Consider the following equation: Y\' = 2 + 0.5X 1 + 1.5D 1 + 0.3D 2 - 0.75D 1 X

Question

Consider the following equation:

Y' = 2 + 0.5X1 + 1.5D1 + 0.3D2 - 0.75D1X1 + 0.6D2X1

All coefficients differ significantly from 0 at a 5 % significance level (? = 0.05). The variables D1 and D2 are used to code the categorical variable K with 3 levels [low, average, high]. See the table below for the exact coding:

The variable X1 is a continuous variable measured on a scale from 1 to 5.

Which of the conclusions below is correct?

category

Compared to the reference category people who score Average on K, when controlling for X1, always have a lower score on Y'.

Compared to the reference category the effect of X1 is stronger for people who score Low on K.

Compared to the reference category the effect of X1 is less strong for people who score Average on K.

Explanation / Answer

B) For D1=0 and D=1,

Y = 2+0.5X1+0.3+0.6x1 =2.3+1.1X1

Hence, score will be higher

C) Y = 2+0.5X1+1.5-0.75X1 =3.5-0.25x1

Hence, effect is not stronger since coefficient is 0.25 which is less than 0.5

D) Effect is more stronger since coefficient of X1 is 1.1 which is more than 0.5

Hence, the correct option is A

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