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=\frac{4}{3}x - 4)
(1 point)
( \bigcirc ) 1.00
( \bigcirc ) - 0.99
( \bigcirc ) 0.90
( \bigcirc ) 2.66

Explanation:

Step1: Identify linear relationship type

The equation $y=\frac{4}{3}x - 4$ is a perfect positive linear function, meaning all data points lie exactly on this upward-sloping line.

Step2: Determine correlation coefficient

For a perfect positive linear association, the Pearson correlation coefficient $r$ equals 1. Rounding to two decimal places gives 1.00.

Step3: Eliminate invalid options

• $-0.99$ represents a strong negative correlation, which does not match the positive slope.
• $0.90$ represents a strong but not perfect positive correlation, which is incorrect here.
• $2.66$ is invalid because correlation coefficients must be between $-1$ and $1$.

Answer:

1.00