Here is a bivariate data set. 39 73.3 47.5 166.3 48 88.7 57.9 81.5 76.4 66.8 70.2 -37 70.4 58.5
Angles in Circles
Angles within a circle are feasible to create with the help of different properties of the circle such as radii, tangents, and chords. The radius is the distance from the center of the circle to the circumference of the circle. A tangent is a line made perpendicular to the radius through its endpoint placed on the circle as well as the line drawn at right angles to a tangent across the point of contact when the circle passes through the center of the circle. The chord is a line segment with its endpoints on the circle. A secant line or secant is the infinite extension of the chord.
Arcs in Circles
A circular arc is the arc of a circle formed by two distinct points. It is a section or segment of the circumference of a circle. A straight line passing through the center connecting the two distinct ends of the arc is termed a semi-circular arc.
![### Bivariate Data Set Analysis
#### Data Set:
Here is a bivariate data set:
| x | y |
|-----|--------|
| 39 | 73.3 |
| 47.5| 166.3 |
| 48 | 88.7 |
| 57.9| 81.5 |
| 76.4| 66.8 |
| 70.2| -37 |
| 70.4| 58.5 |
| 49.3| 77.9 |
| 54.1| 75.5 |
| 55.6| 0.8 |
| 119 | -114.9 |
| 69.4| -24.7 |
| 50.6| 122.8 |
| 46.6| 139.7 |
| 75 | 50.6 |
| 57 | 80.5 |
| 60.8| 98.2 |
| 83.3| 82.4 |
#### Task:
Find the correlation coefficient and report it accurate to three decimal places.
\[ r = \]
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### Explanation:
The table above presents a set of bivariate data consisting of paired values of \( x \) and \( y \). Each pair represents a point in a coordinate system which can be used to determine the correlation between the variables \( x \) and \( y \).
- **Correlation Coefficient (\( r \))**: This value measures the strength and direction of the linear relationship between the two variables. It ranges from -1 to 1. A value close to 1 implies a strong positive linear relationship, -1 suggests a strong negative linear relationship, and 0 means no linear relationship.
To calculate the correlation coefficient, you can use statistical software, a calculator, or perform the calculations manually using the Pearson correlation coefficient 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 \( n \) is the number of data pairs, \( \sum xy \) is the sum of the product of paired scores, \( \](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3e82b789-902b-4bed-91c7-23ced64abede%2Fc7127533-cb4f-465d-8de6-8ab418cdfc55%2Fk6ndafkd_processed.jpeg&w=3840&q=75)
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