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.
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a. Give the Y and X matrices needed to fit the model y = βo + 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.