In Exercise, use technology to find the quadratic regression curve through the given...

In Exercise, use technology to find the quadratic regression curve through the given points. (Round all coefficients to four decimal places.) HINT [See Example 5.]

Example 5:

The following table shows total and projected production of ozone-layer damaging Freon 22 (chlorodifluoromethane) in developing countries (t = 0 represents 2000).*

a. Is a linear model appropriate for these data?

b. Find the quadratic model

that best fits the data.

Solution

a. To see whether a linear model is appropriate, we plot the data points and the regression line using one of the methods of Example 2 in Section 1.4 (Figure 8).

From the graph, we can see that the given data suggest a curve and not a straight line: The observed points are above the regression line at the ends but below in the middle. (We would expect the data points from a linear relation to fall randomly above and below the regression line.)

b. The quadratic model that best fits the data is the quadratic regression model. As with linear regression, there are algebraic formulas to compute a, b, and c, but they are rather involved. However, we exploit the fact that these formulas are built into graphing calculators, spreadsheets, and other technology, and obtain the regression curve using technology (see Figure 9):

Notice from the previous graphs that the quadratic regression model appears to give a far better fit than the linear regression model.This impression is supported by the values of SSE: For the linear regression model SSE ≈ 13,400; for the quadratic regression model SSE is much smaller, approximately 730, indicating a much better fit.

{(−1, 2), (−3, 5), (−4, 3)}