Download hw5_05 - UF-Stat

STA 6127 – Homework 5 – Due April 20
Population Projections
You are a demographer circa 1920, and have just been given the updated
census information from the 1920 U.S. census. You fit the following models
to describe the population growth of the U.S. since the first census (1790).
First, convert population to units of Millions by dividing population by million,
and use decade (not year) as X. Use data only up to 1920 (by Selecting
Cases) to fit models. The first three models can be fit using SPSS by
selecting:
Analyze  Regression  Curve Fitting
Dependent Variable: Population (use in millions form)
Independent Variable: Decade




Model 1: Pop = a + b1X + b2X2
(Quadratic)
2
Model 2: Pop = a + b1X + b2 X + b3X3
(Cubic)
X
Model 3: Pop = ab
(Growth)
Model 4: Pop = a + b1X + b2X2 + b3log(X) (Pearl-Reed)
1. Write out each of the models, in terms of their estimated regression
coefficients.
2. Obtain the fitted values for all years, by first selecting All Cases. Then
computing 4 new variables (where the a’s and b’s are from above):
Transform  Compute 
Fit_quad = a + (b1*decade) + (b2*sqdec)
Fit_cube = a + (b1*decade) + (b2*sqdec) + (b3*cubdec)
Fit_exp = a*(b**decade)
Fit_pr = a + (b1*decade) + (b2*sqdec) + (b3*logdec)
3. Obtain the Forecast errors for 1930-2000 for each Model. First, select
only the cases where year>1920. Then compute 8 new variables:
Transform  Compute 
afe_quad = abs(Pop-Fit_quad)
sfe_quad = afe_quad**2
(Repeat for Cube, Exp, and P-R)
4. Which method provides the best forecasts in terms of mean absolute
forecast error (MAE) and mean squared forecast error (MSE)? Again,
use only years 1930-2000. You can use DESCRIPTIVES to obtain the
MAE and MSE for each method. (Note: You want the method with the
minimum).