11.83 Air pollution regulations for power plants are often written so that the maximum amount of pollutant that can be emitted is increased as the plant’s output increases. Suppose the data in the table below are collected over a period of time:

a Plot the data in a scatterplot.

b Use the least-squares method to fit a straight line relating sulfur dioxide emission to output. Plot the least-squares line on the scatterplot.

c Use a computer program to fit a second-order

(quadratic) model relating sulfur dioxide emission to output.

Output x

(megawatts)

Sulfur Dioxide Emission Y (parts per million)

525 143 452 110 626 173 573 161 422 105 712 240 600 165 555 140 675 210 x1 x2 Y x1 x2 Y 81 87 3.49 79 75 3.45 68 99 2.89 81 62 2.76 57 86 2.73 50 69 1.90 100 49 1.54 72 70 3.01 54 83 2.56 54 52 1.48 82 86 3.43 65 79 2.98 75 74 3.59 56 78 2.58 58 98 2.86 98 67 2.73 55 54 1.46 97 80 3.27 49 81 2.11 77 90 3.47 64 76 2.69 49 54 1.30 66 59 2.16 39 81 1.22 80 61 2.60 87 69 3.23 100 85 3.30 70 95 3.82 83 76 3.75 57 89 2.93 64 66 2.70 74 67 2.83 83 72 3.15 87 93 3.84 93 54 2.28 90 65 3.01 74 59 2.92 81 76 3.33 51 75 2.48 84 69 3.06 a = 0.05 d Conduct a test to determine whether the quadratic model provides a better description of the relationship between sulfur dioxide and output than the linear model.
e Use the quadratic model to estimate the mean sulfur dioxide emission when the power output is 500 megawatts. Use a 95% confidence interval.