Question

If the regression coefficient byx is 0.5, what is the value of a in the given equation: 2Y = aX –16.80​

Answer 1

SOLUTION

GIVEN

The regression coefficient

$\sf{b_{yx}}$ is 0.5, for the given equation :

2y = ax - 16.80

CONCEPT TO BE IMPLEMENTED

If among the two variables x and y in a bivariate distribution, y is taken as dependent variable and x as independent variable then the corresponding regression curve like y = f(x) is known as regression curve of y on x

From this curve we may get approximately the value of the variable y by knowing the variable x

EVALUATION

The given equation of the regression equation of y on x

2y = ax - 16.80

Which can be rewritten as

$\displaystyle \sf{y = \frac{a}{2}x - 8.40 }$

Therefore the regression coefficient

$\displaystyle \sf{b_{yx} = \frac{a}{2} }$

So by the given condition

$\displaystyle \sf{ \frac{a}{2} = 0.5}$

$\implies \sf{a = 2 \times 0.5}$

$\implies \sf{a =1}$

FINAL ANSWER

The required value of a is 1

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