What is the range of values for a coefficient of correlation?
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A. B. C. D. E.Explanation
The closer the value to 1 or -1, the stronger the correlation. The sign +/- just shows the direction, not the strength.
The correct answer is A. -1.0 to +1.0 inclusive.
The coefficient of correlation, also known as the Pearson correlation coefficient, is a statistical measure that quantifies the strength and direction of the linear relationship between two variables. It is denoted by the symbol "r" and can take on values ranging from -1.0 to +1.0, inclusively.
The range of -1.0 to +1.0 represents the extreme values for the coefficient of correlation. When the coefficient of correlation is +1.0, it indicates a perfect positive linear relationship between the variables. This means that as one variable increases, the other variable also increases proportionally. On the other hand, when the coefficient of correlation is -1.0, it represents a perfect negative linear relationship, indicating that as one variable increases, the other variable decreases proportionally.
A coefficient of correlation of 0 indicates no linear relationship between the variables. This means that there is no systematic relationship between the changes in one variable and the changes in the other variable.
The inclusive range of -1.0 to +1.0 is important because it allows for the representation of different degrees and types of relationships. Values closer to -1.0 or +1.0 indicate a stronger linear relationship, while values closer to 0 indicate a weaker or no linear relationship.
In the provided options, answer choice A. -1.0 to +1.0 inclusive correctly represents the range of values for a coefficient of correlation. Answer choice B. Unlimited range is incorrect because the coefficient of correlation is bounded between -1.0 and +1.0. Answer choice C. -3 to +3 inclusive is incorrect as it extends beyond the valid range. Answer choice D. None of these answers is incorrect because answer choice A is the correct range. Answer choice E. 0 to +1.0 is also incorrect as it does not include the negative values that can be taken by the coefficient of correlation.