Question

The coefficient of correlation between two variables x and y are 0.8. While the regression coefficient of y on x is 0.2. Then, find the regression coefficient of x on y.
A. $ - 3.2$
B. $3.2$
C. $4$
D. $0.16$

Answer 1

Hint: In order to solve the question, first write the formula for finding the regression coefficient. Next, square both the LHS and RHS sides. Finally, find the required regression coefficient by simplifying.

Formula Used:
Correlation coefficient, $r = \sqrt {{b_{yx}} \times {b_{xy}}} $

Complete step by step solution:
Given that
The coefficient of correlation $r = 0.8$
The regression coefficient ${b_{yx}} = 0.2$
Here it is asked to find the regression coefficient of x on y that is ${b_{xy}}$.
We know that the correlation coefficient is given as
$r = \sqrt {{b_{yx}} \times {b_{xy}}} $
$0.8 = \sqrt {0.2 \times {b_{xy}}} $
$0.64 = 0.2 \times {b_{xy}}$ . . . . . . (Squaring on both sides)
${b_{xy}} = \dfrac{{0.64}}{{0.2}}$
${b_{xy}} = 3.2$

Option ‘B’ is correct

Additional information:
Correlation coefficient is calculated by the strength of the relationship between two variables.
If the value of correlation coefficient is greater than zero then the relationship is known as positive relation.
If the value of correlation coefficient is less than zero then the relationship is known as negative relation.

Note: Students can get confused while writing the regression coefficients. Remember that the correlation coefficient can give you the measure of how much variation in the value of one variable predicts variation in the value of another. Also, remember that the regression coefficient can estimate how much one variable is affected by another.