( y \) values  
- \( \sum x^2 \) and \( \sum y^2 \) are the sums of squares of \( x \) and \( y \) values  

I will now calculate the Pearson correlation coefficient. numpy as np

# Given data
x = np.array([17, 13, 12, 15, 16, 14, 16, 16, 18, 19])
y = np.array([94, 73, 59, 80, 93, 85, 66, 79, 77, 71])

# Calculate Pearson's correlation coefficient
correlation_coefficient = np.corrcoef(x, y)[0, 1]
correlation_coefficientThe Pearson correlation coefficient (\( r \)) for the given data is approximately **0.3073**. This indicates a weak positive correlation between \( x \) and \( y \).  

Would you like a step-by-step breakdown of the calculation?  

Here are some related questions to explore:  
1. What does the Pearson correlation coefficient tell us about the relationship between two variables?  
2. How can we interpret weak, moderate, and strong correlation values?  
3. What are some real-world applications of Pearson’s correlation coefficient?  
4. How does Pearson’s correlation differ from Spearman’s correlation?  
5. Can a high correlation imply causation?  

**Tip:** If the correlation coefficient is close to 0, it suggests little to no linear relationship between the variables.

Solve the Pearson's correlation and coefficient from the following data: x=17,13,12,15,16,14,16,16,18,19 Y=94,73,59,80,93,85,66,79,77,71

Learn how to calculate the Pearson correlation coefficient for the given data points x=17,13,12,15,16,14,16,16,18,19 and y=94,73,59,80,93,85,66,79,77,71. This solution demonstrates the use of Pearson’s correlation formula and interpretation of results.

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