Question

Find the correlation coefficient of the following linear equation using technology (such as GeoGebra). For your r-value, use the first two decimal places.

y=4/3x−4

Answer 1

To find the correlation coefficient \( r \) for the linear equation \( y = \frac{4}{3}x - 4 \), we first need to recognize that this is a simple linear equation. The correlation coefficient \( r \) measures the strength and direction of a linear relationship between two variables.

In this case, since the equation represents a perfect linear relationship between \( x \) and \( y \), the correlation coefficient \( r \) will be \( 1 \).

However, I can guide you through how you would typically calculate \( r \) using technology like GeoGebra or another statistical tool.

1. **Input Data Points**: You need to collect data points that follow the equation. For instance:
- When \( x = 0 \), \( y = -4 \) (point: (0, -4))
- When \( x = 3 \), \( y = 0 \) (point: (3, 0))
- When \( x = 6 \), \( y = 4 \) (point: (6, 4))
- And so on, you can create a set of points.

2. **Calculate Correlation in GeoGebra**:
- Enter the pairs of \( (x, y) \) data points into GeoGebra.
- Use the command for calculating correlation, such as `Correlation[{(0, -4), (3, 0), (6, 4), ...}]`

3. **Correlation Result**:
- Given that all points generated from a linear equation will perfectly correlate, the output should be \( 1.00 \).

To summarize, since the equation \( y = \frac{4}{3}x - 4 \) describes a perfect line, the correlation coefficient \( r \) is \( 1.00 \).