Question

Regression coefficient is independent of
A. Unit of measurement
B. Scale and origin
C. Both are correct
D. None of them

Answer 1

Hint: We first explain the equation of the Regression coefficient for ${{Y}_{e}}=a+bX$. The part of $b$ is the coefficient of the line which is also the slope. We explain the influence of unit, scale and unit of measurement for the equation.

Complete step-by-step solution:
The regression coefficients are measurements of average functional relationship between variables. One of the variables of those two is independent and the other is dependent. The regression coefficients are independent of the change of the origin. In regression with a single independent variable, the coefficient tells you how much the dependent variable is expected to increase (if the coefficient is positive) or decrease (if the coefficient is negative) when that independent variable increases by one.
The coefficient is dependent on the scale. The option B is not possible.
The coefficient $b$ can be expressed in the equation in the form of ${{Y}_{e}}=a+bX$. It determines the slope of the line.
The units of measurement will not change any value for the equation as the values of ${{Y}_{e}}$ and $X$ will both change with the change of the value of unit of measurement.
The correct option is A.

Note: We need to remember that the parameter $b$ signifies the amount by which change in $X$ must be multiplied to give the corresponding average change in ${{Y}_{e}}$, or the amount ${{Y}_{e}}$ changes for a unit increase in $X$. In this way it represents the degree to which the line slopes upwards or downwards.