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).

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, ŷ = 134.07, sŶ = 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).

x-50 25 100 200 300 20. 136.0 y 91.0 Here is Minitab output from fitting the quadratic regres- sion model (a graph in the cited paper suggests that the authors did this) 133.1 120.8 SE Coef Predictor Constant temp tempsqd 2.100 52.98 0.000 0.03303 9.94 0.010 -0.0010050 0.0001213-8.29 0.014 Coef 111.277 0.32845 S 3.44398 R-Sg 98.1% R-Sq(adj)-96 .3% Analysis of Variance Source Regression Residual Error 2 23.72 11.86 Total DF MS 2 1245.39 622.69 52.50 0.019 4 1269.11