% 16.62x Experimental Projects, Fall 2006
% Introduction to MATLAB Tutorials
% Instructor: Violeta Ivanova, violeta@mit.edu

% EXERCISE 2 MATLAB Linear Regression & Other Line Fitting
% Linear Regression, Polynomials, PDF Fitting, Residuals, Goodness of Fit

% B1. Load data from file world.dat
% year: calendar year from 1950 to 2000
% N: world population
% Nbil: world population in billions
world = load ('worlddata.dat'); 
year = world(:,1);
N = world (:,2);
Nbil = world(:,3);

% B2. Fit a quadratic polynomial for Nbil vs. year with POLYFIT
p2 = polyfit(year, Nbil, 2)

% B3. Fit a quadratic and plot the 95% confidence interval with POLYTOOL
P2 = polytool(year, Nbil, 2)

% B4. Perform linear regression of population in billions (Nbil) vs. year
% and compute 95% confidence interval and R^2 statistic with REGRESS. 
X = [ones(length(Nbil), 1) year]
[B, Bint, R, Rint, stats] = regress(Nbil, X)
rcoplot (R, Rint)

% B5. Use the Curve Fitting Tool to fit different models of Nbil vs. year.
% Compare a quadratic fit to an exponential fit and a Gaussian fit. 
% Compute and compare three predictions for the world population in 2050.
cftool


% B6. use Import Wizard to import the data set Star from file star.txt, 
% which includes the magnitudes of a variable star on 600 consecutive nights. 
% Use the Curve Fitting Tool to fit a Fourier curve to the periodic data.