A study showed that the coefficient of variation for a group of patients with high blood pressure and high serum creatinine are 20 and 15 respectively. Which of the following will be true? (AIIMS Nov 2010)
|A||SD of BP measurements is more than that of serum creatinine|
|B||SD of Creatinine measurements is more than that of BP|
|C||Variation is more in BP as compared to serum creatinine|
|D||Relative variation is more in serum creatinine as compared to BP|
Ref. Park PSM 22nd ed. 790
COEFFICIENT OF VARIANCE is given by the formula SD / mean X 100, where SD is standard deviation.
Coefficient of variation tells us which of the two quantities within the group is more variable.
So the quantity with higher CV is more variable, hence in this case variation is more in BP as compared to S.cholesterol.
In this case, as we are studying same group of patient, n remains constant but the question does not give the mean values of BP and serum creatinine, so higher coefficient of variance means higher variation and not higher SD.
CO-EFFICIENT OF CORRELATION
a. Correlation is a symmetrical measure of the strength of the association between the two factors, while regression describes how one factor depends on the other.
b. Correlation gives us a measure of how closely the 2 variables are associated, how close they are to the unlikely even of their lying on a straight line.
c. If one increases as the other increases, the correlation is positive.
d. Co-efficient of correlation is always between –1 and +1.
e. When zero, it indicates no correlation.
f. When-1 it indicates negative correlation, when +1 it indicates positive correlation.
g. Negative correlation is if one increase, other decrease and vice versa.
h. When there is a sufficient degree of correlation to believe the results approximate to a straight line, it is the regression co-efficient, which is used to measure its slope.
Regression co-efficient can be of any magnitude, therefore and does not have a maximum value like a correlation co-efficient of 1.
Types of regression:
a. Multiple regression
b. Curvilinear regression
Curvilinear regression deals with the problem of predicting the most likely factor for a single particular variable. While multiple linear regression relates more than one independent explanatory or predictor variable, as in our question, where total cholesterol level relates to more than one independent variables i.e. calorie in take, physical activity and BMI.