Question

If the value of any regression coefficient is zero, then two variables are:

• A. Qualitative
• B. Correlation
• C. Dependent
• D. Independent

Answer 1

Answer: (D)

Independent

$\Rightarrow$ If the correlation coefficient of two variables is zero, it signifies that there is no linear relationship between the variables. However, this is only for a linear relationship; it is possible that the variables have a strong curvilinear relationship.

$\Rightarrow$ When the value of r is close to zero, generally between $-0.1$ and $+0.1,$ the variables are said to have no linear relationship or a very weak linear relationship.

$\Rightarrow$ For example, suppose the prices of coffee and of computers are observed and found to have a correlation of $+.0008;$ this means that there is no correlation, or relationship, between the two variables.

$\therefore$ We can say that, if the value of any regression coefficient is zero, then two variables are $Independent$.