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- The United States Department of Agriculture (USDA) tracks yearly farm exports (in billions of dollars). Some of this data is shown below. Find the equation of a polynomial function that best models the amount in billions as function of the years after 1980.

Year Years after 1980 Amount (billions) 1980 41.2 1985 29.0 1990 39.5 1992 43.2 1993 42.9 1994 46.3 1995 56.3 1996 60.4 1997 57.2 1998 51.8 1999 48.5 2000 51.6

L1=x-values =

L2=y-values =Regression Equation:

Looking at a scatter plot does not always give a clear indication of which function is the best model. In this case, use the diagnostic feature R^{2} on the calculator. The coefficient of determination, read R-square, measures how well the regression represents the data. It shows if the model is accurate and reliable for making predictions. It is expressed as a value between zero and one. If *R*^{2} = 1, the regression line passes through every point on the scatter plot. This indicates a very reliable model for future forecasts. A value of zero indicates the regression line is *not* an accurate model for the data.

Step 1:Open the CATALOG; press 2^{nd}, 0 (zero), down arrow to scroll toDiagnosticOn.

Step 2:Turn on the diagnostic feature; press ENTER, ENTER.

In Example 4, you will see how the coefficient of determination is used to help choose the best model for a set of data.