Question

Which of the following statements is/are correct in respect of regression coefficients?
1. It measures the degree of linear relationship between two variables.
2. It gives the value by which one variable changes for a unit change in the other variable.
Select the correct answer using the code given below.
A. 1 only
B. 2 only
C. Both 1 and 2
D. Neither 1 nor 2

Answer 1

Hint: In the above given question, we are given two statements in respect of regression coefficients. We have to determine which of the statements is/are correct. Regression coefficients are useful to determine the relation between two or more variables. Regression coefficients are actually a constant that are multiplied to the variables in the various equations. In the linear equation, such as \[y = mx + c\] , the values \[x\] and \[y\] are variables and the value \[m\] is the regression coefficient and \[c\] is another constant independent of the variables.

Complete step by step answer:
Given that, two statements with respect to the regression coefficients. We have to determine the correct statement for the regression coefficients. Let us consider a linear equation of two variables, that is given by the equation,
\[ \Rightarrow y = mx + c\]
This is actually the equation of a straight line. When the regression line is linear as \[y = mx + c\] then the regression coefficient is the constant \[m\] that represents the rate of change of one variable \[y\] as a function of changes in the other variable \[x\]. Hence, it measures the dependency of one variable on the other but does not always account for the linear relationship between the two variables.

Now let us consider the two given statements.
1. It measures the degree of linear relationship between two variables.
This statement is not correct since a regression coefficient does not tell anything about the degree of the linear relationship between two variables but only the dependency of two variables on each other.

2. It gives the value by which one variable changes for a unit change in the other variable.
This statement is actually correct because in the linear equation \[y = mx + c\] , the regression coefficient \[m\] determines the value by which \[y\] is changing for a unit change in the variable \[x\]. Therefore, only statement 2 is correct.

Hence, the correct option is B.

Note: That equation \[y = mx + c\] represents a straight line where the regression coefficient \[m\] is actually the slope of the straight line. Here, the other constant \[c\] determines the distance of the straight line from the origin and if it is equal to zero, then that means the straight line passes through the origin.