The accompanying data on y = energy output (W) and x 5 temperature difference (K) was provided

The accompanying data on y = energy output (W) and x 5 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 output can 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 x = 30, sŶ = .0611. 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. [e. Interpret the hypotheses H0: µY.35 = 5 versus Ha: µY.35 = 5, and then carry out a test at significance level .05 using the fact that when x = 35, sŶ = .0523.

e.    Interpret the hypotheses H0: mY?35 5 5 versus Ha: mY?35 Þ 5, and then carry out a test at significance level .05 using the fact that when x 5 35, sYˆ 5 .0523.

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23.20 23.50 23.52 24.0 25.10 26.20 27.4028.10 29.30 30.60 3150 32.01 3.78 4.12 4.245.35 587 6.02 6.12 6.4 6.62 6.43 6.13 5.92 2.63 33.23 33.62 34.18 35.43 35.62 36.1636.23 36.8937.90 39.10 41.66 5.64 5.45 5.2 4.98 4.654.50 4.34 4.033.92 3.653.02 2.89 The regression equation is y--134+ 12.7 x-0.377 x"*2+0.00359 x** 3 Predictor Constant Coef SE Coe:f 8.048-16.62 0.000 0.7750 16.440.000 0.02444 -15.41 0.000 0.0035861 0.0002529 14.18 0.000 -133.787 12.7423 -0.37652 S-0.168354 R-Sg 98.0% R-Sg(adi)-97.7% Analysis of Variancee Source Regression Residual Error 20 0.5669 0.0283 Total DF MS 3 27.9744 9.3248 329.00 0.000 23 28.5413