Question

Find the correlation coefficient of the following linear equation using technology (such as GeoGebra). Round your r-value to two decimal places, if necessary.

y=−3/2x+6


(1 point)
r=

Answer 1

To find the correlation coefficient \( r \) for the given linear equation \( y = -\frac{3}{2}x + 6 \), we need to understand that this equation describes a perfect linear relationship between \( x \) and \( y \).

In this case, because it is an exact linear relationship, the correlation coefficient \( r \) will be:

- \( r = 1 \) if the relationship is positive,
- \( r = -1 \) if the relationship is negative,
- \( r = 0 \) if there is no linear relationship at all.

Since the slope of the line is negative (\(-\frac{3}{2}\)), the correlation coefficient for the linear equation \( y = -\frac{3}{2}x + 6 \) is:

\[
r = -1
\]

So, rounded to two decimal places:

\[
r = -1.00
\]

This indicates a perfect negative linear relationship between \( x \) and \( y \).