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= ⅝2- 4
(1 point)
• 0.90
O 2.66
0 -0.99
O 1.00
Item 2
Item 3
Item 4
Item 5
A Graphing Calculator

Answer 1

To find the correlation coefficient \( r \) for the given linear equation \( y = \frac{5}{8}x - 4 \), you need to understand that this equation represents a line and that the correlation coefficient for a perfect linear relationship is either \( 1.00 \) (perfect positive correlation) or \( -1.00 \) (perfect negative correlation).

In this case, since the equation is linear, the correlation coefficient can be determined as follows:

1. **Identify the slope**: The slope of the line is positive (\( \frac{5}{8} \)), which means that as \( x \) increases, \( y \) also increases.
2. **Understanding the correlation**: A linear equation of the form \( y = mx + b \) indicates a perfect correlation. Therefore, we expect a correlation coefficient of either \( 1.00 \) for positive correlation or \( -1.00 \) for negative correlation.

Since the slope is positive, the correlation coefficient \( r \) is \( 1.00 \).

Thus, the answer is:
- **1.00**

If you have any additional data points that represent values of \( x \) and \( y \) from this equation, you could calculate \( r \) numerically, but based on the linear equation alone, \( r = 1.00 \) indicates a perfect positive correlation.