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):

Predictor Coef SE Coef T P Constant 111.277 2.100 52.98 0.000 temp 0.32845 0.03303 9.94 0.010 tempsqd 0.0010050 0.0001213 8.29 0.014 Analysis of Variance Source DF SS MS F P Regression 2 1245.39 622.69 52.50 0.019 Residual Error 2 23.72 11.86 Total 4 1269.11

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, .

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).