Here is a bivariate data set.
x	y
42.1	37.1
34.1	106.2
36.3	29.4
41.1	159.6
25.5	110.1
34.7	133.1
30.5	64.3
28.2	91.3
28.3	104.5
11.6	98.1
44.2	-20
34	116.8
47.9	-33.8
This data can be downloaded as a *.csv file with this link:  Download CSV

Find the correlation coefficient and report it accurate to three decimal places.
r = 


What proportion of the variation in y can be explained by the variation in the values of x? Report answer as a percentage accurate to one decimal place.
R² = 
%

The correlation coefficient \( r \) is \( -0.498 \), accurate to three decimal places.

The proportion of the variation in \( y \) that can be explained by the variation in the values of \( x \) (denoted \( R^2 \)) is approximately \( 24.8\% \).

Do you have any further questions or would you like more details?

Here are five related questions to expand this topic:
1. How do we interpret a negative correlation coefficient?
2. What does an \( R^2 \) value of 24.8% indicate about the strength of the relationship?
3. How can we compute the slope and intercept of the regression line for this data?
4. What methods can we use to visually represent the relationship between \( x \) and \( y \)?
5. How does the value of \( R^2 \) change if outliers are removed?

**Tip**: When interpreting \( R^2 \), remember that it represents the percentage of variation in the dependent variable explained by the independent variable.

Here is a bivariate data set.
x	y
42.1	37.1
34.1	106.2
36.3	29.4
41.1	159.6
25.5	110.1
34.7	133.1
30.5	64.3
28.2	91.3
28.3	104.5
11.6	98.1
44.2	-20
34	116.8
47.9	-33.8
This data can be downloaded as a *.csv file with this link:  Download CSV

Find the correlation coefficient and report it accurate to three decimal places.
r = 

What proportion of the variation in y can be explained by the variation in the values of x? Report answer as a percentage accurate to one decimal place.
R² = 
%

Calculate the correlation coefficient and determine the proportion of variation explained (R²) for a given bivariate data set. This example involves statistical concepts such as correlation and regression analysis. Learn to compute the correlation coefficient r = -0.498 and the R² = 24.8%.

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