Solution Found!
Consider the model: where x1 is a quantitative variable
Chapter 12, Problem 85E(choose chapter or problem)
Consider the model:
\(y= \beta_0+\beta_1 x_1+\beta_2 x_1^2+\beta_3 x_2+\beta_4 x_3+\)
\(\beta_5 x_1 x_2+\beta_6 x_1 x_3+\beta_7 x_1^2 x_2+\beta_8 x_1^2 x_3+\varepsilon\)
where \(x_1\) is a quantitative variable and
\(x_2= \begin{cases}1 & \text { if level } 2 \\ 0 & \text { otherwise }\end{cases}\) \(x_3= \begin{cases}1 & \text { if level } 3 \\ 0 & \text { otherwise }\end{cases}\)
The resulting least squares prediction equation is
\(\hat{y}= 48.8-3.4 x_1+.07 x_1^2-2.4 x_2-7.5 x_3+\)
\(3.7 x_1 x_2+2.7 x_1 x_3-.02 x_1^2 x_2-.04 x_1^2 x_3\)
a. What is the equation of the response curve for E(y) when \(x_2=0\) and \(x_3=0\)? When \(x_2=1\) and \(x_3=0\)? When \(x_2=0\) and \(x_3=1\)?
b. On the same graph, plot the least squares prediction equation associated with level 1, with level 2 , and with level 3.
Questions & Answers
QUESTION:
Consider the model:
\(y= \beta_0+\beta_1 x_1+\beta_2 x_1^2+\beta_3 x_2+\beta_4 x_3+\)
\(\beta_5 x_1 x_2+\beta_6 x_1 x_3+\beta_7 x_1^2 x_2+\beta_8 x_1^2 x_3+\varepsilon\)
where \(x_1\) is a quantitative variable and
\(x_2= \begin{cases}1 & \text { if level } 2 \\ 0 & \text { otherwise }\end{cases}\) \(x_3= \begin{cases}1 & \text { if level } 3 \\ 0 & \text { otherwise }\end{cases}\)
The resulting least squares prediction equation is
\(\hat{y}= 48.8-3.4 x_1+.07 x_1^2-2.4 x_2-7.5 x_3+\)
\(3.7 x_1 x_2+2.7 x_1 x_3-.02 x_1^2 x_2-.04 x_1^2 x_3\)
a. What is the equation of the response curve for E(y) when \(x_2=0\) and \(x_3=0\)? When \(x_2=1\) and \(x_3=0\)? When \(x_2=0\) and \(x_3=1\)?
b. On the same graph, plot the least squares prediction equation associated with level 1, with level 2 , and with level 3.
ANSWER:Step 1 of 6
The complete model is
Where 
The resulting least squares prediction equation is
