Which of the following values could not be a correlation coefficient?
a. .927
b. -1
c. 1.032
True or false: The correlation coefficient is independent of the scale of measurement of the variables.
C, true
The correlation coefficient is a mathematical measure of the strength and direction of the linear relationship between two variables. It ranges from -1 to 1, where -1 indicates a strong negative relationship, 0 indicates no relationship, and 1 indicates a strong positive relationship.
Based on this, option c. 1.032 could not be a correlation coefficient because it falls outside the valid range. The correlation coefficient cannot exceed 1.
As for the second question, true. The correlation coefficient is independent of the scale of measurement of the variables. It only measures the linear relationship, regardless of the units or scales in which the variables are measured.
To determine which value is a correlation coefficient, we need to understand the range of possible values for correlation coefficients.
The correlation coefficient, also known as Pearson's correlation coefficient, typically ranges from -1 to 1.
Therefore, we can conclude that the value in option c (1.032) could not be a correlation coefficient because it is outside the possible range. Options a (.927) and b (-1) could be correlation coefficients as they fall within the valid range.
As for the second question, "True or false: The correlation coefficient is independent of the scale of measurement of the variables." The statement is true. The correlation coefficient measures the strength and direction of the linear relationship between two variables, regardless of the scale of measurement. It only examines the association between the variables and does not depend on the specific units or measurement scales used for the variables.