Which of the followinf could not be the value of a correlation coefficient?
A) -0.683
B) 0.197
C) 1.000
D) -1.369
D
The value of a correlation coefficient can only be in the range of -1<x<1
To determine which of the following values could not be the value of a correlation coefficient, we need to consider the range and interpretation of correlation coefficients.
A correlation coefficient measures the strength and direction of the linear relationship between two variables. Correlation coefficients can range from -1 to 1.
A correlation coefficient of -1 indicates a perfect negative linear relationship, meaning that as one variable increases, the other decreases proportionally. This represents a strong negative correlation.
A correlation coefficient of +1 indicates a perfect positive linear relationship, meaning that as one variable increases, the other also increases proportionally. This represents a strong positive correlation.
A correlation coefficient of 0 indicates no linear relationship between the variables. This represents no correlation.
Based on this information, we can determine the possible values:
A) -0.683: This value falls within the range of -1 to 1 and represents a negative correlation. It could be a valid correlation coefficient.
B) 0.197: This value also falls within the range of -1 to 1 and is closer to 0. It could be a valid correlation coefficient representing a weak positive or weak negative correlation.
C) 1.000: This value falls within the range of -1 to 1 and represents a perfect positive correlation. It could be a valid correlation coefficient.
D) -1.369: This value is outside the range of -1 to 1. Correlation coefficients cannot be less than -1, so it could not be a valid correlation coefficient.
Therefore, the option that could not be the value of a correlation coefficient is D) -1.369.