An experiment was conducted to investigate the effect of extrusion pressure P and temperature at extrusion T on the strength y of a new type of plastic. Two plastic specimens were prepared for each of five combinations of pressure and temperature. The specimens were then tested in random order, and the breaking strength for each specimen was recorded. The independent variables were coded as follows to simplify computations:

The data points are listed in the table. 

a. Give the Y and X matrices needed to fit the model y = β_o + β₁x + β₂x² + ∈.

b. Find the least-squares prediction equation. Interpret the β estimates.

c. Find SSE, s², and s. Interpret the value of s.

d. Does the model contribute information for the prediction of y? Test using α = .05.

e. Find R² and interpret its value.

f. Test the null hypothesis that β₁ = 0. Use α = .05. What is the practical implication of the test?

g. Find a 90% confidence interval for the mean strength of the plastic for x₁ = - 2 and x₂ = 2.

h. Suppose a single specimen of the plastic is to be installed in the engine mount of a Douglas DC-10 aircraft. Find a 90% prediction interval for the strength of this specimen if x₁ = - 2 and x₂ = 2.

Transcribed Image Text:

Р- 200 10 Т- 400 X2 25