Question

Consider the model y= β₀ + β₁x₁ + β₂x₂ + β₃ + 3+ z where x₁ is a quantitative variable and x₂​ and x₃​

are dummy variables describing a qualitative variable at three levels using the coding scheme
x₂ =
1 if level 2
0 otherwise

x₃​ =
​ 1 if level 3
0 otherwise

The resulting least squares prediction equation is y = 163 + 23x₁ + 3.5x₂ + 18x₃. What is the response line (equation) for E(y) when x₂ =0 and x₃=1 ?

A. y = 16.3+2.3x₁
B. y = 16.3+4.1x₁
C. y = 18.6 + 2.3x₁
D. y = 18.1 + 2.3x₁

Answer 1

The response line for E(y) when x₂=0 and x₃=1 is y = 181 + 23x₁.

Step-by-step explanation:

The response line (equation) for E(y) when x₂=0 and x₃=1 can be found by substituting the given values into the prediction equation.

Given: y = 163 + 23x₁ + 3.5x₂ + 18x₃. Substituting x₂=0 and x₃=1 into the equation, we get:

y = 163 + 23x₁ + 3.5(0) + 18(1) = 163 + 23x₁ + 18 = 181 + 23x₁.

Therefore, the response line (equation) for E(y) when x₂=0 and x₃=1 is y = 181 + 23x₁.