A correlation of 1 indicates what?

• A. A perfect correlation
• B. No correlation
• C. A negative correlation
• D. A weak correlation

Answer: (A)

A correlation coefficient of 1 signals a perfect positive linear relationship between the two variables. This means every data point lies exactly on a straight line with a positive slope, so as one variable increases, the other increases in perfect proportion. In practical terms, you could predict the second variable from the first with 100% accuracy in the linear sense, with no scatter around the line. The correlation value ranges from -1 to +1, so +1 is the strongest possible positive relationship, while 0 indicates no linear relationship and -1 indicates a perfect negative linear relationship. If the relationship isn’t perfectly linear, the magnitude would be less than 1.