The accompanying data on y = energy output (W) and x = temperature difference (°K) was...

The accompanying data on y = energy output (W) and x = temperature difference (°K) was provided by the authors of the article “Comparison of Energy and Exergy Efficiency for Solar Box and Parabolic Cookers” (J. of Energy Engr., 2007: 53–62). The article’s authors fit a cubic regression model to the data. Here is Minitab output from such a fit.

a. What proportion of observed variation in energy outputcan be attributed to the model relationship?

b. Fitting a quadratic model to the data results in R² = .780. Calculate adjusted R² for this model and compare to adjusted R² for the cubic model.

c. Does the cubic predictor appear to provide useful information about y over and above that provided by the linear and quadratic predictors? State and test the appropriate hypotheses.

d. When . Obtain a 95% CI for true average energy output in this case, and also a 95% PI for a single energy output to be observed when temperature difference is 30. Hint: = . 0611.

e. Interpret the hypotheses versus , and then carry out a test at significance level .05 using the fact that when