find the correlation corfficient of the following linear equation. for your r-value, use the first two decimal places. y = 4/3 x - 4

1 answer

To find the correlation coefficient (r-value) of the linear equation \( y = \frac{4}{3}x - 4 \), we can recognize that this equation represents a perfect linear relationship between \( x \) and \( y \).

In a perfect linear relationship, the correlation coefficient \( r \) is either:

  • \( r = 1 \) if the relationship has a positive slope,
  • \( r = -1 \) if the relationship has a negative slope.

Since the slope of your equation \( y = \frac{4}{3}x - 4 \) is positive (\(\frac{4}{3} > 0\)), the correlation coefficient is:

\[ r = 1 \]

Thus, the correlation coefficient \( r \) rounded to two decimal places is:

\[ \boxed{1.00} \]