You wish to determine if there is a linear correlation between the two variables at a significance level of  
α
=
0.10
 . You have the following bivariate data set.

x	y
57.2	93.8
48.4	90.3
47.3	130.5
79.4	121.7
64.1	149
80	80.6
75.1	146.9
36	60.2
63.5	28.5
47.1	126.1
47.9	68.7
34.2	106.4
48.9	93.5
30.7	29.1
44.7	94.7
25.2	20.4
77.9	213.9
54	66.6
43.6	29.6
29.5	-22.8
77.4	132.3
47.4	11.3
64.5	104.5
33.6	-8.9
68.8	81.9


What is the correlation coefficient for this data set?
r = 


To determine the correlation coefficient \( r \) for this data set, we can use the Pearson correlation formula, defined as:

\[
r = \frac{\sum (x_i - \bar{x})(y_i - \bar{y})}{\sqrt{\sum (x_i - \bar{x})^2 \cdot \sum (y_i - \bar{y})^2}}
\]

where:
- \( x_i \) and \( y_i \) are individual data points for variables \( x \) and \( y \),
- \( \bar{x} \) and \( \bar{y} \) are the mean values of \( x \) and \( y \),
- \( \sum \) denotes summation across all data points.

I'll calculate this correlation coefficient now.The correlation coefficient \( r \) for this data set is approximately:

\[
r = 0.651
\]

This indicates a moderate positive linear relationship between \( x \) and \( y \). 

Would you like to proceed with further analysis to test the significance of this correlation at \( \alpha = 0.10 \)?

Here are five additional questions related to this problem:

1. What is the interpretation of this correlation coefficient in the context of the data?
2. How can we test if this correlation is statistically significant?
3. What would a correlation coefficient close to 1 or -1 indicate?
4. How do outliers affect the correlation coefficient?
5. What other methods can be used to measure correlation besides Pearson’s \( r \)?

**Tip:** Always visualize your data with a scatter plot to gain insights into the pattern before calculating correlation.

You wish to determine if there is a linear correlation between the two variables at a significance level of α = 0.10. You have the following bivariate data set. What is the correlation coefficient for this data set?

Discover how to calculate the Pearson correlation coefficient for a bivariate data set and test its significance at a 0.10 significance level. This statistical analysis explores linear relationships and provides insight into correlation strength and direction.

Math Problem Statement

You wish to determine if there is a linear correlation between the two variables at a significance level of
α

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