The accompanying data on output (W) and 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.

x 5 temperature y 5 energy yˆ 5 134.07, sY

ˆ 5 2.38 S 5 3.44398 R-Sq 5 98.1% R-Sq(adj) 5 96.3%

viscosity 5 400 The regression equation is Predictor Coef SE Coef T P Constant 133.787 8.048 16.62 0.000 x 12.7423 0.7750 16.44 0.000 x**2 0.37652 0.02444 15.41 0.000 x**3 0.0035861 0.0002529 14.18 0.000 Analysis of Variance Source DF SS MS F P Regression 3 27.9744 9.3248 329.00 0.000 Residual Error 20 0.5669 0.0283 Total 23 28.5413

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

b. Fitting a quadratic model to the data results in .

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: 5 .0611.

e. Interpret the hypotheses versus

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