Solution Found!
Consider the model:y = ?0 + ?1x1 + ?2x2 + ?3x3 + ?where x1
Chapter 12, Problem 84E(choose chapter or problem)
Consider the model:
\(y=\beta_0+\beta_1 x_1+\beta_2 x_2+\beta_3 x_3+\varepsilon\)
where \(x_1\) is a quantitative variable and \(x_2\) and \(x_3\) are dummy variables describing a qualitative variable at three levels using the coding scheme
\(x_2= \begin{cases}1 & \text { if level } 2 \\ 0 & \text { otherwise }\end{cases}\) \(x_3= \begin{cases}1 & \text { if level } 3 \\ 0 & \text { otherwise }\end{cases}\)
The resulting least squares prediction equation is
\(\hat{y}=44.8+2.2 x_1+9.4 x_2+15.6 x_3\)
a. What is the response line (equation) for E(y) when \(x_2=x_3=0\)? When \(x_2=1\) and \(x_3=0\)? When \(x_2=0\) and \(x_3=1?\)
b. What is the least squares prediction equation associated with level 1? Level 2? Level 3? Plot these on the same graph.
Questions & Answers
QUESTION:
Consider the model:
\(y=\beta_0+\beta_1 x_1+\beta_2 x_2+\beta_3 x_3+\varepsilon\)
where \(x_1\) is a quantitative variable and \(x_2\) and \(x_3\) are dummy variables describing a qualitative variable at three levels using the coding scheme
\(x_2= \begin{cases}1 & \text { if level } 2 \\ 0 & \text { otherwise }\end{cases}\) \(x_3= \begin{cases}1 & \text { if level } 3 \\ 0 & \text { otherwise }\end{cases}\)
The resulting least squares prediction equation is
\(\hat{y}=44.8+2.2 x_1+9.4 x_2+15.6 x_3\)
a. What is the response line (equation) for E(y) when \(x_2=x_3=0\)? When \(x_2=1\) and \(x_3=0\)? When \(x_2=0\) and \(x_3=1?\)
b. What is the least squares prediction equation associated with level 1? Level 2? Level 3? Plot these on the same graph.
ANSWER:Step 1 of 6
The complete model is
Where 
The resulting least squares prediction equation is
