AP Statistics / Mr. Hansen				Name: _____________________________
10/25/2004

The original plan was to do this in class. However, if you do it as part of your homework, we will stay
on schedule. Work alone or in small groups to answer the questions posed underneath the data set.
You may leave when you have answered all the questions satisfactorily. Remember that there is also
homework due for tomorrow.

[data source: http://www.publicdebt.treas.gov/opd/opdpdodt.htm on 10/25/2004]

FY End Date	CodedDate	Debt ($billions)	Plot for homework
6/30/1950	1950.5	257.4	YES
6/29/1951	1951.5	255.2
6/30/1952	1952.5	259.1
6/30/1953	1953.5	266.1
12/31/1953	1954	275.2
12/31/1954	1955	278.7	YES
12/30/1955	1956	280.8
12/31/1956	1957	276.6
12/31/1957	1958	274.9
12/31/1958	1959	282.9
12/31/1959	1960	290.8	YES
12/30/1960	1961	290.2
12/29/1961	1962	296.2
12/31/1962	1963	303.5
12/31/1963	1964	309.3
12/31/1964	1965	317.9	YES
12/31/1965	1966	320.9
12/30/1966	1967	329.3
12/29/1967	1968	344.7
12/31/1968	1969	358.0
12/31/1969	1970	368.2	YES
12/31/1970	1971	389.2
12/31/1971	1972	424.1
12/29/1972	1973	449.3
12/31/1973	1974	469.9
12/31/1974	1975	492.7	YES
12/31/1975	1976	576.6
12/31/1976	1977	653.5
12/30/1977	1978	718.9
12/29/1978	1979	789.2
12/31/1979	1980	845.1	YES
12/31/1980	1981	930.2
12/31/1981	1982	1028.7
12/31/1982	1983	1197.1
12/31/1983	1984	1410.7
12/31/1984	1985	1663.0	YES
12/31/1985	1986	1945.9
9/30/1986	1986.75	2125.3
9/30/1987	1987.75	2350.3
9/30/1988	1988.75	2602.3
9/29/1989	1989.75	2857.4	YES
9/28/1990	1990.75	3233.3
9/30/1991	1991.75	3665.3
9/30/1992	1992.75	4064.6
9/30/1993	1993.75	4411.5
9/30/1994	1994.75	4692.7	YES
9/29/1995	1995.75	4974.0
9/30/1996	1996.75	5224.8
9/30/1997	1997.75	5413.1
9/30/1998	1998.75	5526.2
9/30/1999	1999.75	5656.3	YES
9/29/2000	2000.75	5674.2
9/28/2001	2001.75	5807.5
9/30/2002	2002.75	6228.2
9/30/2003	2003.75	6783.2
9/30/2004	2004.75	7379.1	YES

1.	The federal fiscal year (FY) has changed twice during the past 55 years. Explain the
	rationale for the coding of the years (column 2). Hint: It's similar to what we saw this
	morning with Michael Cromwell's data set.


2.	Sketch a scatterplot of debt (y) as a function of coded date (x). To save time, you
	may use every fifth data point (i.e., the points marked YES in the data set). Be sure to
	label your axes correctly.












3.	Compute the LSRL and the r value. Overlay the LSRL on your scatterplot above.
	Show its equation here: ____________________________________

4.	In the space below, sketch the residual plot for the LSRL. Show x values on the x-axis
	and residual values on the y-axis. Is your plot sufficiently random? _______________














5.	Compute an additional data column (perhaps L₃ on your calculator) as follows: Make
	this column equal to the common logarithm of your y values. This can be done in one
	step if you know how your calculator works. Raise your hand so that I can verify this.
6.	Compute a new LSRL, not by regressing the original y values on x, but by regressing
	the logs you found in step 5 against x. Record its equation and r value here.
	Equation: __________________________________
	r = _________________

7.	Sketch the residual plot for the LSRL you found in step 6. Is this more random? _____












8.	Explain why saying that there is a good linear fit between x and (log y) is equivalent to
	saying that there is a good exponential fit between x and y itself. Algebra is required.






















9.	Echoing the algebra that you performed in step 8, compute the exponential fit for yhat
	as a function of x. Show all the steps and write the equation of your final exponential
	model here: ___________________________________




















10.	Check your work in step 9 by performing a STAT CALC 0 (exponential regression)
	between x and y. The syntax is the same as for the LSRL (STAT CALC 8). In other
	words, if your x list is in L₁ and your y list is in L₂, you can perform the regression and
	store the equation into function Y₁ with the command STAT CALC 0 L₁,L₂,Y₁ ENTER.
	Raise your hand when you have accomplished this step.

11.	Explain what the r value you found in step 10 signifies.



12.	Sketch the new residual plot produced by the exponential regression.