A cardiologist found a highly significant correlation coefficient (r = 0.90) between systolic BP and serum cholesterol values of the patients attending his clinic. Which of the following statements is a wrong interpretation of the correlation coefficient observed?
Ans. is 'a' i.e., Since there is a high correlation, the magnitude of both the measurements are likely to be close to each other It has already been explained that correlation coefficient tells about the strength of association between two variables, but does not tell about the magnitude (quantity). Correlation coefficient in this question is 0.9 (r = 0.90), i.e. there is strong positive correlation between systolic BP and serum cholesterol; therefore, a patient with high level of systolic BP is likely to have high level of serum cholesterol and a patient with low level of systolic BP is likely to have low level of serum cholesterol (option b and c are correct). To know the percentage of variation in a dependent variable that is explained by the Independent variable, coefficient of determination (r2) is used which interprets the value of coefficient of correlation between two variables: Coefficient of determination = (coefficient of correlation) 2 = (0.9)2= 0.8 I (81%) That means 81% of variation in systolic BP among patients can be explained by their serum cholesterol values.
Since there is a high correlation, the magnitude of both the measurements are likely to be close to each other
A patient with a high level of systolic BP is also likely to have a high level of serum cholesterol.
A patient with a low level of systolic BP is also likely to have a low level of serum cholesterol
About 80% of the variation in systolic BP among his patients can be explained by their serum cholesterol values