The amounts y of the Federal budget deficit over a 15 year period in billions of dollars are as
follows. (1977, 53.6), (1978, 59.2), (1979, 40.2), (1980, 73.8), (1981, 78.9), (1982, 127.9),
(1983, 207.8), (1984, 185.3), (1985, 212.3), (1986, 221.2), (1987, 149.7), (1988, 155.1),
(1989, 153.4), (1990, 220.4), (1991, 320.1)
(a) Let t be the time in years, with t = 0 corresponding to 1984. Use the regression capabilities
to find an appropriate model for the data. What is the domain of the model?
Try linear model: y = ax + b, quadratic model: y = ax^2; + bx; + c,
cubic model: y = ax^3; + bx^2; + cx; + d, or a quadric model: y = ax^4; + bx^3; + cx^2; + dx; + e.
Modify the solved example.
(b) Graph the data and model. Find the best fitting model among the above four models.
Answer the following questions for the best fit model:
(c) For which year does the model most accurately estimate the actual data? During which
year is it least accurate?
(d) By extending the curve on the hard copy, estimate the budget deficit for 1992.