Understanding Coefficient of Correlation: 0.70

A

The coefficient of correlation, r, is just the square root of the coefficient of determination r-squared.

A coefficient of correlation measures the strength and direction of the linear relationship between two variables. It ranges between -1 and +1, with -1 indicating a perfect negative correlation, +1 indicating a perfect positive correlation, and 0 indicating no linear correlation.

In this case, the coefficient of correlation is given as 0.70. This value indicates a relatively strong positive correlation between the two variables. However, let's analyze the provided answer choices:

A. Coefficient of determination is 0.49: The coefficient of determination (R-squared) represents the proportion of the variation in the dependent variable that is explained by the independent variable(s). It is calculated by squaring the coefficient of correlation. In this case, 0.70 squared is 0.49, so this answer is correct.

B. Almost no correlation because 0.70 is close to 1.0: This answer is incorrect. While it is true that 0.70 is not as close to 0 as it is to 1, it still represents a relatively strong positive correlation.

C. 70% of the variation in one variable is explained by the other: This answer is incorrect. While the coefficient of determination (R-squared) can be interpreted as the proportion of variation explained, the coefficient of correlation itself does not provide information about the percentage of variation explained.

D. Coefficient of non-determination is 0.30: The term "coefficient of non-determination" is not a recognized concept in statistics or correlation analysis. Therefore, this answer is incorrect.

E. None of these answers: This answer is incorrect, as we have identified that answer choice A is correct.

In summary, the correct answer is A. A coefficient of correlation of 0.70 means that the coefficient of determination is 0.49, indicating that approximately 49% of the variation in the dependent variable is explained by the independent variable(s).