Question

If the regression coefficient of y on x is 0.40, then find the regression coefficient of x on y.
A. 1.6
B. 6.4
C. 5.1
D. 3.2

Answer 1

Hint: Use the relation between the regression coefficient of x on y and y on x to obtain the required answer. Divide 1 by 0.40 to obtain the required result.

Formula used:
The product of the regression coefficient of x on y and y on x in always less than equal to 1.
That is,
\[{b_{xy}}.{b_{yx}} \le 1\]
Here, \[{b_{xy}}\] is the regression coefficient of x on y and \[{b_{yx}}\]is the regression coefficient of y on x.

Complete step by step solution:
It is given that \[{b_{yx}} = 0.40\] .
Now, we know that,
\[{b_{xy}}.{b_{yx}} \le 1\]
\[ \Rightarrow 0.40{b_{xy}} \le 1\]
\[ \Rightarrow {b_{xy}} \le \dfrac{1}{{0.40}}\]
\[ \Rightarrow {b_{xy}} \le 2.5\]
Therefore, the correct option is A.

Additional information:
The average functional relationship between variables is measured statistically using the regression coefficients. One variable is dependent and another is independent in a regression analysis. Additionally, it measures how much one variable is dependent on another (s).The association between the heights of dads and their sons was first analysed using the regression coefficient. The slope coefficient is another name for regression coefficients. Considering that it establishes the slope of the line, which is the change in the independent variable for the change in the independent variable expressed as a unit.

Note: To solve this type of question one must have the knowledge of regression coefficient. If one regression coefficient is equal to one, then the other one will be less than one- this is the key concept of the question.