Question

Researchers are examining the effects of several variables on health literacy. The first variable is
proximity to a health center in kms (X1

), the second is years of education (X2

), and the third is number of

household members (X3
).

The research resulted in the multivariate regression equation Y = 4 + 0.2(X1
) + 5(X2
) - 6(X3
)

1. Everything else being equal,
which variable has the most effect
on health literacy?

2. Everything else being equal, as
proximity to a health center in kms
increases,

3. Everything else being equal, as
number of household members
increases,

a) Proximity to a health center
b) Years of education
c) Number of household
members

a) Health literacy increases
b) Health literacy decreases

a) Health literacy increases
b) Health literacy decreases

Answer 1

1. Ans: Number of household members

If you just vary the independent variables one by one, the variable X3(number of household members) has the most effect on Health literacy. This is determined by looking at the absolute value of the coefficients of X1, X2, and X3. Since |-6|=6>5,3, X3 causes the most effect.

2. Ans: Health Literacy increases

Fix some values for X2, and X3, and vary X1 to see how X1 effects Y.

If X1= x then Y=4+0.2(x)+5X2-6X3

Say X1 increases by t now

X1=x+t

then new Y is Y'=4+0.2(x+t)+5X2-6X3=4+0.2(x)+5X2-6X3+0.2t=Y+0.2t

Thus, Y increases by 0.2t, meaning Health literacy increases.

3. Health literacy decreases

In the exact way described in 2 we get this conclusion. Only thing to note here is that the coefficient of X3 is negative, so an in increase in X3 will decrease Y.