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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).