The growth of the federal debt is one of the characteristic features of the U.S. economy. The rapidity of the increases from 1996 to 2006, as shown in the table below, suggests an exponential model.

(a) Find the best-fitting exponential curve, using the method of least squares together with an appropriate linearizing transformation. Use the sums

(b) The official Office of Management and Budget prediction for 2007 was $9 trillion. Compare this figure to the projection using the model from part (a).
(c) Even though the model of part (a) is considered €œgood€ by a criterion to be given in Section 11.4 (r squared), plot the residuals and consider what they say about the exponential fit.

Transcribed Image Text:

Gross Federal Debt (in $ trillions), y Year Years after 1995, r 1996 1997 1998 1999 2001 2002 2003 2004 2005 2006 5.181 5.396 5.478 5.606 5.629 5.770 6.198 6.760 7.355 7.905 8.451 10 20 20 Σ In yī = 20. 16825 and ΣΧί , In yi = 126.33786.