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Concept explainers
The accompanying data on y 5 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.
x | 23.20 | 23.50 | 23.52 | 24.30 | 25.10 | 26.20 | 27.40 | 28.10 | 29.30 | 30.60 | 31.50 | 32.01 |
y | 3.78 | 4.12 | 4.24 | 5.35 | 5.87 | 6.02 | 6.12 | 6.41 | 6.62 | 6.43 | 6.13 | 5.92 |
x | 32.63 | 33.23 | 33.62 | 34.18 | 35.43 | 35.62 | 36.16 | 36.23 | 36.89 | 37.90 | 39.10 | 41.66 |
y | 5.64 | 5.45 | 5.21 | 4.98 | 4.65 | 4.50 | 4.34 | 4.03 | 3.92 | 3.65 | 3.02 | 2.89 |
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,
e. Interpret the hypotheses
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Chapter 13 Solutions
Probability and Statistics for Engineering and the Sciences
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