Chapter 13.3, Problem 30E

The accompanying data was extracted from the article “Effects of Cold and Warm Temperatures on Springback of Aluminum-Magnesium Alloy 5083- H111” (J. of Engr. Manuf., 2009: 427–431). The response variable is yield strength (MPa), and the predictor is temperature (°C).

x	-50	25	100	200	300
y	91.0	120.5	136.0	133.1	120.8

Here is Minitab output from fitting the quadratic regression model (a graph in the cited paper suggests that the authors did this):

a. What proportion of observed variation in strength can be attributed to the model relationship? b. Carry out a test of hypotheses at significance level .05 to decide if the quadratic predictor provides useful information over and above that provided by the linear predictor.

c. For a strength value of 100, $\hat{y}=134.07$ , $s_{\hat{y}}=2.38$. Estimate true average strength when temperature is 100, in a way that conveys information about precision and reliability.

d. Use the information in (c) to predict strength for a single observation to be made when temperature is 100, and do so in a way that conveys information about precision and reliability. Then compare this prediction to the estimate obtained in (c).