The materials cost per kilometre of constructing a gas pipeline depends on the diameter of the pipe, and the table below summarizes such costs in thousands of dollars per kilometre for two recent years from the Oil and Gas Journal:

a) Taking the two years together, obtain a linear regression of materials cost per kilometre as a function of pipe diameter.

b) Larger pipes are also made of thicker metal, so the cost may be dependent on the square of the diameter. Obtain a linear regression of materials cost per kilometre as a function of the square of pipe diameter.

c) Compare the results of (a) and (b). Which do you prefer?

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Year 1 Materials Year 2 Materials Cost ($K/km) Cost ($K/km) Diameter (inches) 380 117.5 12 450.625 199.375 16 302.5 179.375 211.25 20 395 326.875 24 389.375 30 431.25 637.5 36 691.25 875.625