Question

What are the assumptions of the correlation coefficient?
I. There is a nonlinear relationship between the two variables.
II. The two variables have a cause and effect relationship
III. Each variable is affected by a large number of independent causes
IV. If the error is reduced to a minimum, the coefficient of correlation is more reliable
(a) I, II and III
(b) II, III and IV
(c) I, II and IV
(d) All of the above

Answer 1

Hint: To solve this question, we will first of all define what a correlation coefficient is and what are the assumptions and parameters that define the correlation coefficients. After that, we will match this definition with the given assumption of the question to see which one is correct.

Complete step by step answer:
Let us define the correlation coefficient. The correlation coefficient is a statistical measure of the relationship between the related movements of two variables. The values range between – 1.0 and 1.0. A calculated number greater than 1.0 or less than – 1.0 means that there was an error in the correlation measurement. A correlation – 1.0 shows a perfect negative correlation and 1.0 shows a perfect positive correlation.
A correlation of 0.0 shows no linear relationship between the movements of the two variables. Let us consider the options given.
(I) There is a non – linear relationship between the two variables.
No this is not always true. Hence (I) is not correct.
(II) The two variables have a cause and effect relationship.
For the calculation of correlation, it is assumed that there exists a cause and effect relationship between the variables.
Hence, (II) is the correct answer.
(III) Each variable is affected by a large number of independent causes.
This is correct as having more number of independent causes affects variables, so (III) is the correct answer.
(IV) If the error is reduced to a minimum, the coefficient of correlation is more reliable
Yes, this is correct, as if the error is reduced to a minimum the coefficient is more reliable.

So, the correct answer is “Option c”.

Note: There are several nonlinear relationships and linear relationships. The relationships are given by the graphs.

And the graph of the nonlinear relationship is