The general procedure for Projections was to express the variable to be projected as a percent of a "base" variable. These percents were then projected and applied to projections of the "base" variable. For example, the number of 18-year-old college students was expressed as a percent of the 18-year-old population for each year from 1972 through 1995. This percent was then projected through the year 2008 and applied to projections of the 18-year-old population from the Bureau of the Census.
Enrollment projections are based primarily on population projections. Projections of classroom teachers, high school graduates, earned degrees conferred, and expenditures are based primarily on enrollment projections.
Exponential smoothing and multiple linear regression are the two major projection techniques used in this publication. Single exponential smoothing is used when the historical data have a basically horizontal pattern. On the other hand, double exponential smoothing is used when the time series is expected to change linearly with time. In general, exponential smoothing places more weight on recent observations than on earlier ones. The weights for observations decrease exponentially as one moves further into the past. As a result, the older data have less influence on projections. The rate at which the weights of older observations decrease is determined by the smoothing constant selected.
P = 
Xt + (1-)Xt-1
+ (1-)2Xt-2
+ (1-)3Xt-3
+....
Where:
P = projected value
= smoothing constant (0
< <1)
Xt = observation for time t
This equation illustrates that the projection is a weighted average based
on exponentially decreasing weights. For a high smoothing constant, weights
for earlier observations decrease rapidly. For a low smoothing constant, decreases
are more moderate. Projections of enrollments and public high school graduates
are based on a smoothing constant of
= 0.4.
The farther apart the observations are spaced in time, the more likely it is that there are changes in the underlying social, political, and economic structure. Since the observations are on an annual basis, major shifts in the underlying process are more likely in the time span of just a few observations than if the observations were available on a monthly or weekly basis. As a result, the underlying process tends to be unstable from one observation to the next. Another reason for using high smoothing constants for some time series is that most of the observations are fairly accurate, because most observations are population values rather than sample estimates. Therefore, large shifts tend to indicate actual changes in the process rather than noise in the data.
Multiple linear regression is also used in making projections, primarily in the areas of teachers, earned degrees, and expenditures. This technique is used when it is believed that a strong causal relationship exists between the variable being projected (the dependent variable) and independent causal variables. However, this technique is used only when accurate data and reliable projections of the independent variables are available.
The functional form primarily used is the multiplicative model. When used with two independent variables, this model takes the form:
Y=aX1b1 X2b2
This equation can easily be transformed into the linear form by taking the natural log(ln) of both sides of the equation:
lnY = ln(a) + b1 lnX1 + b2 lnX2
The multiplicative model has a number of advantages; it is a reasonable way to represent human behavior. Constant elasticities are assumed; this says that a 1 percent change in lnX will lead to a given percent change in lnY. This percent change is equal to b1. And it lends itself easily to "a priori" analysis because the researcher does not have to worry about units of measurement when specifying relationships. In fact, the multiplicative model is considered the standard in economic problems. For additional information, see Long-Range Forecasting: From Crystal Ball to Computer by J. Scott Armstrong (John Wiley and Sons, 1978, pp. 180-181).
For most projections, low, middle, and high alternatives are shown. These alternatives reveal the level of uncertainty involved in making projections, and they also point out the sensitivity of projections to the assumptions on which they are based.
Many of the projections in this publication are demographically based. Bureau of the Census middle series projections of the population by age were used. These middle series population projections are based on the 1990 census. The future fertility rate assumption, which determines projections of the number of births, is the key assumption in making population projections. The middle series population projections assume an ultimate complete cohort fertility rate of 2.10 births per woman by the year 2008 and a net immigration of 820,000 per year. This assumption plays a major role in determining population projections for the age groups enrolled in nursery school, kindergarten, and elementary grades. The effects of the fertility rate assumption are more pronounced toward the end of the projection period.
For enrollments in secondary grades and college, the fertility assumption is of no consequence, since all students enrolled at these levels were already born when the population projections were made. For projections of enrollments in elementary schools, only middle series population projections were considered. Projections of high school graduates are based on projections of the percent of grade 12 enrollment that are high school graduates. Projections of associate, bachelor's, doctor's, and first-professional degrees are based on projections of college-age populations and higher education enrollment, by sex, attendance status and level enrolled by student, and by type of institution. Projections of higher education enrollment are based on projections of disposable income per capita and unemployment rates. Many of the projections of classroom teachers and expenditures of public elementary and secondary schools and institutions of higher education are based on projections of disposable income per capita and various revenue measures of state and local governments. Projections of disposable income per capita and unemployment rates were obtained from the WEFA Group. Therefore, the many assumptions made in projecting disposable income per capita and unemployment rates also apply to those projections based on projections of these variables.
