A cardiologist found a highly significant correlation coefficient (r = 0.90, p = 0.01) between the systolic blood pressure values and serum cholestrol values of the patients attending his clinic. Which of the following statements is a wrong interpretation of the correlation co-efficiency observed?
Correlation reflects the strength & direction of relationship between two quantitative measurements. It can be used to predict the trend of an association, (e.g. patients with high serum cholesterol will have high BP) but it is not necessary for independent magnitudes of both the measurement to be close to each other. In fact, the individual measurements may be widely different, yet, with a strong positive correlation, an increase in one measurement will cause an increase in the other. + Sign means that there is a positive correlation between blood pressure values & serum cholesterol values. 0.9 means association is strong (since 0.9>0.5) R = 0.9 hence r2 = 0.9 x 0.9 = 0.81 or 81% of the variance in blood pressure in this study accounted for by variance in serum cholesterol & vice versa. Ref: High Yield Biostatistics By Anthony Glazer, Page 47; Fundamentals of Biostatistics By Bernard Rosner, 2010, Page 452
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 blood pressure among his patients can be explained by their serum cholesterol values and vice a versa