Complete the question to practice graphing data and choosing an appropriate regression model for the data.

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      1. 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 R2 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 R2 = 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 2nd, 0 (zero), down arrow to scroll to DiagnosticOn.

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.