Singularity refers to what in variable relationships?

Singularity refers to what in variable relationships?

• A. Perfect correlation (r = 1 or −1)
• B. No correlation
• C. Another name for heteroscedasticity
• D. The same as central tendency

Answer: (A)

Singularity shows up when two variables move together perfectly, with no deviation from a straight line. In correlation terms, that means the Pearson correlation coefficient is exactly 1 or -1. When r is ±1, every increase in one variable is matched by a proportional increase or decrease in the other, so all data points lie on a single straight line. That perfect linear relationship is why this option is correct. The other ideas describe different things: no correlation would be r = 0, meaning the variables don’t follow a linear pattern at all. Heteroscedasticity is about the spread of residuals changing with the level of the predictor, not about a perfect relationship between the variables. Central tendency concerns a single measure like the mean, not the relationship between two variables.

Singularity shows up when two variables move together perfectly, with no deviation from a straight line. In correlation terms, that means the Pearson correlation coefficient is exactly 1 or -1. When r is ±1, every increase in one variable is matched by a proportional increase or decrease in the other, so all data points lie on a single straight line. That perfect linear relationship is why this option is correct.

The other ideas describe different things: no correlation would be r = 0, meaning the variables don’t follow a linear pattern at all. Heteroscedasticity is about the spread of residuals changing with the level of the predictor, not about a perfect relationship between the variables. Central tendency concerns a single measure like the mean, not the relationship between two variables.