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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=−32x+6


(1 point)
r=

1 answer

To find the correlation coefficient \( r \) for the linear equation \( y = -32x + 6 \), we can summarize the characteristics of this equation without computations from outside technology. This is a simple linear equation in the slope-intercept form.

The correlation coefficient \( r \) indicates the strength and direction of a linear relationship:

  • If \( r = 1 \), it indicates a perfect positive linear relationship.
  • If \( r = -1 \), it indicates a perfect negative linear relationship.
  • If \( r = 0 \), it indicates no linear relationship.

In the case of the equation \( y = -32x + 6 \):

  1. The slope \( -32 \) is negative, which indicates a negative linear relationship.
  2. Since this is a perfect linear equation, the correlation is perfect in its nature.

Therefore, the correlation coefficient \( r \) is \( -1 \).

So, the answer is:

\[ r = -1 \]