Question

when all the points fall on the regression line; the value of the correlation coefficient is

Explanation:

Step1: Recall correlation - coefficient concept

The correlation coefficient $r$ measures the strength and direction of a linear relationship between two variables. Its range is $[- 1,1]$. When all points fall on the regression line, there is a perfect linear relationship.

Step2: Determine the value

A perfect positive linear relationship has $r = 1$ and a perfect negative linear relationship has $r=-1$. Since all points are on the line, the value of the correlation coefficient is either $1$ or $- 1$.

Answer:

$1$ or $-1$