If 2 3x1 5x2 8x3 then controlling for x2 and x3 the ch

If ? = 2 + 3x₁ + 5x₂ + - 8x_3, then controlling for x₂ and x₃, the change in the estimated mean of Y when x₁ is increased from 10 to 20

A. Equals 30

B. Equals 0.3

C. Cannot be given

Solution

y = 2 + 3x1 + 5x2 + - 8x3

Controlling x2 and x3 mean they are not varying and they can be treated as constant.

Thus x1 is the only variable

dy/dx1 = rate of change of y wrt x1 = 3

So when x1 is increased from 10 to 20 by 10 units

y increases by 3(10) = 30 units

Option A