What does the notation r = +1 indicate in scatterplot correlation?

The notation ( r = +1 ) in the context of scatterplot correlation indicates a perfect positive correlation between the two variables being analyzed. This means that as one variable increases, the other variable increases in a perfectly linear manner. In a scatterplot, this would be represented by all the data points lying exactly on a straight line with a positive slope.

In practical terms, when one variable has a value of zero, the other variable will also have a corresponding value of zero, and for every increase in the first variable, there will be a consistent, proportional increase in the second variable. This strong correlation can be crucial for various analyses in statistics as it suggests a reliable relationship between the two variables, allowing for predictions based on one variable’s value to directly infer the value of the other.

The other options represent varying types and strengths of correlation. Perfect negative correlation would be indicated by ( r = -1 ), while no correlation is represented by ( r = 0 ). Low positive correlation would be represented by values closer to 0 but still positive, such as ( r = 0.2 ) or similar. Each of these indicates a different degree of relationship between two variables, making ( r = +1 ) distinct