Question

If one regression coefficient be unity, then the other will be
A) Greater than unity
B) Greater than or equal to unity
C) Less than or equal to unity
D) None of the above

Answer 1

Hint: Regression is a technique which is used to analyze and model the relationships between the variables and oftentimes how they are related to producing a particular outcome together. A linear regression refers to a regression model that is completely made up of linear variables.

Complete step-by-step solution:
Linear regression is very intuitive to understand and interpret.
In regression analysis, one variable is independent and the other variable is dependent. This technique measures the degree of dependence of one variable on the others.
Also, the coefficients of the regressions are co-related with each other on the bases of their signs (positive or negative) and their values.
If one coefficient of the regression is greater than one, then the other will be numerically less than it. Similarly, if one coefficient of the regression is unity i.e. equal to one, then the other will be less than or equal to unity.
Hence, the other regression coefficient must be equal to or less than unity.
So, the correct answer to the given problem is option (C).

Note: One must have sufficient knowledge of the concept of the technique of regression and its relationship with the variables and their coefficients. We should know that the word ‘unity’ in mathematics means the number one. So, if one regression coefficient is equal to one, then the other one will be less than one. This concept can be used in other questions revolving around the property directly as a result.