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= 4/3x -4
A: -0.99 B: 0.90 C:1.00 D: 2.66

Answer 1

To find the correlation coefficient (r-value) for the linear equation \( y = \frac{4}{3}x - 4 \), we first note that this is a linear equation of the format \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.

Since this equation describes a perfect linear relationship between \( x \) and \( y \), the correlation coefficient \( r \) will be exactly 1 when the relationship is positive and -1 when the relationship is negative. In this case, the slope \(\frac{4}{3}\) is positive, indicating that as \( x \) increases, \( y \) also increases.

Thus, the correlation coefficient \( r \) for the line \( y = \frac{4}{3}x - 4 \) is:

**C: 1.00**

This indicates a perfect positive linear correlation.