Question

Find the correlation coefficient of the following linear equation. Round your r-value to two decimal places, if necessary.

y=−3/2x+6

Answer 1

To find the correlation coefficient \( r \) for the linear equation \( y = -\frac{3}{2}x + 6 \), we can observe the nature of the relationship described by the equation.

The correlation coefficient \( r \) measures the strength and direction of a linear relationship between two variables. For a linear equation of the form \( y = mx + b \) (where \( m \) is the slope and \( b \) is the y-intercept):

1. If \( m > 0 \), then \( r > 0 \).
2. If \( m < 0 \), then \( r < 0 \).
3. If \( m = 0 \), then \( r = 0 \).
4. The value of \( r \) is always between -1 and 1.

In this case, the slope \( m = -\frac{3}{2} \), which is negative. This indicates a negative correlation.

For a perfect linear relationship, the correlation coefficient is:

- \( r = 1 \) for a perfect positive linear relationship.
- \( r = -1 \) for a perfect negative linear relationship.
- Since the equation corresponds to a perfect line (as it's a deterministic linear equation), we can conclude that \( r = -1 \).

Thus, the correlation coefficient \( r \) for the given linear equation \( y = -\frac{3}{2}x + 6 \) is:

\[
r = -1
\]